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Making Everything Easier!

Learn to:

• Score higher to qualify for the military job
you want

' Build word knowledge and paragraph
comprehension

' Test your skills with practice problems
for each of the test's nine subtests

' Take three full-length practice tests plus
one AFQT

Rod Powers

U.S. military expert and military guide
forAbout.com

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by Rod Powers

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About the Author

Rod Powers joined the United States Air Force in 1975 intending to become a spy. He was
devastated to learn that he should've joined the CIA instead because the military doesn't
have that particular enlisted job. Regardless, he fell in love with the military and made it
both a passion and a career, retiring with 23 years of service. Rod spent 11 of those years
as a first sergeant, helping to solve the problems of the enlisted corps.

Since his retirement from the military in 1998, Rod has become a world renowned military
careers expert. Through his highly popular U.S. Military Information Web site on About.com
(http: //usmilitary. about .com), Rod has advised thousands of troops about all
aspects of U.S. Armed Forces career information.

Rod is the proud father of twin girls, both of whom enjoy successful careers in the United
States Air Force. Rod currently resides in Daytona Beach, Florida, where he attempts to
prove that there's no such thing as too much sunshine. Even today, Powers tries to run his
life according to long-lived military ideals and standards, but he gets a bit confused about
why nobody will obey his orders anymore.

Dedication

To Jeanie and Chrissy — because everything is for you. Always.

Author's Acknowledgments

I want to thank Leigh Richards for reviewing the manuscript for technical accuracy. I would
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all the artwork and text revisions and reviews.

Finally, I send more special thanks to the recruiting commands of the United States
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information.

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•

Contents at a Glance

Introduction /

Part 1: Making Sense of the ASVAB 5

Chapter 1: Putting the ASVAB Under a Microscope 7

Chapter 2: Knowing What It Takes to Get Your Dream Job 17

Chapter 3: Getting Acquainted with Test-Taking and Study Techniques 23

Part 11: Words to Live Bu: Communication Skills 31

Chapter 4: Word Knowledge 33

Chapter 5: Paragraph Comprehension 43

Chapter 6: All's Well That Tests Well: Communication Practice Questions 55

Part HI: Making the Most of Math: Arithmetic Skills 63

Chapter 7: Mathematics Knowledge and Operations 65

Chapter 8: Reasoning with Arithmetic: Math Word Problems 91

Chapter 9: Brother, Can You Spare an Equation? Arithmetic Practice Questions 97

Part IV: The Whole Ball of Facts: Technical Skills 105

Chapter 10: General Science 107

Chapter 11: Auto and Shop Information 127

Chapter 12: Mechanical Comprehension 141

Chapter 13: Electronics Information 157

Chapter 14: Assembling Objects 171

Chapter 15: Facing the Facts: Technical Skills Practice Questions 179

Part V: Practice ASVAB Exams 189

Chapter 16: Practice Exam 1 191

Chapter 17: Practice Exam 1: Answers and Explanations 221

Chapter 18: Practice Exam 2 233

Chapter 19: Practice Exam 2: Answers and Explanations 265

Chapter 20: Practice Exam 3 277

Chapter 21: Practice Exam 3: Answers and Explanations 309

Chapter 22: Practice AFQT Exam 321

Chapter 23: Practice AFQT Exam: Answers and Explanations 337

Part VI: The Part of Tens 3b3

Chapter 24: Ten Surefire Ways to Fail the ASVAB 345

Chapter 25: Ten Tips for Doing Well on the AFQT 349

Chapter 26: Ten Ways to Boost Your Math and English Skills 353

Appendix: Matching ASVAB Scores to Military Jobs 357

Index 375

Table of Contents

•

Introduction 7

About This Book 1

Conventions Used in This Book 2

What You're Not to Read 2

Foolish Assumptions 2

How This Book Is Organized 2

Part I: Making Sense of the ASVAB 3

Part II: Words to Live By: Communication Skills 3

Part III: Making the Most of Math: Arithmetic Skills 3

Part IV: The Whole Ball of Facts: Technical Skills 3

Part V: Practice ASVAB Exams 3

Part VI: The Part of Tens 3

Appendix 3

Icons Used in This Book 4

Where to Go from Here 4

Part 1: Making Sense of the ASVAB 5

Chapter 1: Putting the ASVAB Under a Microscope 7

Knowing Which Version You're Taking 7

Mapping Out the ASVAB Subtests 8

Deciphering ASVAB Scores 10

Defining all the scores 10

Understanding the big four: Your AFQT scores 12

Do-Over: Retaking the ASVAB 14

U.S. Army retest policy 15

U.S. Air Force retest policy 15

U.S. Navy retest policy 15

U.S. Marine Corps retest policy 16

U.S. Coast Guard retest policy 16

Chapter 2: Knowing What It Takes to Get Your Dream Job 17

Eyeing How ASVAB Scores Determine Military Training Programs and Jobs 17

Understanding How Each Branch Computes Line Scores 18

Line scores and the Army 19

Line scores and the Navy and Coast Guard 19

Line scores and the Marine Corps 20

Line scores and the Air Force 21

Chapter 3: Getting Acquainted with Test-Taking and Study Techniques 23

Taking the Test: Paper or Computerized? 23

Writing on hard copy: The advantages and disadvantages

of the paper version 24

Going paperless: The pros and cons of the computerized test 24

Tackling Multiple-Choice Questions 25

When You Don't Know an Answer: Guessing Smart 27

Studying and Practicing for the ASVAB 28

Making Last-Minute Preparations: 24 Hours and Counting 29

Table of Contents (/jj

Part 11: Wonts to Live By: Communication Skills 31

Chapter 4: Word Knowledge 33

Grasping the Importance of Word Knowledge 33

Checking Out the Word Knowledge Question Format 34

Building Words from Scratch: Strategies to Help You Decipher Word Meanings 35

From beginning to end: Knowing prefixes and suffixes 35

Determining the root of the problem 37

Word families: Finding related words 38

Ying and Yang: Understanding Synonyms and Antonyms 39

You Are What You Speak: Improving Your Vocabulary, Improving Yourself 39

Reading your way to a larger vocabulary 40

Keeping a list and checking it twice 40

Crosswords: Making vocabulary fun 41

Sounding off by sounding it out 41

Chapter 5: Paragraph Comprehension 43

The Importance of Paragraph Comprehension for Military Jobs 43

Eyeing the Physique of the Paragraph Comprehension Subtest 44

Trying the Four Flavors of Comprehension Questions 44

Treasure hunt: Finding specific information 45

Cutting to the chase: Recognizing the main idea 45

If the shoe fits: Determining word meaning in context 46

Reading between the lines: Understanding implications 46

Do You Get My Point? 48

What's the big idea? Determining the main idea in a paragraph 48

Extra, extra! Identifying subpoints 49

Analyzing What You've Read: Guessing at What the Writer Really Means 50

Faster than a Speeding Turtle: Tips for Slow Readers 51

Read more, Watch less

If you're a slow reader, chances are you don't do a lot of reading. If you have plenty of
time before you're due to take the ASVAB, start reading more — right now. It's in your best
interest.

You don't have to pick up A Tale of Two Cities or War and Peace; you can start with the
newspaper, a biography of a person you admire, or magazines you find at the library.
(Sorry, but the instruction guide to your favorite video game doesn't count.) You don't need
to enroll in a speed-reading course. If you devote at least one hour a day simply to reading,
you'll see your reading comprehension and speed increase within a month or so.

Several studies have shown that folks who enjoy reading as a pleasurable pastime score
better on reading comprehension tests than individuals who dislike reading. Sounds obvi-
ous, right? So why study it? The idea is if you grow to enjoy reading, you'll want to read
more. You'll become a better reader and thereby score better on reading comprehension
tests. How do you discover an enjoyment of reading? Simple — choose reading material in
subject areas that interest you.

Become a lean, mean Word machine

People sometimes read slowly because they don't have a large vocabulary and don't under-
stand everything they read. If you can identify with this situation, improving your vocabu-
lary is your first step toward increasing your reading comprehension and your reading
speed. (Chapter 4 gives you info on building your word knowledge. Check it out.)

Keep a pocket dictionary handy while reading so you can look up words you don't know. If
you're reading articles on the Internet, keep a window open to one of the online dictionaries
(such as www. dictionary, com, www.yourdictionary . com, or www.m-w. com) so you
can quickly find the definition of words you find confusing. Your reading will become more
enjoyable, and you'll be adding to your vocabulary knowledge to boot.

Build your confidence

Another reason people read slowly is that they don't have confidence in themselves.
They're not convinced that they understand what they're reading, so they read a passage
several times, trying to make sure they haven't missed anything. But just like people who

j%£ Part II: Words to Live By: Communication Skills

*JABE*

check that the front door is locked 15 times before leaving for vacation and still lie awake at
night wondering whether they locked the door, reading and rereading a passage doesn't
give you confidence that you understand the text. You get confidence from proving that you
understand it.

How do you prove to yourself that you understand what you're reading? Here are a couple
of tips:

u* Get out a textbook or even an encyclopedia (preferably a volume that contains some
subject matter that interests you) and read one or two paragraphs straight through
without going back and rereading anything. Then close the book (keeping your place
marked) and write, in your own words, a brief description of what you've read. Finally,
turn back to the passage and compare your description to the information on the page.

u* Play the 20-questions game. Read an article from a magazine, encyclopedia, or text-
book. Then ask someone to pick out facts from the article and ask you questions.

v* Create motivation and interest by reading the daily newspaper or news magazines.
Discuss the news events with your classmates, friends, or co-workers. Stronger interest
equals greater comprehension.

Is your written version of the article close in meaning to the original? Are you getting most
of the 20 questions correct? Do you feel comfortable discussing current events with others?
If so, you understand what you're reading, and that should build your confidence. If not,
don't toss the book or magazine aside in frustration or go ballistic on your mom for asking
you tough questions. Keep working on it, and your comprehension will improve. Do the pre-
ceding confidence-building drills a few times a day until you feel like you can read any para-
graph or two and understand the content without having to reread the information.

The Paragraph Comprehension subtest tests your ability to understand what you read, not
how quickly you can read it. When you sit down to take this subtest, try to go as quickly as
you can without sacrificing accuracy. Being methodical in your reading isn't a bad thing as
long as you're getting the answers right. Just try to read a little faster than normal without
panicking or missing the point. It's better to read the paragraphs carefully and answer the
questions correctly on half of the questions and guess on the other half of the questions
than it is to speed through all the reading and get none of the answers right.

Test-Taking Tips far Reading and Gleaning

Although no shortcuts exist for improving your reading comprehension skills (besides prac-
tice), you can do a few things on test day to make sure that you score as high as possible on
this part of the ASVAB.

<$m

If you're running out of time on this subtest or you're not sure whether you can identify the
main idea of a passage, take a guess. If you think that's a good piece of advice, check out
these tried-and-true tactics for test day:

i*" Read first, ask questions later. Read the passage all the way through before glancing
at the question and answer options.

«*" Take it one question at a time. Some passages have more than one question associ-
ated with them, but look at only one question at a time.

Chapter 5: Paragraph Comprehension 3^3

v* Understand each question. What's the question asking you to do? Are you supposed
to find the main point? Draw a conclusion? Find a word that's nearest in meaning?
Make sure you know what the question is asking before you choose among the answer
options. This tip may seem obvious, but when you're in a hurry, you can make mis-
takes by misunderstanding the questions.

i*" Read each answer option carefully. Don't just select the first answer that seems right.
Remember, on the Paragraph Comprehension subtest, one answer is often most right
and others are almost right. You want to choose the most right answer, not the almost
right answer. And to do that, you have to read all the answers.

k" Check your feelings at the door. Answer each question based on the passage, not
your own opinions or views on the topic.

v* Don't choose vague answer options. They're incorrect 99.99 times out of 100. (Oh heck,
call it 100 times out of 100.) If an answer strikes you as not quite true but not totally
false, that answer is incorrect. Those nasty ASVAB test-makers have put those answers
in there to throw you off. Don't give them the satisfaction of falling for their trap!

j-" (Almost) never select never. For the most part, answer options that are absolutes are
incorrect. Never, always, and related words are often a sign that you should select a dif-
ferent answer. Words like generally and usually are more likely to be correct.

Qn Part II: Words to Live By: Communication Skills

Chapter 6

All's Well That Tests Well:
Communication Practice Questions

In This Chapter

Proving your knowledge of word meanings
Demonstrating that you can retain what you read

m o help you hone your communication skills a little further, this chapter contains some
m Word Knowledge and Paragraph Comprehension practice questions to get you rolling.

Don't sweat. This test is just for practice, and it doesn't count for a score. (Plus, sweating

makes your answer sheet soggy so it's harder to mark.)

The communication subtests of the ASVAB are very important because they comprise a sig-
nificant portion of your AFQT score. (I promised I'd keep pounding this concept into your
head — and I wouldn't lie to you, ever!)

On the paper version of the ASVAB (and on the full-length practice tests later in this book),
you see 35 Word Knowledge questions and 15 questions about Paragraph Comprehension.
The CAT-ASVAB has 16 Word Knowledge questions and 11 Paragraph Comprehension ques-
tions. In this chapter, you get 25 total questions just to help you warm up for the practice
tests later on in this book.

Word Knowledge Practice Questions

.WEn

In the stem of each of the following Word Knowledge practice questions, you see an under-
lined word. Select the choice that best answers the question in relation to the underlined
word.

Pay attention to the wording of each question. Some questions ask you to select the choice
closest in meaning to the underlined word. Some questions may ask you to select the word
most opposite in meaning. On other questions, you see the underlined word used in a sen-
tence. In that case, your task is to select the choice most similar in meaning to the under-
lined word as it is used in the context of the sentence.

1. Acclaim most nearly means

(A) enthusiastic approval.

(B) religion.

(D) program.

Used as a noun, acclaim means a shout of approval, so the answer is Choice (A).

j%Q Part II: Words to Live By: Communication Skills

2. The college student met with the bursar to discuss tuition payment options.

(A) planner

(B) treasurer

(D) ghost

Bursar is similar to the word reimburse. The question gives context clues about tuition pay-
ment, and that should give you enough clues to select the correct answer, Choice (B).

3. Estrange most nearly means

(A) sharp.

(B) small.

(D) shiny.

Estrange means to alienate, Choice (C). Note that estrange is a verb, and the only answer
choice that's also a verb is Choice (C); the others are adjectives.

4. Momentous most nearly means

(A) significant.

(B) small.

(D) postpone.

Momentous is an adjective and means very significant, Choice (A).

5. The mother chastised her child.

(A) comforted

(B) carried

(D) supervised

Chastised means disciplined or punished, so Choice (C) is the most correct choice. Choices
(A), (B), and (D) are unrelated.

6. Obtrude most nearly means

(A) condition.

(B) absorb.

(D) impose.

The correct answer is Choice (D). Obtrude means to intrude or to impose oneself on
another. The other choices are unrelated.

Chapter 6: All's Well That Tests Well: Communication Practice Questions jy 7

7. We often wondered why Daniel lived in such an opulent apartment.

(A) run-down

(B) lavish

(D) hideous

Opulent is an adjective that means wealthy, rich, or affluent. Choice (B) is the answer clos-
est in meaning. The other choices are unrelated or opposite of the meaning.

8. Now that you've read through it once, it's time to recapitulate the Word Knowledge chapter.

(A) discuss

(B) summarize

(D) reread

Recapitulate is a verb that means to summarize. It's also the longer version of the word
recap. The correct answer is Choice (B). Choice (A) is somewhat close, but Choice (B) is the
closest in meaning.

9. Clemency most nearly means

(A) mercy.

(B) force.

(D) compliment.

Clemency means forgiveness or leniency in punishing a person. Choice (A) is the correct
answer. The other choices are unrelated.

Knowing prefixes can be useful when determining the definitions of many words. For exam-
ple, you may have heard the word inclement used to describe stormy, severe weather. If you
know that the prefix in- can mean not, you can conclude that clement is likely to be mild or
gentle, traits related to mercy. (See Chapter 4 for more info on using prefixes and word fami-
lies to guess what words mean.)

10. This year the Paris fashion industry has decided to eschew short skirts and high heels.

(A) favor

(B) manufacture

(D) sell

Eschew is a verb that means to avoid or keep away from. Choice (C) is the correct answer,
and the other answers are unrelated.

Gq Part II: Words to Live By: Communication Skills

11. Pollute most nearly means

(A) eliminate.

(B) contaminate.

(D) confuse.

Pollute means to contaminate, Choice (B).

12. Latent most nearly means

(A) hidden

(B) dull

(D) active

Latent means present but not visible or noticeable, so Choice (A) is the correct answer.
Latent can also mean dormant, but none of the answer choices relate to that definition.

13. Paul sent all of his friends a salutary message on the Internet.

(A) beneficial

(B) profane

(D) interesting

Salutary is an adjective meaning beneficial, so Choice (A) is correct. If you took Spanish in
high school, you may remember that a related word, salud, relates to health and well-being,
making (A) a good guess.

Paragraph Comprehension Practice Questions

The last half of the questions in this chapter is designed to present you with an opportunity
to practice your Paragraph Comprehension skills. Read each short paragraph, followed by
one or more questions regarding information contained in that passage. Make sure to read
the paragraph carefully before selecting the choice that most correctly answers the question.

Passage one

Mrs. Berry's was my first coup de main. The house was at the top of a high hill with more
steps to climb to reach the porch which spanned a plain but scrupulously neat living room.
The floor was freshly scrubbed with white sand, there was a deal table also scrubbed to
snowy whiteness and a few splint bottomed chairs scrubbed likewise. All this I noticed
standing on the threshold of the front door which stood wide open from habit, one could
see, rather than with any notion of inviting wayfarers to enter. I knocked on the floor with
the point of my umbrella and after some minutes a comely little black woman appeared in
the doorway just opposite and stood with hands crossed in front of her waiting to learn the
cause of the intrusion.

Chapter 6: All's Well That Tests Well: Communication Practice Questions %Q

14. When the narrator arrives at the house, she

(A) knocks on the door.

(B) knocks on the floor.

(D) rings the doorbell.

The correct answer is Choice (B) — she knocks on the floor using her umbrella. If you
missed this one, read the passage more carefully.

15. The woman's crossed hands imply that she's

(A) bothered.

(B) excited.

(D) bored.

The correct answer is Choice (A). The passage states that the woman is waiting to see "the
cause of the intrusion," which indicates she is bothered or annoyed.

Passage Mo

Some people argue that baking is an art, but Chef Debra Dearhorn says that baking is a sci-
ence. She says that if you follow a recipe carefully, assembling the ingredients accurately,
cooking at the specified temperature for the specified period of time, your cookies will
always turn out right. Chef Dearborn says the best baking is like the best experiment —
anyone can duplicate it.

16. In this passage, the word assembling most nearly means

(A) measuring.

(B) putting together.

(D) storing.

Although measuring is something you do when baking, it doesn't most nearly mean the
same thing as assembling. Putting together does. Therefore, Choice (B) is the correct answer.

17. According to the passage, a person who's all thumbs in the kitchen

(A) should get out of the kitchen.

(B) is an artist.

(D) is Chef Dearborn.

The passage states that if you follow a recipe carefully, "your cookies will always turn out
right." The correct answer is Choice (C).

qQ Part II: Words to Live By: Communication Skills

Passage three

At dinner-time tonight I was feverish to do three things at once: write out my day's Journal,
eat my food, and read the Journal of Marie Bashkirtseff. Did all three — but unfortunately not
at once, so that when I was occupied with one I would surreptitiously cast a glance side-
ways at the other — and repined.

18. Which of the following was the author NOT planning to do?

(A) go shopping

(B) eat food

(D) read a journal

The passage's first sentence tells you everything you need to know — it mentions writing
and reading journals and eating food. Shopping isn't mentioned, so the correct answer is
Choice (A).

Passage four

To motivate your people, give them tasks that challenge them. Get to know your people and
their capabilities, so you can tell just how far to push each one. Give them as much respon-
sibility as they can handle and then let them do the work without looking over their shoul-
ders and nagging them. When they succeed, praise them. When they fall short, give them
credit for what they've done and coach or counsel them on how to do better next time.

19. According to the above paragraph, if your subordinates fail to adequately perform their
tasks, you should

(A) punish them.

(B) praise them.

(D) both B and C.

If you didn't read the passage, praising someone who didn't measure up may seem like a
bad idea. However, the last sentence states you should give your subordinates credit for
the parts of the task they performed correctly and counsel them how to do better the next
time. Although that sentence doesn't use the word praise, you can infer that giving someone
credit means the same thing. The correct answer is Choice (D).

20. After assigning responsibility for the tasks at hand to your subordinates, you should

(A) supervise them closely to ensure the tasks are performed correctly.

(B) let them do the work on their own.

(D) schedule sufficient work-breaks to avoid job burnout.

Choices (C) and (D) sound like good ideas, but they aren't suggestions discussed in the para-
graph. Remember to avoid the trap of answering based on your personal feelings. Choice (A)
is the opposite of what the passage suggests — the writer says to "let [employees] do the
work without looking over their shoulders." Choice (B) is the correct answer.

Chapter 6: All's Well That Tests Well: Communication Practice Questions Q J

Passage fitfe

Approximately 15,000 years ago the first Native Americans may have appeared in Colorado.
The earliest inhabitants were hunters and nomadic foragers on the plains, as well as the
western plateau. Agricultural settlements began appearing along river valleys in the eastern
part of Colorado from approximately 5,000 B.C. as people learned farming techniques from
the Mississippi River Native Americans.

21. The first Native Americans in Colorado were

(A) farmers.

(B) traders.

(D) originally from the Mississippi River region.

The second sentence states that the original inhabitants "were hunters and nomadic forag-
ers," and because none of the other answer options include hunters, you can deduce that
nomadic foragers means gatherers. The correct answer is Choice (C).

Passage six

Organizational leaders influence several hundred to several thousand people. They do this
indirectly, generally through more levels of subordinates than do direct leaders. The addi-
tional levels of subordinates can make it more difficult for them to see results. Organizational
leaders have staffs to help them lead their people and manage their organizations' resources.
They establish policies and the organizational climate that support their subordinate leaders.

22. Organizational leaders provide

(A) direct leadership.

(B) general policies.

(D) daily work schedules.

The passage mentions direct leaders but only to contrast them with organizational leaders,
so (A) is wrong. According to the passage, organizational leaders "establish policies and the
organizational climate that support their subordinate leaders." The correct answer is
Choice (B).

23. In order to become more efficient, organizational leaders make significant use of

(A) computer technology.

(B) rules and regulations.

(D) staffs.

Organizational leaders have staffs to help them efficiently lead their subordinates and
manage the organization. Therefore, Choice (D) is the correct answer.

^2 ^ art "' Words to Live By: Communication Skills

Passage set/en

His name is Frank Clarke, but his real name isn't really as real as the one the children gave
him — The Toyman — because he's always making the kids things, such as kites and tops,
sleds and boats, jokes and happiness and laughter. His face is as brown as saddle leather,
with a touch of apple red in it from the sun. His face is creased, too, because he laughs and
jokes so much. Sometimes when The Toyman appears to be solemn you want to laugh most,
for he's only pretending to be solemn. And, best of all, if you hurt yourself or if your pet
doggie hurts himself, The Toyman knows how to fix it to make it all well again.

24. Frank Clarke's face could best be described as

(A) rugged.

(B) pink and smooth.

(D) feminine.

According to the passage, Frank's face is "brown as saddle leather," and he has wrinkles
from laughing often. Choice (A) is the correct answer.

25. Clarke received his nickname because he was always

(A) fixing toys.

(B) making toys for the children.

(D) playing with toys.

The first sentence in the passage explains why the children gave Frank the nickname of The
Toyman. Frank knows how to fix things, but that's not how he got his name. The correct
answer is Choice (B).

Part III

Making the Most of Math
Arithmetic Skills

The 5 th Wave

By Rich Tennant

"The iwage is getting clearer now., I can almost seeit...Yes,' there
it is. The answer is 3ab*x7d?--VjflL-i-u3£ 1 'f*± lco.O$)l% + Q6Q"

In this part . . .

i\J\ any military careers require a solid understanding
/r lof math principles. Even though the military will
spring for a calculator, you're expected to know how to
add and subtract before you hit boot camp. And you can't
use a calculator on the ASVAB.

Part III gives you a chance to brush up on your numbers
knowledge. It includes all kinds of information that can
help you do well on the two math-related subtests that
the ASVAB throws at you: Arithmetic Reasoning and
Mathematics Knowledge. I also give you a ton of tips on
everything from how to guess whether you're running out
of time to what to do if you forget how to solve a quadratic
equation.

Chapter 7

Mathematics Knowledge
and Operations

In This Chapter

Getting more terminology under your belt
Revisiting high school: Algebra and geometry review
Performing calculations without the calculator
Perfecting your way to a higher score

*J*BE*

XM lbert Einstein once said, "Do not worry about your problems with mathematics.
V \ I assure you mine are far greater." The good professor obviously never faced an
upcoming ASVAB exam! Okay, just kidding. You don't have to be a mathematical theoreti-
cian to score well on the Mathematics Knowledge subtest. This subtest asks questions
about basic high school mathematics. No college or graduate degrees needed.

On the paper version of the ASVAB, the Mathematics Knowledge subtest consists of
25 questions, and you have 24 minutes to complete the subtest. The CAT-ASVAB offers
16 questions in 20 minutes. You don't necessarily have to rush through each calculation,
but the pace you need to set doesn't exactly give you time to daydream. You have to focus
and concentrate to solve each problem quickly and accurately. And no calculators allowed!

Most of the time, the Mathematics Knowledge subtest contains only one or two questions
testing each specific mathematical concept. For example, one question may ask you to mul-
tiply fractions, the next may ask you to solve a mathematical inequality, and the question
after that may ask you to find the value of an exponent. (If you're freaked out by the last
sentence, calm down. I cover these concepts in this chapter.)

All this variety forces you to shift your mental gears quickly to deal with different concepts.
You can look at this situation from two perspectives. These mental gymnastics can be diffi-
cult and frustrating, especially if you know everything about solving for x but nothing about
finding a square root. But variety can also be the spice of life. If you don't know how to
solve a specific type of problem, any oversight may only cause you to get one or two ques-
tions wrong.

To qualify for certain jobs in the military, you have to score well on the Mathematics
Knowledge subtest. You also have to do well on this subtest, which is part of the AFQT dis-
cussed in Chapter 1, in order to enlist. Turn to the Appendix A to find out more about the
subtest scores needed for specific military jobs.

In this chapter, I go over the basic arithmetic, algebra, and geometry you need to know.
This info also comes in handy when solving word problems on the Arithmetic Reasoning
subtest, which I cover in Chapter 8.

00 Part III: Making the Most of Math: Arithmetic Skills

Just When l/ou Thought \lou Were bone
With Vocab: Math Terminology

Math has its own vocabulary. In order to understand what each problem on the
Mathematical Knowledge subtest asks, you need to understand certain mathematical terms:

u* Integer: An integer is any positive or negative whole number or zero. The ASVAB often
requires you to work with integers, such as -6, 0, or 27.

u* Factors: Factors are integers (whole numbers) that can be divided evenly into another
integer. To factor a number, you simply determine the numbers that you can divide
into it. For example, 8 can be divided by the numbers 2 and 4 (in addition to 1 and 8),
so 2 and 4 are factors of 8.

Numbers may be either composite or prime, depending on how many factors they have:

• Composite number: A composite number is a whole number that can be divided
evenly by itself and by 1, as well as by one or more other whole numbers; in other
words, it has more than two factors. Examples of composite numbers are 6
(whose factors are 1, 2, 3, and 6), 9 (whose factors are 1, 3, and 9), and 12 (whose
factors are 1, 2, 3, 4, 6, and 12).

• Prime number: A prime number is a whole number that can be divided evenly by
itself and by 1 but not by any other number, which means that it has exactly two
factors. Examples of prime numbers are 2 (whose factors are 1 and 2), 5 (whose
factors are 1 and 5), and 11 (whose factors are 1 and 11).

u* Exponent: An exponent is a shorthand method of indicating repeated multiplication.
For example, 15 x 15 can also be expressed as 15 2 , which is also known as "15 squared"
or "15 to the second power." The small number written slightly above and to the right
of a number is the exponent, and it indicates the number of times you multiply the
number it accompanies by itself. Note that 15 2 (15 x 15, which equals 225) isn't the
same as 15 x 2 (which equals 30).

To express 15 x 15 x 15 using this shorthand method, simply write it as 15 3 , which is
also called "15 cubed" or "15 to the third power." Again, 15 3 (which equals 3,375) isn't
the same as 15x3 (which equals 45).

u* Base: A base is a number that's used as a factor at least two times — it's a number
raised to an exponent. For instance, the term 4 3 (which can be written 4x4x4, and in
which 4 is a factor three times) has a base of 4.

j*" Square root: The square root of a number is the number that, when multiplied by itself
(squared), equals the original number. For example, the square root of 36 is 6. If you
square 6, or multiply it by itself, you produce 36. (Check out "Getting to the Root of the
Problem," later in this chapter.)

J-" Factorial: A factorial is represented by an exclamation point (!). You calculate a facto-
rial by finding the product of (multiplying) a whole number and all the whole numbers
less than it down to 1. So 6 factorial (6!) is 6x5x4x3x2x1 = 720.

*J|lBBf

A factorial helps you determine permutations — all the different possible ways an event
may turn out. For example, if you want to know how many different ways six runners
could finish a race (permutation), you would solve for 6! — 6x5x4x3x2x1.

i*" Reciprocal: A reciprocal is the number by which another number can be multiplied to
produce 1; if you have a fraction, its reciprocal is that fraction turned upside down. For

example, the reciprocal of 3 is ^. If you multiply 3 times ^, you get 1. The reciprocal of

i o 1 9 Q

-r is y (which is the same thing as 6); -~ x 6 = 1. The reciprocal of ^ is ^. Get the idea?

Chapter 7: Mathematics Knowledge and Operations ^ 7

V Rounding: Rounding is limiting a number to a few (or no) decimal places. You perform
rounding operations all the time — often without even thinking about it. If you have a
$1.97 in change in your pocket, you may say, "I have about two dollars." The rounding
process simplifies mathematical operations.

Often, numbers are rounded to the nearest tenth. The ASVAB may ask you to do this.
For any number that ends in 5 and over, round up; for any number under 5, round down.
For example, 1.55 can be rounded up to 1.6, and 1.34 can be rounded down to 1.3.

Many math problems require rounding — especially when you're doing all this
without a calculator. For example, pi (n) represents a number approximately equal to
3.141592653589793238462643383 (and on and on and on). However, in mathematical
operations, it's common to round n to 3.14.

Operations: What \lou Do to Numbers

When you toss numbers together (mathematically speaking), you perform an operation. When
you add or multiply, you perform a basic operation. But because math functions according
to yin-yang-like principles, each of these basic operations also has an opposite operation
called an inverse operation. Thus, the inverse of addition is subtraction, and the inverse of
multiplication is division. And of course, the inverse of subtraction is — you got it — addi-
tion. The inverse of division is multiplication.

^\NG/

Don't confuse opposite with inverse. When you're doing mathematical operations, such as
adding and multiplying, the inverse operation is the opposite operation. But when you're
talking numbers, opposite and inverse don't mean the same thing. The opposite of a posi-
tive number is a negative number, so the opposite of x is -x But the inverse of a number is
its reciprocal — that number turned on its head! The inverse of x is — . The inverse of -^ is y
(or just 5).

First things first: following the order of operations

Operations must be performed in a certain order. For example, when you have parentheses
in a math problem, the calculation in the parentheses must be done before any calculations
outside of the parentheses. In the equation 2 x (16 + 5) = ?, you first add 16 to 5 to arrive at
21, and then you multiply by 2 to come up with a total of 42. You get a different (and wrong)
answer if you simply calculate from left to right: 2x16 = 32, and 32 + 5 = 37. And you better
believe that both results will be choices on the test!

Naming the answers

The result of each operation — addition, subtraction, j*" When you subtract, all that remains is a difference.
multiplication, or division — goes by a different name:

v When you add two numbers together, you arrive at

a sum.

v* When you multiply, you come up with a product.
w When you divide, you're left with a quotient.

0$ Part III: Making the Most of Math: Arithmetic Skills

cjftBEtf

To figure out which mathematical operation you should perform first, second, third, and so
on, follow these rules, otherwise known as the order of operations:

1. Parentheses take precedence.

You should do everything contained in parentheses first. In cases where parentheses
are contained within parentheses, do the innermost parentheses first.

Note: If you're dealing with a fraction, treat the top as though it were in parentheses
and the bottom as though it were in parentheses, even if the parentheses aren't written

in the original state. Suppose you have the problem: ^ — ^ = ? Add the numbers below
the fraction bar before dividing. The answer is # - 1. (For more on fractions, see later

section "Working on Both Sides of the Line: Fractions.") The square root sign (V) is also
a grouping symbol, so you solve for whatever's under the top bar of the square root
sign before doing any other operation in the problem.

2. Exponents come next.

Remember that the exponent goes with the number or variable that it's closest to. If
it's closest to a parenthesis, then you already should've performed the calculation
inside the parentheses in Step 1. For example, (5 x 2) 2 = 10 2 = 100. The square root sign
(V) is also treated as an exponent, so you take the square root during this step.

3. Multiplication and division are next.

Do these operations in left-to-right order (just like you read).

4. Addition and subtraction are last.

Perform these operations from left to right as well.

Check out the following example for a little practice with order of operations:

(15 * 5) x 3 + (18 - 7) = ?
Do the work in parentheses:

3x3 + 11 =?

No exponents are present, so division and multiplication come next (in this problem, only
multiplication is needed):

9+ 11 =?

Finally, do the addition and subtraction (in this problem, only addition is needed). Your
final answer is 20.

Completing a number sequence

The Arithmetic Reasoning (AR) subtest often includes questions that test your ability to
name what comes next in a sequence of numbers. Generally, these problems are the only
AR questions that aren't word problems (which I cover in Chapter 8). However, sequence
questions do test your ability to do arithmetic and to reason, because you have to deter-
mine how the numbers relate to each other. And to do this, you must be able to perform
mathematical operations quickly.

Chapter 7: Mathematics Knowledge and Operations Q Q

Suppose you have a sequence of numbers that looks like this: 1, 4, 7, 10, ?

Each new number is reached by adding 3 to the previous number: 1+3 = 4, 4 + 3 = 7, and so
on. So the next number in the sequence is 10 + 3, or 13. But of course, the questions on the
ASVAB aren't quite this simple. More likely, you'll see something like this: 2, 4, 16, 256, ?

In this case, each number is being multiplied by itself, so 2x2 = 4, 4x4= 16, and so on. The
next number in the sequence is 256 x 256, which equals 65,536 — the correct answer. You
may also see sequences like this: 1, 2, 3, 6, 12, ?

In this sequence, the numbers are being added together: 1+2 = 3, and 1 + 2 + 3 = 6. The next
number is 1 + 2 + 3 + 6 = 12. So the next number would be 24.

Finding the pattern

To answer sequence questions correctly, you need to figure out the pattern as quickly as
possible. Some people, blessed with superior sequencing genes, can figure out patterns
instinctively. The rest of the population has to rely on a more difficult, manual effort.

Finding a pattern in a sequence of numbers requires you to think about how numbers work.
For instance, seeing the number 256 after 2, 4, 16 should alert you that multiplication is the
operation, because 256 is so much larger than the other numbers. On the other hand,
because the values in 1, 2, 3, 6, 12 don't increase by much, you can guess that the pattern
requires addition.

beatinq With more than one operation in a sequence

Don't forget that more than one operation can occur in a sequence. For example, a sequence
may be "add 1, subtract 1, add 2, subtract 2." That would look something like this: 2, 3, 2, 4, ?

Because the numbers in the sequence both increase and decrease as the sequence contin-
ues, you should suspect that something tricky is going on.

Make sure to use your scratch paper! Jot down notes while you're trying to find the pattern
in a sequence. Writing your work down helps you keep track of which operations you've
tried.

Working on Both Sides of the Line: Fractions

I don't know why, but it seems almost all math textbooks explain fractions in terms of pies.
(I think most mathematicians must have a sweet tooth.) But I like pizza, so I'm going to use
pizza instead. If a whole number is a pizza, a fraction is a slice of pizza. A fraction also illus-

trates the slice's relationship to the whole pizza. For example, consider the fraction ^. If

you accuse your cousin of eating -^ of the pizza when he comes over for movie night, you're

saying that the pizza is divided into five equal-sized slices — fifths — and your cousin ate
three of those five slices. Can anyone say pig?

The number above the fraction bar — the three slices your cousin ate — is called the
numerator. The number written below the fraction bar — the total number of slices the
pizza is divided into — is called the denominator.

0^B

YQ Part III: Making the Most of Math: Arithmetic Skills

Common denominators: Preparing to
add and subtract fractions

To add and subtract fractions, the fractions must have the same denominator (bottom
number), which is called a common denominator. If the fractions don't have a common
denominator, you have to find one. There are two basic methods to use. Sound fun?
Read on.

Method one

Finding a common denominator can be easy, or it can be as hard as picking off all the

o o

anchovies. Suppose you want to add 4 and ^. Getting a common denominator is easy here,

and you use this process whenever you can evenly divide one denominator by another.
Follow these steps:

1. Divide the larger denominator by the smaller denominator.

If there's a remainder, then you can't use this method, and you have to use method two
(see the next section). In this case, 10 can be divided evenly by 5. The quotient
(answer) that results is 2.

2. Take the fraction with the smaller denominator I ^ J; multiply both the numerator

(top number) and the denominator (bottom number) by the answer that resulted in
Step 1.

Multiply 3 by 2, and the result is 6 — that's your new numerator. Multiply 5 by 2, and
the result is 10 — that's your new denominator.

3. Replace the numerator and denominator with numbers from Step 2.

You can also express ^ as -^r. (If you cut the pizza into 10 slices instead of 5 and your
cousin eats 6 slices instead of 3, he's eaten exactly the same amount of pizza.)

After you've found a common denominator, you add the two fractions by simply adding the
numerators together: A. + -^ = ^-. Think of it this way: If your cousin eats ^r of the pizza

(which is just another way of saying -^) and you eat ^ of the pizza, together you've eaten
q o 10

^ of the pizza.

Method Mo

O 1

Suppose your cousin eats ^ of one pizza and your sister eats ^ of another pizza (one that
was cut into 6 slices instead of 5), and you want to know how much pizza has been eaten. In

o 1

this case, you need to add ^ and -±-.

5 6

Adding these fractions is a bit more difficult because you can't divide either denominator
by the other. You have to find a common denominator that both 5 and 6 divide into evenly.
Here's how:

1. Multiply the denominator of the first fraction by the denominator of the second
fraction.

In the example case, 5 x 6 = 30. The common denominator for both fractions is 30.

2. Express the first fraction in terms of the new common denominator.

5 "30

Chapter 7: Mathematics Knowledge and Operations 7 /

0tSEH

3. Multiply the numerator by the number that you multiplied by to result in the new
denominator.

To convert the denominator (5) to 30, you multiply by 6, so multiply the numerator (3)

O I Q

by 6. The result is 18. Therefore, the fraction 4 can be expressed as ^4.

o 30

When you're trying to find the common denominator for a fraction, always multiply the
numerator and the denominator by the same number. Otherwise, you change the value
of the fraction.

With this example, you multiply the numerator and the denominator by 6, discovering

O 1 Q

that 4 is the same thing as ^4. But if you were to multiply only the denominator by 6,

3 o

you'd have a new number — 4 and t4 don't have the same value.

4. Next, express the second fraction in terms of the new common denominator.

I- JL
6 30

5. Multiply the numerator of the second fraction by the number you used to result in
the denominator.

To get 30, you have to multiply 6 by 5. Multiply the numerator by the same number:

You find that 1 x 5 = 5, so the fraction j, can be expressed as -£r.

b 60

After all that work, you can finally add the fractions: J^ + J^r = ^. Now pause and take a bite
of pizza.

Finding common denominators for three or more fractions

If you have more than two fractions with different denominators, you have to find a common

12 3

denominator that all the denominators divide into. Suppose you need to add 4; + 4 + 4.

Zoo

A simple way to find a common denominator is to take the largest denominator (in this
case 5) and multiply it by whole numbers, starting with 1, 2, 3, 4, and so on until you find a
denominator that the other denominators also divide into evenly.

If you multiply 5 by 2, you get 10, but 3 doesn't divide evenly into 10. So keep going: 5x3 =
15, 5 x 4 = 20, and so on until you find a number that 2, 3, and 5 can divide into evenly. In
this case, 30 is the first number you can find that 2, 3, and 5 can divide into evenly, so 30 is
your common denominator.

0»Uft

Multiplying and reducing fractions

Multiplying fractions is easy. You just multiply the numerators and then multiply the

?. You multiply 1x3x3 = 9 (the

1 3 3
denominators. So look at the following equation: ± x 4 x 4

numerators) and then 2 x 4 x 5 = 40 (the denominators) to result in -^.

Occasionally, when you multiply fractions, you end up with an extremely large fraction that
can be simplified or reduced. To express a fraction in its lowest terms means to put it in
such a way that you can't evenly divide the numerator and the denominator by the same
number (other than 1).

A number that you can divide into both the numerator and the denominator is called a
common factor. If you have the fraction y^-, both the numerator (6) and the denominator

(10) can be divided by the same number, 2. If you do the division, 6 + 2 = 3 and 10 + 2 = 5,

72 Part lll: Making the Most of Math: Arithmetic Skills

you find that ^ can be expressed in the simpler terms of y. You can't reduce (simplify) y
any further; the only other number that both the numerator and denominator can be
divided by is 1, so the result would be the same, y.

Remember, you can't use a calculator on the ASVAB, so multiplying large numbers can take
extra steps and valuable time. You can make your work easier by canceling out common

factors before multiplying. For example, suppose you have the problem 4r x t$-- Multiplying

the numerators (20 x 14 = 280), then multiplying the denominators (21 x 25 = 525), and

finally reducing the fraction I ^50.

rate multiplication/division problems. But you can save time if a numerator and denomina-
tor have common factors. Here, the numerator of the first fraction (20) and the denominator
of the second (25) have a common factor of 5, so you can divide both of those numbers by

5: Your problem becomes yrX ^. The numerator of the second fraction (14) and the

denominator of the first fraction (21) are both divisible by 7, so you can cancel out a 7:

Divide 14 and 21 by 7. This changes the equation to y x -f = ^-, a much simpler math problem.

-°-j may require you to write out three or more sepa-

Sjt&Et

Dividing fractions

Dividing fractions is simple if you remember this rule: Dividing a fraction by a number is the
same as multiplying it by the inverse (reciprocal) of that number. Of course, there are
always exceptions. You can't use this operation on zero. Zero has no inverse. No one knows
why — it just is.

The inverse of a number is obtained by reversing the number. That means that if you want

to divide a fraction by 5, you simply multiply the fraction by the inverse of 5, which is i.

You can understand this process more easily if you remember that 5 is the same thing as y.

In other words, 5 divided by 1 equals 5 (that is, 5 * 1 = 5). And the inverse of y is y. To come
up with the inverse of a number, simply stand the number on its head.

So to divide a fraction, use the inverse of the number that follows the division symbol (+)

and substitute a multiplication symbol (x) for the division symbol. Therefore, y ■*■ 2 is

11
expressed as y x y, and you already know how to multiply fractions. (If not, check out the

"Multiplying and reducing fractions" section earlier in the chapter.) 1x1 = 1 and 3x2 = 6,

so the product of y x y = ^. Therefore, y + 2 = y.

Converting improper fractions to mixed
numbers . . . and back again

If you have a fraction with a numerator larger than its denominator, you have an improper

■7

fraction. For example, y is an improper fraction. To put an improper fraction into simpler

7
(proper) terms, you can change y into a mixed number (a number that includes a whole

number and a fraction). Simply divide the numerator by the denominator: 7 divided by 3 gives
you a quotient of 2 with a remainder of 1. There's something left over because 3 doesn't
divide evenly into 7. The remainder becomes a numerator over the original denominator,

1 7 1

so y is left over. Therefore, y is the same as 2y.

Chapter 7: Mathematics Knowledge and Operations 7 A

j^BE/f

If you want to multiply or divide a mixed number, you need to convert it into a fraction —
an improper fraction. To make the change, convert the whole number into a fraction and
add it to the fraction you already have. Here's how:

1 . Multiply the whole number by the denominator (bottom number) of the existing

fraction to arrive at a new numerator.

o
Suppose you have 7lr. Multiply 7 by 3: 7x3 = 21

2. Place this new numerator over the existing denominator.

21
3

3. Add that fraction to the original fraction to get the final answer.

21, 2_23
3 3 3

Check out the "Adding and subtracting fractions" section earlier in this chapter for the
complete scoop on adding fractions.

Or if you want to get technical, you can look at the whole process this way, too:
n 2 7x3 + 2 23

0RHt

Expressing a fraction in other forms:
Decimals and percents

A fraction can also be expressed as a decimal and as a percent. Here's how to convert
between forms:

u* To change a fraction into a decimal: Divide the numerator (top number) by the

denominator (bottom number). Given that handy explanation, ^ (or 3 + 5) converted
into decimal form is 0.6.

Some fractions convert to repeating decimals — a decimal in which one digit is repeated
infinitely. For instance, ^ is the same as 0.66666... (with the sixes never stopping).

Repeating decimals are often rounded to the nearest hundredth; therefore, ^ rounds to

0.67. (Remember: The first space to the right of the decimal is the tenths place, the
second space is the hundredths place, and the third is the thousandths, and so on.)

u* To make a decimal into a percent: Move the decimal point two spaces to the right and
add a percent sign. For example, 0.6 becomes 60%.

See the following sections for more thorough discussions of decimals and percents.

Adding and subtracting decimals

To add and subtract decimals, put the numbers in a column and line up the decimal points.
Then add or subtract as if the decimals were whole numbers, keeping the decimal point in
the same position in your answer.

1.4583
Here are two examples: +0.55

2.0083

1.4583
-0.55
0.9083

You can add zeros to the end of a decimal if performing the calculations this way is easier
for you. So 0.1 can be 0.100 without changing its value. In the preceding problems, 0.55 can
be 0.5500 to help you line up the decimal points and perform the operation.

7 (l Part III: Making the Most of Math: Arithmetic Skills

&*$!

Multiplying decimals

Multiplying a decimal is like multiplying a regular, everyday whole number, except that you
have to place the decimal point in the correct position after you reach an answer.

1. Multiply as though you were multiplying whole numbers, without the decimal
points.

Suppose you're multiplying 3.77 x 2.8. In this example, 377 x 28 = 10556.

2. Count and add the number of decimal places (to the right of the decimal point) in
the numbers being multiplied.

If one of the numbers you're multiplying is 3.77, you have two decimal places. If the
other number you're multiplying is 2.8, you have one more decimal place, so the total
number of decimal places in your answer will be three.

If you're multiplying a number that has only zeros to the right of the decimal point,
then those decimals don't count. For instance, 3 can also be expressed as 3.0, but you
wouldn't count the as a decimal place. All the zeros to the right of the decimal point
don't count unless a number other than zero comes after them. For instance, 3.000007
has six decimal spaces, 3.0070 has three decimal spaces, and 3.000 has none, at least
not for the purpose of multiplying.

3. In the answer, move the decimal point back to the left the number of places you
counted in Step 2.

This time, zeros do count. You counted three total decimal places in 3.77 and 2.8, so
you move the decimal point in 10566 back to the left three places. The resulting prod-
uct is 10.556.

If your answer doesn't include enough numbers for the decimal spaces you need, then
add as many zeros as necessary to the left of the answer. Suppose your answer is 50,
and you have to move the decimal point to the left three spaces. There aren't three
spaces in 50, so you add a zero to the left to make 050 and put the decimal point in its
proper position: 0.050 is your answer.

Here's another example: 0.04 x 0.25. Multiply the decimals as if they were whole numbers:
4 x 25 = 100. Count and add the number of decimal places in the original two numbers; there
are four. Then put the decimal point in the correct place in the answer. For 100, count from
right to left four places, and put the decimal point there: 0.0100, or 0.01. Here's the method
behind the madness:

100 100

100 1

10,000 100

= 0.01 for 0.0100)

$mn

bitfidinq decimals

Decimals are divided according to slightly different rules, depending on whether both num-
bers in the problem are decimals.

Dividing decimals by whole numbers

Here's how to divide a decimal by a whole number:

1. Move the decimal point over to the right until the decimal is a whole number, count-
ing the number of decimal places.

For example, if you want to find 1.25 * 4, change 1.25 to 125 by moving the decimal two
decimal places to the right. Remember how many places you moved the decimal —
you need that info later.

2. Perform the division operation on the whole number.

125*4 = 31.25

Chapter 7: Mathematics Knowledge and Operations (5

3. In your answer, move the decimal point to the left the number of places you moved
it in Step 1.

To make up for moving the decimal point two places to the right when you made 1.25
into a whole number, move the decimal point two places to the left in 31.25. Your
answer is 0.3125.

bioidinq decimals by decimals

Here's how to divide a decimal by another decimal in which there are the same number of
places after the decimal point:

1. Make the divisor (the decimal going into the other number) into a whole number: Move
the decimal point all the way to the right, counting the number of places you move it.

Suppose you want to divide 0.15 by 0.25 (that is, 0.15 * 0.25). Move the decimal point in
0.25 two places to the right: It then becomes 25.

2. Move the decimal in the dividend (the number being divided) the same number of
decimal places.

Move the decimal point in 0.15 two places: 0.15 becomes 15.

3. Divide.

When you divide 15 by 25, the result is 0.60. You don't need to move any more deci-
mals around — 0.60 is your final answer.

If the dividend is a longer decimal than the divisor, you follow the same steps, but you have
to do an extra step at the end. So if your problem is 0.125 * 0.50, first move the decimal
point in the divisor (0.5) one place to the right so that you have the whole number 5. Then
move the decimal point in the dividend one place to come up with 1.25.

Now the problem looks like this: 1.25 * 5. Convert the first number (1.25) to a whole number by
moving the decimal point two places to the right. Now perform the division operation on the
whole numbers: 125 + 5 = 25. Move the decimal point two places to the left (to make up for moving
it two places to the right when you converted 1.25 to a whole number). The answer is 0.25.

When the divisor is a longer decimal than the dividend, such as 0.50 + 0.125, move the decimal
point in the divisor all the way to the right, in this case making 0.125 into 125, counting places.
Then move the decimal the same number of places in the dividend, adding zeros as needed:
0.5 then becomes 500. Then 500 * 125 = 4, which is the correct answer (0.50 * 0.125 = 4).

Playing With percents

A percent is a fraction based on one-hundredths. Five percent (5%) is the same as yj^y or

0.05. The ASVAB often asks you to calculate "10% off" or "an increase of 15%" on the
Arithmetic Reasoning subtest. You need to be able to convert percents to fractions or
decimals to answer these questions correctly.

To add, subtract, multiply, or divide using percents, change the percent to a fraction or a
decimal. Here are some helpful hints for figuring percents:

u* Remember, a percent is just hundredths, so 3% is y^r or 0.03, 22% is -^- or 0.22, and

i i r\ 1U0 1UU

110% is |^ or 1.10.

f To convert a percent to a decimal, just drop the percent sign and move the decimal
point two places to the left, adding zeros as needed.

p" The decimal point always starts to the right of a whole number, so 60 is the same thing
as 60.0. Moving the decimal point two spaces to the left leaves you with 0.6.

After you do the conversion, follow the rules outlined in the earlier sections for performing
specific operations on fractions or decimals.

Y0 Part III: Making the Most of Math: Arithmetic Skills

Showing comparisons With ratios

A ratio shows a relationship between two things. For example, if Margaret invested in her
tattoo parlor at a 2:1 (or 2 to 1) ratio to her business partner Julie, then Margaret put in $2
for every $1 that Julie put in. You can express a ratio as a fraction, so 2:1 is the same as y.

Or suppose you fill up your brand-new, shiny SUV, and you want to compute your gas
mileage — miles per gallon. You drive for 240 miles and then refill the tank with 15 gallons
of gas, so the ratio of miles to gallons is 240:15. You can compute your gas mileage by divid-
ing the number of miles by the number of gallons: 240 miles + 15 gallons. You're getting
16 miles per gallon. Time for a tune up!

In this section, I cover some uses for ratios, including scale drawings and rates such as speed.

Navigating scale drawings

Scale, particularly when used on the ASVAB, relates to scale drawings. For example, a map
drawn to scale may have a 1-inch drawing of a road that represents 1 mile of physical road
in the real world. The Arithmetic Reasoning portion of the ASVAB often asks you to calcu-
late a problem based on scale, which can be represented as a standard ratio (1 inch:l mile)

or a fraction

1 inch \
1 mile f

On a map with a scale of 1 inch to 1 mile, the ratio of the scale is represented as 1:1. But ques-
tions are never this easy on the ASVAB. You're more likely to see something like, "If a map
has a scale of 1 inch to every 4 miles. . . ." That scale is expressed as the ratio 1:4, or i

Try your hand with the following common scale problem:

If the scale on a road map is 1 inch = 250 miles, how many inches would represent 1,250 miles?

The problem wants you to determine how many inches on the map represent 1,250 miles if
1 inch is equal to 250 miles. You know that 1 inch = 250 miles, and you also know that some
unknown number of inches, which you can call x, equals 1,250 miles. The problem can be

expressed as two ratios set equal to each other, known as a proportion;
you have to do is solve for x:

1 _ x
250

1 x

250"U50

Now all

1 vl OKC\

250 Xi ' ZDU " 1,250

1,250
x x 1,250

1,250
250

*»££?

So if 1 inch is equal to 250 miles, then 5 inches would be equal to 1,250 miles. If this problem
causes you to scratch your head, check out the upcoming section "An Unknown Quantity:
Reviewing Algebra" for info on solving for x.

Almost every military job makes use of scales, which is why scale-related questions are so
common on the ASVAB. Whether you're reading maps at Mountain Warfare School or orga-
nizing trash pickup around the base, you need to use and interpret scales frequently.

Remembering important rates

A rate is a fixed quantity — a 5% interest rate, for example. It can mean the speed at which
one works (John reads at the rate of one page per minute). Or it can mean an amount of
money paid based on another amount (life insurance may be purchased at a rate of $1 per
$100 of coverage). A rate is often a speed, something per a unit of time.

cjftBEtf

Chapter 7: Mathematics Knowledge and Operations 7 7

Word problems often ask you to solve problems that involve speed or simple interest rates.
Here are two rate formulas you should commit to memory:

j*" Simple interest: / = Prt, where / represents the amount of interest, P is the principal
(the initial amount invested), r is the interest rate, and t is the length of time the money
is invested.

v* Distance: d - rt, where d represents the distance traveled, r is the rate (speed) of travel,
and t is the amount of time traveled.

In a rate, you can generally think of the word per as a division sign. For instance, suppose
someone drives 141 miles in 3 hours, and you have to find the average speed. You want the
rate of speed in miles per hour, so you take miles (distance) divided by hours (time): 141
miles + 3 hours = 47 miles/hour. Using algebra, you can rearrange the distance formula to
say the same thing: d + t = r.

A Powerful Shorthand: Writing
in Scientific Notation

Scientific notation is a compact format for writing very large or very small numbers.
Although it's most often used in scientific fields, you may find a question or two on the
Mathematics Knowledge subtest of the ASVAB, asking you to covert a number to or from
scientific notation.

Scientific notation separates a number into two parts: a number between 1 and 10 and a
power of ten (such as 10 7 , 10 21 , or 10~ 18 ; see the earlier section "Just When You Thought You
Were Done with Vocab: Math Terminology" for info on powers and exponents). Therefore,
1.25 x 10 4 means 1.25 x 10 to the fourth power, or 12,500; 5.79 x 10" 8 means 5.79 * 10 to
the eighth power, or 0.0000000579. The exponent tells you how many places to move the
decimal point and whether to move it left or right (depending on whether it's positive or
negative).

Getting to the Root of the Problem

cjftBE/?

A square root is the factor of a number that, when multiplied by itself, produces the number.
Take the number 36, for example. One of the factors of 36 is 6. If you multiply 6 by itself (6 x 6),
you come up with 36, so 6 is the square root of 36. The number 36 has other factors, such as
18. But if you multiply 18 by itself (18 x 18), you get 324, not 36. So 18 isn't the square root of 36.

All whole numbers are grouped into one of two camps when it comes to roots:

u* Perfect squares: Only a few whole numbers, called perfect squares, have exact square
roots. For example, the square root of 25 is 5.

v* Irrational numbers: Other whole numbers have square roots that are decimals that go
on forever and have no pattern that repeats (nonrepeating, nonterminating decimals),
so they're called irrational numbers. The square root of 30 is 5.4772255 with no end to
the decimal places, so the square root of 30 is an irrational number.

The sign for a square root is called the radical sign. It looks like this: V. Here's how you use
it: J36 means "the square root of 36" — in other words, 6.

7$ Part III: Making the Most of Math: Arithmetic Skills

Perfect squares

Square roots can be difficult to find at times without a calculator, but because you can't use
a calculator during the test, you're going to have to use your mind and some guessing meth-
ods. To find the square root of a number without a calculator, make an educated guess and
then verify your results.

To use the educated-guess method (see the next section), you have to know the square
roots of a few perfect squares. One good way to do this is to memorize the squares of the
square roots 1 through 12:

/"" 1 is the square root of 1 (1 x 1 = 1)
v* 2 is the square root of 4 (2 x 2 = 4)
p" 3 is the square root of 9 (3 x 3 = 9)

V 4 is the square root of 16 (4 x 4 = 16)
i* 5 is the square root of 25 (5 x 5 = 25)
e* 6 is the square root of 36 (6 x 6 = 36)
e" 7 is the square root of 49 (7 x 7 = 49)

V 8 is the square root of 64 (8 x 8 = 64)
W 9 is the square root of 81 (9 x 9 = 81)

V 10 is the square root of 100 (10 x 10 = 100)

V 11 is the square root of 121 (11 x 11 = 121)

V 12 is the square root of 144 (12 x 12 = 144)

Irrational numbers

When the ASVAB asks you to figure square roots of numbers that aren't perfect squares, the
task gets a bit more difficult. In this case, the ASVAB usually asks you to find the square
root to the nearest tenth.

Suppose you run across this problem:

J54

Think about what you know: You know that the square root of 49 is 7, and 54 is slightly
greater than 49. You also know that the square root of 64 is 8, and 54 is slightly less than 64.
So if the number 54 is somewhere between 49 and 64, the square root of 54 is somewhere
between 7 and 8. Because 54 is closer to 49 than to 64, the square root will be closer to 7
than to 8, so you can try 7.3 as the square root of 54.

Multiply 7.3 by itself: 7.3 x 7.3 = 53.29, which is very close to 54. Now try multiplying 7.4 by
itself to see if it's any closer to 54: 7.4 x 7.4 = 54.76, which isn't as close to 54 as 53.29.
Therefore, 7.3 is the square root of 54 to the nearest tenth without going over.

Other roots

The wonderful world of math is also home to concepts like cube roots, fourth roots, fifth
roots, and so on. A root is a factor of a number that when cubed (multiplied by itself

Chapter 7: Mathematics Knowledge and Operations 7Q

three times), taken to the fourth power (multiplied by itself four times), and so on produces
the original number. A couple of examples seem to be in order:

v* The cube root of 27 is 3. If you cube 3 (also known as raising it to the third power or
multiplying 3x3x3), the product is 27.

v* The fourth root of 16 is the number that, when multiplied by itself four times, equals
16. Any guesses? Drumroll, please: 2 is the fourth root of 16 because 2x2x2x2 = 16.

An Unknown Quantity: Rei/ieu/iny Algebra

Some people freak out just hearing the word algebra. But algebra is just a way to put prob-
lems into mathematical language using the simplest mathematical terms possible. In fact,
it's almost impossible to solve most word problems without some use of algebra.

**M*

The letters in an algebra problem are called variables. In an algebra equation, if the same
letter is used more than once, it stands for the same number. In 3x + 2x = 10, the first x will
never be a different number from the second x. In this case, x = 2 (both times).

^PLE

Solving for x

In algebra, you often hear about "solving for x" or "solving for the unknown," but what's the
unknown? The unknown is the answer you want find. Check out this example:

Rod's mom has worked up a powerful thirst solving a ton of math problems and asked Rod
to run to the corner store and get her one of those super-duper gigantic nuclear soft drinks.
If a regular-sized soft drink costs $0.50 and the super-duper gigantic nuclear size costs three
times the cost of the regular size, how much will Rod have to spend?

You can express this problem in terms of x, with x being the cost of the super-duper sized
drink: x equals 3 (the price difference) x 50 cents. Written a bit more formally, the equation
looks like this: x = 3(0.50) or 3(0.50) = x.

What if you don't know how much the regular sized soft drink costs? You can express this
missing piece of information in an equation as well: x (how much it will cost to buy a super-
duper size) equals 3 (the cost increase) times p (the price of one regular sized drink). Once
again, written a bit more formally, the equation looks like this: x = 2>p or x - 3 • p.

You can remove the multiplication symbol in algebraic expressions when using a combina-
tion of letters and numbers. Therefore, the equation x = 3 x p can also be written x - 3p. The
multiplication symbol is implied. It's also common to use parentheses or the dot multiplica-
tion symbol, •, to indicate multiplication. Most people avoid using the x because it looks so
close to the letter x.

When alt things are equal: Keeping
an alqebra equation balanced

Algebra problems are equations, which means that the quantities on both sides of the equal
sign are equal — they're the same. For instance, 2 = 2, 1 + 1 = 2, and 3 - 1 = 2. In all these cases,
the quantities are the same on both sides of the equal sign. To solve an algebra equation,
you find out what the variable equals by getting it by itself on one side of the equal sign. So
if x = 2, then x is 2 because the equal sign says so.

Part III: Making the Most of Math: Arithmetic Skills
&£*

You can perform any calculation on either side of an equation as long as you do it to both
sides of the equation. That keeps the equation equal.

You can also combine like terms — terms that have matching variables — when operating
on algebraic expressions: 3x + 3x = (3 + 3)x = 6x, However, 3x + 3y doesn't equal 6xy, nor
does x 2 + x 3 = x 5 (see the section "Explaining exponents in algebra," later in this chapter, to
find out more about algebra involving exponents).

Solving one-step equations involving addition and subtraction

If x + 1 = 2, then x must be 1, because only 1 added to 1 is 2. So far, so simple, so good. But
what if the equation is a little more complicated?

x + 47,432 = 50,000

To solve the problem, you need to isolate x on one side of the equal sign. To get that job
done, move any other numbers on the x side of the equal sign to the other side of the
equal sign.

By looking at the x side of the equation, you can see that it's an addition problem. To move
the number on the x side to the opposite side, you have to perform the inverse operation.
The inverse operation of addition is subtraction. (For a full rundown on inverse operations,
check out the earlier section "Operations: What You Do to Numbers.") So to move 47,432
from the x side to the non-x side of the equation, simply subtract that number from both
sides:

x + 47,432 - 47,432 = 50,000 - 47,432

Performing these operations removes the 47,432 from the x side of the equation (47,432 -
47,432 = 0, so that side of the equation is x + or simply x~) and gives you 2,568 on the non-x
side of the equation (50,000 - 47,432 = 2,568). You're left with the final answer: x = 2,568

To double-check that this answer is correct, you can plug your answer into the original
problem:

x + 47,432 = 50,000
2,568 + 47,432 = 50,000

0tm

If you plug the answer in and it doesn't work, you've made an error in your calculations.
Start again; remember that you're trying to isolate x on one side of the equation.

Multiplying and dividing

In multiplication and division, if the two terms being operated on (on either side of the
equal sign) are both positive numbers or both negative numbers, the answer will be a posi-
tive number. If one number is negative and the other is positive, the answer will be negative.

To solve the problem -6x = 36 (don't forget, 6x is the same thing as 6 x x), you need to iso-
late x. So perform an inverse operation; the inverse operation of multiplication is division.
Division in algebra is usually represented with a fraction bar:

-6x
-6

36
-6
-6

The answer is a negative number because the two terms, 36 and -6, have different signs.

Chapter 7: Mathematics Knowledge and Operations £ /

Solving multistep equations

Not all algebra problems have one-step solutions. (That would be too easy, and you
wouldn't sweat nearly as much.) Solving algebra problems on the ASVAB often requires you
to perform several steps.

An example of a multistep equation is one in which x shows up on both sides of the equal
sign. Then you have to get rid of x on one side of the equation by moving x terms from one
side to the other. You do this by performing the inverse operation.

Suppose you want to solve this equation: 3x + 3 = 9 + x. To remove the x from one side of
the equation, perform the inverse operation. The right side of the equation adds an x, so
subtract x from both sides of the equation:

3x + 3-x = 9+x-x
3x+3-lx = 9 +
2x + 3 = 9

&£*

To get the x term, 2x, by itself, subtract 3 from each side of the equation:

2x +3-3 = 9-3
2x=6

Divide both sides of the equation by 2 to isolate x:

2x_6
2 2
x = 3

When you have a variable by itself, such as x, it's always equal to 1 times that variable (or
one of that variable), like lx, even if the 1 isn't written out. In fact, any number is equal to 1
times itself, so you could also say 2 = 2x1.

.tfABE*

Explaining exponents in alqebva

Exponents are an easy way to show that a number is to be multiplied by itself a certain
number of times. For example, 5 2 is the same as 5 x 5, and y 3 is the same as yxyxy. The
number or variable that's multiplied by itself is called the base, and the number or variable
showing how many times it is to be multiplied by itself is called the exponent or power.

Here are important rules when working with exponents in algebra:

j-" Any base raised to the power of one equals itself: x 1 = x

f Any base raised to the zero power (except 0) equals 1: x° = 1

v* To multiply terms with the same base, add the exponents: x 2 (x 3 ) = x 2+3 = x 5

So if x = 2, then 2 2 = 4 and 2 3 = 8, and 4(8) = 32. That's the same as 2 5 = 32, which
equals 2x2x2x2x2.

v* To divide terms with the same base, subtract the exponents: x 5 * x 2 = x 5-2 = x 3

J-" If a base has a negative exponent, it's equal to its reciprocal (inverse) with a positive

-i 1
exponent: x = -v

e* When a product has an exponent, each factor is raised to that power: (xy) 3 = x 3 y 3

£2 Part " l: Making tne Most of Math: Arithmetic Skills

A step back: Factoring algebra expressions
to find original numbers

Now and then, the ASVAB gives you a product (the answer to a multiplication problem),
and you have to find the original numbers that were multiplied together to produce that
product. This process is called factoring. You use factors when you combine like terms and
add fractions.

Putting out the greatest common factor

Your task may be to pull out the greatest common factor from two or more terms. Take, for
example, this product: Axy + 2x 2 . To factor this product, follow these steps:

1. Find the greatest common factor — the highest number that evenly divides all the
terms in the expression.

Look at both the constants (numbers) and variables. In this case, the highest number
that divides into 4 and 2 is 2. And the highest variable that divides into both xy and x 2
is x. Take what you know to this point, and you can see that the greatest common
factor is 2x.

2. Divide both terms in the expression by the greatest common factor.

When you divide Axy and 2x 2 by 2x, the resulting terms are 2y + x.

3. Multiply the entire expression (from Step 2) by the greatest common factor (from
Step 1) to set the expression equal to its original value.

Doing so produces 2x(2y + x).

Factoring a three-term equation (x 2 + bx + c)

Time to try something a little more complicated: factoring a trinomial (an expression with
three terms). Suppose you start with x 2 -\2x + 20. Follow these steps:

1. Find the factors of the first term of the trinomial.

The factors of the first term, x 2 , are x and x (x ■ x = x 2 ). Put those factors (x and x) on
the left side of two sets of parentheses: (x )(x ).

2. Determine whether the parentheses will contain positive or negative signs.

You can see that the last term in the trinomial (+20) has a plus sign. That means the
signs in the parentheses must be either both plus signs or both minus signs. (Why?
Because two positive numbers multiplied equals a positive number, and two negative
numbers multiplied equals a positive number, but a negative number times positive
number equals a negative number.)

Because the second term (-12x) is a negative number, both of the factors must be neg-
ative: (x - )(x - ).

3. Find the two numbers that go into the right sides of the parentheses.

This part can be tricky. The factors of the third term, when added or subtracted
together, must equal the second term of the trinomial.

In this example, the third term is 20 and the second term is -12x. You need to find the
factors of 20 (the third term) that add to give you -12. The two factors you want are -2
and -10, because -2 x -10 = 20 (the third term) and -2 + -10 = -12 (the second term).
Plug in these numbers: (x - 2)(x - 10)

Thus, the factors of x 2 - 12x + 20 are (x - 2) and (x - 10).

Chapter 7: Mathematics Knowledge and Operations Oj

cjABE*

«>*5!?

Making alphabet soup: Solving
quadratic equations

So what's a quadratic equation? Sounds a little scary, huh? The Mathematics Knowledge
subtest may ask you to solve one of these equations, but have no fear. You've come to the
right place.

A quadratic equation is an equation that includes the square of a variable. The exponent in
these equations is never higher than 2 (because it would then no longer be the square of an
unknown but a cube or something else). Here are some examples of quadratic equations:

u* x 2 - Ax = -A
(-" 2x 2 = x + 6
V x 2 = 36

Simple quadratic equations (those that consist of just one squared term and a number) can
be solved by using the square root rule:

If x 2 = k, then x = ±*Jk, as long as k isn't a negative number.

Remember to include the ± sign, which indicates the answer is a positive or negative
number. Take the following simple quadratic equation: ly 2 = 28.

First get rid of the pesky 7 by dividing both sides by 7: y 2 = 4. Using the square root rule,
take the square root of both sides of the equation. You know that ^jy 2 = y and >/4 = ±2, so

y = ±2.

When you're solving a complex quadratic equation, you put all the terms on one side of the
equal sign, making the equation equal zero. In other words, get the quadratic equation into
this form: ax 2 + bx + c = 0, where a, b, and c are numbers and x is unknown. Take a look at
the following equation: x 2 - 2x = 15. You can convert this equation to standard form by sub-
tracting 15 from both sides of the equation: x 2 - 2x - 15 = 0.

The most efficient way to solve most quadratic equations is by factoring the equation and
then setting each separate factor equal to zero. See the section "A step back: Factoring
algebra expressions to find original numbers" earlier in this chapter for info on factoring.

Look at the factored equation:

x 2 -2x-15 =
(x-5)(x + 3) =

For the left side of the equation to equal zero, one of the quantities in parentheses has to
equal zero (because zero times any number equals zero). That means you can split the
equation in two, setting each factor equal to zero:

x-5 =
x = 5

or x + 3 =

x = -3

The solution forx 2 - 2x- 15 is x = 5 or -3.

$A Part III: Making the Most of Math: Arithmetic Skills

Alt math isn't created equal: Solving inequalities

Some algebra problems state that two quantities aren't equal to each other; thus, they're
inequalities. In an inequality, the first number is either greater than or less than the second.

Just like with equations, the solution to an inequality is a value that makes the inequality
true. For the most part, you solve inequalities the same as you would solve a normal equa-
tion. There are some facts of inequality life you need to keep in mind, however. Short and
sweet, here they are:

v* Negative numbers are less than zero.

j-" Zero is less than positive numbers but greater than negative numbers.

J-" Positive numbers are greater than zero.

A regular algebraic equation includes the equal sign (=), because the very basis of the equa-
tion is that one side of the equation must equal the other. Quite the opposite is true with
inequalities, and they have their own special symbols, used to express the differences:

V ^ means does not equal in the way that 3 does not equal 4, or 3 ^ 4.

J-" > means greater than in the way that 4 is greater than 3, or 4 > 3.

v* < means less than in the way the 3 is less than 4, or 3 < 4.

v* < means less than or equal to in the way that x may be less than or equal to 4, or x < 4.

v* > means greater than or equal to in the way that x may be greater than or equal to 3,
orx> 3.

To solve an inequality, you follow the same rules as you would for solving any other equa-
tion. For example, check out this inequality: 3 + x > 4

To solve it, simply isolate x by subtracting 3 from both sides of the equation:

3+x-3>4-3
x>l

*J*BE*

Therefore, 1 or any number greater than 1 makes this inequality true.

The only special rule for inequalities takes effect when you multiply or divide both sides of
the inequality by a negative number. In that case, the inequality sign is reversed. So if you
multiply both sides of the inequality 3 < 4 by -4, your answer is -12 > -16. And if you divide
both sides of -2x < 14 by -2, your answer is x > -7.

Looking at Math from a different Anqle:
Geometry ReVieu)

Geometry is the branch of mathematics that makes grown adults cry — end of discussion.
What? You want a more specific explanation of geometry than that? Okay, geometry is the
branch of mathematics concerned with measuring things and defining the properties of and
relationships among shapes, lines, points, angles, and other such objects. Hey, don't blame
me; you asked for it.

vtfBE/?

Chapter 7: Mathematics Knowledge and Operations o5

Before you read any further, you should note a few things:

f Arcs of a circle and angles are measured in degrees and (not very often) in minutes or
even seconds; 1 degree equals 60 minutes, and 1 minute equals 60 seconds.

v A circle has 360 degrees (360°). Any arc that isn't a complete circle measures less
than 360°.

j"* A quadrilateral (a shape with four sides, such as a square or rectangle) has angles that
add up to 360°.

Outlining angles

Angles are formed when two lines intersect (cross) at a point. Angles are measured in
degrees. The greater the number of degrees, the wider the angle is:

\^ A straight line is 180°.

*>* A right angle is exactly 90°.

V An acute angle is more than 0° but less than 90°.

(<«* An obtuse angle is more than 90° but less than 180°.

v Complementary angles are two angles that equal 90° when added together.

J"* Supplementary angles are two angles that equal 180° when added together.

Take a look at the different types of angles in Figure 7-1.

Straight Line

90°

Right Angle

Acute Angle

Figure 7-1:

Types of
angles. Obtuse Angle

Complementary
Angles

Supplementary
Angles

Pointing out triangle types

A triangle consists of three straight sides whose three angles always add up to 180°.
Triangles can be classified according to the relationship among their angles or the relation-
ship among their sides:

c" Isosceles triangle: An isosceles triangle has two equal sides; the angles opposite the
equal sides are also equal.

V Equilateral triangle: An equilateral triangle has three equal sides; each of the angles
measures 60°.

§f(J Part III: Making the Most of Math: Arithmetic Skills

SjABEft

J*" Right triangle: A right triangle has one right angle (90°); therefore, the remaining two
angles are complementary (add up to 90°). The side opposite the right angle is called
the hypotenuse, which is the longest side of a right triangle. The other two sides are
called legs.

The Pythagorean theorem states that if you know the lengths of two sides of a right tri-
angle, you can determine the length of the third side using the formula a 2 + b 2 = c 2 ,
where a and b represent the legs and c is the hypotenuse.

Check out Figure 7-2 to see what these triangles look like.

Figure 7-2:

Isosceles,

equilateral,

and right

triangles.

Isosceles Triangle

If sides a and care equal,
then angles 1 and 2 are equal.

Equilateral Triangle

Sides a, b, care equal.
Angles 1, 2,3 are equal.

hypotenuse

Right Triangle
a 2 +b 2 =c 2

«*BEff

You can find the perimeter — the distance around a shape — of a triangle by adding
together the lengths of the three sides. The area — the space within a shape — of a triangle
is one-half the product of the base (the bottom or the length) and the height (the tallest
point of the triangle), or A = -^bh.

Back to square one: Quadrilaterals

Quadrilaterals — shapes with four sides — all contain angles totaling 360°. Many types of
quadrilaterals exist (see Figure 7-3):

v* Squares have four sides of equal length, and all the angles are right angles.

u* Rectangles have all (four) right angles.

v* Parallelograms have opposite sides that are parallel, and their opposite sides and
angles are equal. The angles don't have to be right angles.

k" Rhombuses have four sides of equal length, but the angles don't have to be right angles.

u* Trapezoids have exactly two sides that are parallel.

Figure 7-3:

Types of
quadri-
laterals.

Rectangle

Parallelogram

Rhombus

Trapezoid

WER

To determine the perimeter of a quadrilateral, simply add the lengths of all the sides. You can
write the formula for the perimeter of a rectangle as P = 2(1 + ui) or P =21 + 2w, where / is length
and w is width. And to figure the area of a rectangle, including squares, multiply length times
width: A = Iw.

Chapter 7: Mathematics Knowledge and Operations £ 7

men

Going around in circles

A circle is formed when the points of a closed line are all located an equal distance from its
center. A circle always has 360°. Here are some key circle terms (see Figure 7-4, which
shows the parts of a circle):

Figure 7-4:

The parts of
a circle.

u* Circumference (C): The closed line of a circle ■
circle — is called its circumference.

that is, the distance around the

is* Radius (r): The radius of a circle is the measurement from the center of the circle to
any point on the circumference of the circle.

v* Diameter (d): The diameter of the circle is measured as a line passing through the
center of the circle, from a point on one side of the circle all the way to a point on the
other side of the circle.

The diameter of a circle is always twice as long as the radius of a circle: d = 2r.

..^c^erence^

jcJABE/?

Navigating the circumference

To measure the circumference of a circle, use the number pi (71). Although n is a lengthy
number, it's generally rounded to 3.14 or 4p If you round n so you can solve a problem, the

equal sign isn't used because the answer isn't equal to the actual length. The approximation
symbol («) is used.

The formula for circumference is circumference = n x diameter, or C = nd. Because the
radius of a circle is half its diameter, you can also use the radius to determine the circum-
ference of a circle. Here's the formula: C = 2nr.

Suppose that you know that the pie you just baked has a diameter of 9 inches. You can
determine its circumference by using the circumference formula:

C= nd
C=3.14x9
C= 28.26 inches

j^5£* Mapping out the area

Determining the area of a circle also requires the use of 71. Area
cle's radius, or A = nr 2 .

n x the square of the cir-

$£[ Part III: Making the Most of Math: Arithmetic Skills

To determine the area of a 9-inch-diameter pie, multiply n by the square of 4.5. Why 4.5 and
not 9? Remember, the radius is always half the diameter, and the diameter is 9 inches.

A = nr 2

^-3.14x4.5 2
A « 3.14 x (4.5x4.5)
A» 3.14x20.25
A ~ 63.585 inches

Fitting 'er up: Calculating Volume

Volume is the space a solid (three-dimensional) shape takes up. You can think of volume as
how much a shape would hold if you poured water into it. Volume is measured in cubic
units. The formula for finding volume depends on the object:

v* Boxes: For rectangular objects, you multiply length x width (depth) x height. This is
possible because the length, width, and height of a rectangle are consistent throughout
the whole shape. The formula looks like this: V = Iwh.

For a box that measures 5 feet long, 6 feet deep, and 2 feet tall, you simply multiply
5 x 6 x 2 to arrive at a volume of 60 cubic feet, or 60 ft. 3

v* Cylinders: A cylinder has two circles for its bases. The volume equals n x the radius
squared x height, or V = n^h.

Basically, you're multiplying the area of the cylinder's circular base (A = nr 2 ) times the
height (h) of the cylinder. For a cylinder that has a radius of 2 inches and a height of 10
inches, here's the deal: Multiply the value of n (approximately 3.14) times 4 (which is
the radius squared) times 10, or 3.14 x 4 x 10 = 125.6 cubic inches.

Test-Taking Techniques far \lour
Mathematical Journey

As with most of the other subtests on the ASVAB, guessing on the Mathematics Knowledge
subtest doesn't count against you. So scribble in an answer, any answer, on your answer sheet
because, if you don't, your chances of getting that answer right are zero. But if you take a shot
at it, your chances increase to 25%, or 1 in 4. In the following sections, you find some tips that
can help you improve those odds, even when you don't know how to solve the problem.

If you're not confident in your math skills, you may want to invest some extra study time.
Check out Algebra For Dummies by Mary Jane Sterling, Geometry For Dummies by Mark
Ryan, and SAT II Math For Dummies by Scott Hatch — all published by Wiley.

Knowing what the question is asking

The Mathematics Knowledge subtest presents the questions as straightforward math prob-
lems, not word problems, so knowing what the question is asking you to do is relatively
easy. However, reading each question carefully, paying particular attention to plus (+) and
minus (-) signs (which can really change the answer) is still important. Finally, make sure
you do all the calculations needed to produce the correct answer. Check out this example:

Chapter 7: Mathematics Knowledge and Operations ft Q

Find the value of V81 2 .

(A) 9

(B) 18

(D) 6,561

If you're in a hurry, you may put 9 down as an answer because you remember that the
square root of 81 is 9. Or in a rush, you could multiply 9 (the square root of 81) by 2 instead
of squaring it, as the exponent indicates you should. Or you may just multiply 81 by 81 to
get 6,561 without remembering that you also need to then find the square root, which gives
you the correct answer, Choice (C). So make sure you perform all the operations needed
(and that you perform the correct operations) to find the right answer. Here, noticing that
you're both squaring 81 and taking the square root of 81 2 should make it easy for you to rec-
ognize that the answer is actually just 81, without having to work out the multiplication.

Figuring out what you're solving for

Right out of the gate, read the question carefully. Some questions can seem out of your
league at first glance, but if you look at them again, a light may go on in your brain. Suppose
you get this question:

2 1
Solve for s:s = F x-^.
d z

(A)2l
(B) 2
(C)I

At first glance, you may think, "Oh, no! Solve for an unknown, s. I don't remember how to do
that!" But if you look at the question again, you may see that you're not solving for s at all.

2 1 9

You're simply multiplying a fraction. So you take £■ times -^ and arrive at -^-, but you should

, " d Z 10

reduce that fraction to get ^-- The correct answer is Choice (C).

Solving what you can and guessing the rest

Sometimes a problem requires multiple operations for you to arrive at the correct answer.
If you don't know how to do all of the operations, don't give up. You can still narrow down
your choices by doing what you can.

Suppose this question confronts you:
What's the value of (0.03) 3 ?

(A) 0.0027

(B) 0.06

(D) 0.0009

(}Q Part III: Making the Most of Math: Arithmetic Skills

Say you don't remember how to multiply decimals. All isn't lost! If you remember how to
use exponents, you know that you have to multiply 0.03 x 0.03 x 0.03. So if you simplify the
problem and just multiply 3x3x3, without worrying about those pesky zeros, your answer
will have a 27 in it. With this pearl of wisdom in mind, you can see that Choice (B), which
adds 0.03 to 0.03, is wrong. It also means that Choice (D), which multiplies 0.03 and 0.03, is
wrong. Now you have two possible answers, and you've improved your chances of guessing
the right one to 50 percent! Multiply 3 x 3 x 3 to get 27, and don't forget to put the decimal
points back in. You have six places to make up, so move the decimal from 27 six places to
the left to get 0.000027. The correct answer is Choice (C).

Using the process of elimination

Another method for when you run into questions and draw a total blank is to plug the possi-
ble answers into the equation and see which one works. Say the following problem is staring
you right in the eyes:

Solve for x: x - 5 = 32

(A) x = 5

(B) x = 32

(D) x = 37

If you're totally stumped and can't think of any possible way of approaching this problem,
simply plugging in each of the four answers to see which one is correct is your best bet.

v* Answer (A): 5 - 5 = 32, which you know is wrong
v* Answer (B): 32 - 5 = 32, which is wrong
v* Answer (Q: -32 - 5 = 32, which is wrong
v* Answer (D): 37 - 5 = 32, which is correct

Don't forget that plugging in all the answers is time-consuming, so save this procedure until
you've answered all the problems you can answer. If you're taking the computer version,
you can't skip a question, so remember to budget your time wisely. If you don't have much
time, just make a guess and move on. You may be able to solve the next question easily.

Chapter 8

Reasoning with Arithmetic:
Math Word Problems

In This Chapter

Solving life's little (math) problems
Multiplying your chances for a better score

Wow many miles per gallon does your brand-new SUV get? How long does it take to go
over the river and through the woods to Grandmother's house? How much wood
could a woodchuck chuck? These are examples of everyday questions that can be answered
by arithmetic reasoning. (Okay, maybe the woodchuck situation doesn't happen every day.)

The rest of the world calls this type of question math word problems. The ASVAB calls them
Arithmetic Reasoning. No matter what they're called, these problems help you apply mathe-
matical principles to the real world (at least the real world according to the people who
think up word problems). Your job is to read a word problem, determine what the question
asks, and select the correct answer.

Arithmetic Reasoning is an important part of the Armed Forces Qualification Test (AFQT)
score, which is used to determine your general qualification for enlistment in all the service
branches (see Chapter 1 for more information). Also, certain military jobs require that you
score well on this subtest (see Appendix A).

The test administrator will supply you with scratch paper and a trusty number two pencil,
but one thing he or she won't give you (or even let you bring) is a calculator. You can
use your paper and lead to clarify the data, write formulas, and mathematically solve the
problem. You can even use them to draw pretty pictures to help you understand the prob-
lem. Don't get too artistic, though — you have only 36 minutes to answer 30 questions if
you're taking the paper version and 39 minutes to answer 16 questions if you're taking the
CAT-ASVAB.

To do well on the Arithmetic Reasoning subtest, you have to remember that there are two
parts: arithmetic and reasoning. You usually have to use both of these skills for each prob-
lem. The arithmetic part comes in when you have to perform mathematical operations such
as addition, subtraction, multiplication, and division. The reasoning comes in when you
figure out which numbers to use in your calculations. In other words, Arithmetic Reasoning
tests how you apply your ability to perform calculations to real-life problems. If you slept
through high school math, don't worry. This chapter helps you decipher these math prob-
lems, focusing on the reasoning part. For additional info on the arithmetic, flip to Chapter 7.

^2 Part lll: Makin 9 the Most of Math: Arithmetic Skills

Tackling the Real World of Word Problems

Test-takers often waste a lot of time reading and rereading word problems as if the answer
might reveal itself to them by some miracle; however, correctly solving math word prob-
lems requires you to perform a series of organized steps:

1. Read the problem completely.

2. Figure out what the question is asking.

3. Dig out the relevant facts.

4. Set up one or more equations to arrive at a solution and then solve the problem.

5. Review your answer.

I cover these steps in detail throughout this section.

Reading the entire problem

The first step in solving a word problem is reading the entire problem to discover what it's
all about. Try forming a picture about the problem in your mind or — better yet — draw a
sketch of the problem on your scratch paper. Ask yourself whether you've ever seen a prob-
lem like this before. If so, what's similar about it, and what did you do to solve it in the past?

«,^P L E

As plain as the nose on a fly: Figuring
out What the question is asking

The second and most important step in solving a word problem is to determine exactly
what the question is asking. Sometimes the question is asked directly. At other times, iden-
tifying the actual question may be a little more difficult. Suppose you're asked the following
question:

What's the volume of a cardboard box measuring 12 inches long by 14 inches wide by
10 inches tall?

(A) 52 cubic inches

(B) 88 cubic inches

(D) 1,680 cubic inches

The problem directly asks you to determine the volume of a cardboard box. Recall from
your high school algebra and geometry classes that the volume of a rectangular container is
length x width x height, or V = Iwh. So 12 x 14 x 10 = 1,680. The correct answer is Choice (D).

Now take a look at the next example:

How many cubic inches of sand can a cardboard box measuring 12 inches long by 14 inches
wide by 10 inches tall contain?

(A) 52 cubic inches

(B) 88 cubic inches

(D) 1,680 cubic inches

Chapter 8: Reasoning with Arithmetic: Math Word Problems Q A

This is the same problem, but the question you need to answer isn't as directly stated.
Therefore, you have to use clues embedded in the problem to figure out what the actual
question is. Would figuring out the perimeter of the box help you with this question? Nope.
Would figuring out the area of one side of the box help you? Nope — you're not painting the
box; you're filling it. The question wants you to determine the volume of the container.

Clue words can be a big help when trying to figure out which question is being asked. Look
for the following clue words:

u* Addition: Sum, total, in all, perimeter, increased by, combined, added

v* Division: Share, distribute, ratio, quotient, average, per, out of, percent

u* Equals: Is, was, are, were, amounts to

u* Multiplication: Product, total, area, cubic, times, multiplied by, of

u* Subtraction: Difference, how much more, exceed, less than, fewer than, decreased

Digging for the facts

After you figure out which question you're answering in the first place, the next step is to
figure out which data is necessary to solve the problem and which data is extra. Start by
identifying all the information and variables in the problem and listing them on your scratch
paper. Make sure you attach units of measurement contained in the problem (miles, feet,
inches, gallons, quarts, and so on). After you've made a list of the facts, try to eliminate
those facts that aren't relevant to the question. Look at the following example:

To raise money for the school yearbook project, Tom sold 15 candy bars, Becky sold
12 candy bars, Debbie sold 17 candy bars, and Jane sold the most at 50. How many
candy bars were sold by the girls?

The list of facts may look something like this:

Tom =15 bars
Becky =12 bars
Debbie =17 bars
Jane = 50 bars
? = total sold by the girls

Because the question is the total number of candy bars sold by the girls, the number of bars
sold by Tom isn't relevant to the problem and can be scratched off the list. Just add the
remaining bars from your list. The answer is 79.

Setting up the problem and Working
your Way to the answer

You need to decide how the problem can be solved and then use your math skills to arrive
at a solution. For instance, a question may ask the following:

Joan just turned 37. For 12 years, she's dreamed of traveling to Key West to become a beach
bum. To finance this dream, she needs to save a total of $15,000. How much does Joan need
to save each year if she wants to become a beach bum by her 40th birthday?

Write down, in mathematical terms, what the question is asking you to determine. Because
the question is asking how much money Joan needs to save per year to reach $15,000, you

(fA Part III: Making the Most of Math: Arithmetic Skills

can say y (years Joan has to save) x m (money she needs to save each year) = $15,000. Or to
put it more mathematically,

ym = $15,000

You don't know the value of m (yet) — that's the unknown you're asked to find. But you can
find out the value of y — the number of years Joan has to save. If she's 37 and wants to be a
beach bum by the time she's 40, she has 3 years to save. So now the formula looks like this:

3m = 15,000

To isolate the unknown on one side of the equation, you simply divide each side by 3, so
3m * 3 = 15,000 * 3. (If you don't remember how to isolate unknowns, flip to Chapter 7.)
Therefore, your answer is

m = 5,000

Joan needs to save $5,000 each year for 3 years to reach her goal of $15,000 by the time
she's 40. You may be tempted to include the 12 years Joan has been dreaming of this trip
in your formula. This number was put into the problem as a distraction. It has no bearing on
solving the problem.

RerieWinq yow answer

Before marking your answer sheet or punching in that choice on the computer, review your
answer to make sure it makes sense. Review by asking yourself the following questions:

v* Does your solution seem probable? Use your common sense. If you determine that a
12- x 16-foot roof is covered in only 12 shingles, you've probably made a mistake in
your calculations.

J-" Does it answer the question asked? Reread the problem. For example, if a question
asks you to calculate the number of trees remaining after 10 percent of the total was
cut down, the correct answer wouldn't be 10 percent of the trees but rather the 90 per-
cent still standing.

v* Are you sure? Double-check your answer. Those tricky test-makers often supply false
answers, which are very, very close to the correct answer.

J*" Is your answer expressed using the same units of measurement as used in the prob-
lem? A question may ask how many cubic feet of concrete is required to cover a drive-
way. Your answer in cubic yards would have to be converted to cubic feet so you can
select the correct answer choice.

.flXNG.

Although you may have been taught in school to round 5 or above up and below 5 down,
rounding real-world problems requires a different mindset. For example, if someone needs
2.2 cans of paint for a particular job, she really needs 3 cans of paint to make sure she has
enough, even though you'd generally round down. And if someone gets a 15-minute break
for every 4 hours of work but works only 7 hours, he'd get only one break, even though 7
divided by 4 equals 1.75, which is generally rounded up to 2.

You may find that the solution you arrived at doesn't fit the facts presented in the problem.
If this is the case, back up and go through the steps again until you arrive at an answer that
seems probable.

Chapter 8: Reasoning with Arithmetic: Math Word Problems Qjy

The Guessing Game: Putting Reason
in l/aur Guessing Strategy

Guessing wrong on any of the ASVAB subtests doesn't count against you. If you don't guess,
your chances of getting that answer right are zero, but if you take a shot at it, your chances
increase to 25%, or 1 in 4. Eliminate two wrong answers, and you have a 50-50 shot.

If you're taking the paper version of the ASVAB, you can always skip the tough questions
and come back to them after you've finished the easier ones. If you're taking the computer-
ized version of the ASVAB, the software won't let you skip questions, so you need to make
your guess right then and there.

If you're taking the paper version of the test and elect to skip questions until later, make
sure you mark the next answer in the correct space on the answer sheet. Otherwise, you
may wind up wearing out the eraser on your pencil when you discover your error at the end
of the test. Or even worse, you may not notice the error and wind up getting several
answers wrong because you mismarked your answer sheet.

Using the process of elimination

Guessing doesn't always mean "pick an answer, any answer." You can increase your chances
of picking the right answer by eliminating answers that can't be right. To eliminate some
obvious wrong answers, you can do the following:

v* Make sure the answer is realistic in relation to the question asked. For example, if a
question asks you how much water would be required to fill a child's wading pool,
17,000 gallons isn't a realistic answer. You can save time by eliminating this potential
answer choice immediately.

v* Pay attention to units of measurement. If a question asks how many feet of rope you'll
need, answer choices listed in inches or cubic feet are probably incorrect.

v* Consider easier answer choices first. Remember, you're not allowed to use a calcula-
tor on the ASVAB, so math answers that you'd arrive at by using complicated formulas
are probably not correct.

Solving What you can and guessing the rest

Sometimes you may know how to solve part of a problem but not all of it. If you don't know
how to do all the calculations — or don't have time for them — don't give up. You can still
narrow down your choices by doing what you can. Here's how partially solving problems
can help:

u* When adding mixed numbers (a whole number and a fraction), add the whole-number
parts first; then immediately eliminate answer choices that are too low. Or when
adding lengths, add full feet first and cross off choices that are too small, even before
considering the inches.

v* Multiply just the last digits and cross off all answers that don't end in the right num-
bers (assuming the answers aren't rounded).

(ffi Part III: Making the Most of Math: Arithmetic Skills

Making use of the ansuter choices

If you're stuck on a particular problem, sometimes plugging possible answers into an equa-
tion can help you find the right answer. Here's how using the answer choices can improve
your guessing:

v* Plug in each remaining answer choice until you get the right answer. Plugging in all
the answer choices is time-consuming, so make sure you eliminate obviously wrong
choices first.

v* Estimate and plug in numbers that involve easy mental calculations. For instance, if
Choice (A) is 9 and Choice (B) is 12, plug in 10 and solve the equation in your head.
Think about whether the right answer has to be higher or lower than 10, and choose
from there.

v* Using a little logic, do calculations with an obviously wrong answer choice.

Sometimes a wrong answer choice — especially one that differs drastically from the
other answers — represents an intermediate step in the calculations, so you can use it
to solve the problem. For instance, take this example:

A security guard walks the equivalent of six city blocks when he makes a circuit around the
building. If he walks at a pace of eight city blocks every 30 minutes, how long will it take him
to complete a circuit around the building, assuming he doesn't run into any thieves?

(A) 20.00 minutes

(B) 3.75 minutes

(D) 24.00 minutes

Choice (B) is obviously way too low to be the right answer, but it would be a logical guess
for the security guard's rate for a single lap. Multiply 3.75 minutes/block by 6 blocks, and
you probably have a good candidate for the right answer — 22.50 minutes, Choice (C).

Chapter 9

Brother, Can You Spare an Equation?
Arithmetic Practice Questions

In This Chapter

Putting your mathematical reasoning to the test
Practicing your arithmetic skills

m t's time to put those calculators, pocket computers, and abacuses away — the actual
«C ASVAB doesn't allow you to use anything except paper, pencil, and a winning personality
to solve the math problems. You should use the old-fashioned way on these practice ques-
tions, too. Tell you what: Instead of a number two pencil, you can use a number three or
four instead. Heck, you can even use a pen. See? I'm easy. No pressure here!

You may be tired of hearing this by now (if you've taken any of the tests in this book), but
the math subtests of the ASVAB are very important because they're used in calculating
your AFQT score, which makes or breaks you as far as your eligibility to join the military.
Additionally, every technical-oriented job in the military requires good to excellent math
scores. Chapter 1 explains the AFQT in more detail.

On the paper version of the ASVAB (and on the full-length practice tests later in this book),
you see 30 Arithmetic Reasoning questions and 25 Mathematics Knowledge questions. On
the CAT-ASVAB, you get 16 questions on each math subtest. In this chapter, you only have
to sweat through 25 total questions.

Arithmetic Reasoning (Math Word Problems )
Practice Questions

Arithmetic Reasoning questions are math problems expressed in a story format. Your goal
is to determine what the question is asking by picking out the relevant factors needed to
solve the problem, set up mathematical equations as needed, and arrive at the correct solu-
tion. Sounds easy, right? Check out Chapter 8 for more help with Arithmetic Reasoning.

1. If apples are on sale at 15 for $3, what's the cost of each apple?

(A) 50 cents

(B) 25 cents

(D) 30 cents

Divide $3 by 15. The answer is $0.20, so the correct answer is Choice (C).

(f$ Part III: Making the Most of Math: Arithmetic Skills

2. A noncommissioned officer challenged her platoon of 11 enlisted women to beat her record
of performing a 26-mile training run in 4 hours. If all the enlisted women match her record,
how many miles will they have run?

(A) 71.5 miles

(B) 6.5 miles

(D) 312 miles

Multiply 26 x 11. The other information in the question is irrelevant — it's there to throw
you off. The correct answer is Choice (C). You can immediately eliminate Choice (B)
because it isn't a reasonable answer. Identifying unreasonable answers (through the pro-
cess of elimination) can help you choose the correct answer choice faster.

3. Margaret gets her hair cut and colored at an expensive salon in town. She's expected to
leave a 15% tip for services. If a haircut is $45 and a color treatment is $150, how much of a
tip should Margaret leave?

(A) $22.50

(B) $29.25

(D) $224.25

Add 45 and 150 to get the cost of the services ($45 + $150 = $195); then multiply the answer
by 0.15 (15%) to find the tip. The question asks for the amount of the tip, so the correct
answer is Choice (B), $29.25. You can immediately eliminate Choice (D), because the
amount is far too high to make sense.

4. A bag of sand holds 1 cubic foot of sand. How many bags of sand are needed to fill a square
sandbox measuring 5 feet long and 1 foot high?

(A) 25 bags

(B) 5 bags

(D) 15 bags

To find the volume of the sandbox, you take length times width times height (V = Iwti). Don't
forget that the measurements are for a square sandbox, so you can assume that if the box is
5 feet long, then it's also 5 feet wide. So 5 x 5 x 1 is 25 cubic feet. Each bag holds 1 cubic foot
of sand, and 25 + 1 = 25. Choice (A) is the correct answer. If you were thinking answer
Choice (B) sounded good, remember that the answer should make sense. Five cubic feet of
sand would not fill a very large sandbox, would it?

5. The day Samantha arrived at boot camp, the temperature reached a high of 90 degrees in
the shade and a low of -20 at night in the barracks. What was the average temperature for
the day?

(A) 35 degrees

(B) 45 degrees

(D) 62 degrees

Add the two temperatures: 90 + (-20) = 70. Divide 70 by 2 to reach the average temperature, 35.
Choice (A) is the correct answer.

Chapter 9: Brother, Can You Spare an Equation? Arithmetic Practice Questions Q Q

6. Farmer Beth has received an offer to sell her 320-acre farm for $3,000 per acre. She agrees to
give the buyer $96,000 worth of land. What fraction of Farmer Beth's land is the buyer getting?

(A)

1
4

(B)

(C)

1
5

(D)

2
3

The buyer's price, $96,000, divided by $3,000 (price per acre) equals 32 acres. Thirty-two

acres divided by 320 acres (total of the farm) equals 10%, or y^, of the land. The correct
answer is Choice (B).

7. A large wall map is drawn so that 1 inch equals 3 miles. On the map, the distance from

Kansas City to Denver is 192-4 inches. How far is the round trip from Kansas City to Denver
in miles?

(A) 192^ miles

(B) 577^ miles

(D) 1,155 miles

Multiply 192.5 x 3 to get the distance in miles, and then double the answer to account for
both legs of the trip. Choice (D) is the correct answer. Note: A quick approach here involves
rounding. The distance is about 200 inches, or 400 inches round trip. Multiply that by 3, and
you get 1,200 miles. The only choice that comes close is (D).

8. Margaret and Julie can sell their tattoo parlor for $150,000. They plan to divide the proceeds
according to the ratio of the money they each invested in the business. Margaret put in the
most money at a 3:2 ratio to Julie's contribution. How much money should Julie get from
the sale?

(A) $50,000

(B) $30,000

(D) $90,000

According to the ratio, Margaret should get -^ of the money and Julie should get ^ of the

money. You calculate the fractions by adding both sides of the ratio together (3 + 2 = 5) to
determine the denominator — Margaret gets 3 parts of the total, and Julie gets 2 parts, so
there are 5 total parts. Each side of the ratio then becomes a numerator. Multiply the total
amount of money by the fraction representing Julie's share: Multiply $150,000 by 2, and
then divide the answer by 5 to determine Julie's share of the money. The correct answer is
Choice (C).

/ 00 Part lll: Makin 9 the Most of Math: Arithmetic Skills

9. What is the fifth number in the series 4, 8, 16, 32?

(A) 48

(B) 64

The pattern is to double each number: 4 + 4 = 8; 8 + 8 = 16; 16 + 16 = 32; so 32 + 32 = 64. The
correct answer is Choice (B).

10. In the military, i of an enlisted person's time is spent sleeping and eating, -^ is spent

1 9

standing at attention, ± is spent staying fit, and £ is spent working. The rest of the time is
b ' 5

spent at the enlisted person's own discretion. How many hours per day does this discre-
tionary time amount to?

(A) 6.0 hours

(B) 1.6 hours

(D) 3.2 hours

Calculate this answer by first assigning a common denominator of 60 to all the fractions and

adjusting the numerators accordingly: ±£, -£r, ^, and £±. Add the fractions to find out how

60 60 60 60

much time is allotted to all of these tasks. The total time is ^, which leaves ^ or ^ of the

bU bU 1U

day to the enlisted person's discretion. One-tenth of 24 hours is 2.4 hours. Therefore,

Choice (C) is the correct answer.

11. A designer sells a square yard of carpet for $15.00. The same carpet can be purchased at
the carpet outlet store for $12.50. As a percentage, how much more expensive is the design-
er's carpet?

(A) The designer's carpet costs about 17% more than the outlet-store carpet.

(B) The designer's carpet costs about 20% more than the outlet-store carpet.

(D) The designer's carpet costs about 12% more than the outlet-store carpet.

You want the cost of the designer's carpet in terms of the outlet-store carpet, so divide the
difference in costs by the lower price: $15.00 - $12.50 = $2.50, and $2.50 * $12.50 = 0.20 = 20%.
The correct answer is Choice (B) — the designer's carpet is 20% more expensive.

12. Terry got a haircut for $32.50, a hair color for $112.20, and a manicure for $17.25. How much
total money did she spend at the salon?

(A) $167.45

(B) $144.70

(D) $156.95

Simply add the amounts together: $32.50 + $112.20 + $17.25 = $161.95. Choice (C) is the cor-
rect answer.

Chapter 9: Brother, Can You Spare an Equation? Arithmetic Practice Questions / Q /

13. Mailing the first ounce of a letter costs $0.39, and it costs $0.24 to mail each additional
ounce. How much does it cost to mail a 5-ounce letter?

(A) $1.85

(B) $1.16

(D) $1.35

The first ounce costs $0.39. The next 4 ounces cost $0.24 each. Multiply $0.24 x 4 and then
add $0.39 to determine how much mailing a 5-ounce letter costs: $0.24 x 4 = $0.96, and $0.96 +
$0.39 = $1.35, the cost of mailing a 5-ounce letter. Choice (D) is the correct answer.

Math Knowledge Practice Questions

The remaining practice questions are straightforward math. You won't have to wonder how
Terry got so much money to spend at the salon in the first place (like in the previous sec-
tion). Remember, these questions are designed for high school level and below. You won't
be solving equations to calculate the orbit of Mars around the sun here.

14. Which of the following fractions is the largest?

2
3

(A)
(B)
(C)
(D)

To arrive at the answer, find a common denominator that all the denominators divide into
evenly. In this case, the common denominator is 48. Next, convert all fractions to 48ths. In

O 1 c oo

the case of Choice (A), multiply ^ x |§ to reach ^. Perform the same type of calculation for

all the other fractions, figuring out what number times the denominator gives you 48, and
then multiplying each numerator by that number; then compare numerators. The largest

on oo oc

numerator is the largest fraction. The other fractions are equal to ^, ^, and ^. Choice (D)
. ., . 4o 4o 4o

is the correct answer.

15. What's the product of ^36 and >/49?

(A) 1,764

(B) 42

The square root of 36 is 6, and the square root of 49 is 7. The product of those two numbers
(6 x 7) is 42. The correct answer is Choice (B).

1 02 Part lll: Makin 9 the Most of Math: Arithmetic Skills

16. Solve for x: 2x - 3 = x + 7.

(A) 10

(B) 6

(D) -10

Isolate the x's on the left side of the equation by subtracting x from both sides: 2x - 3 - x =
x + 7 - x, or x - 3 = 7. Continue to perform operations to isolate x: Add 3 to both sides of the
equation to get rid of the -3 on the left: x - 3 + 3 = 7 + 3, or x = 10. The correct answer is
Choice (A).

17. A circle has a radius of 15 feet. What's most nearly its circumference?

(A) 30 feet

(B) 225 feet

(D) 150 feet

The circumference of a circle is n times the diameter; the diameter equals two times the
radius. Therefore, 3.14 x 30 feet = 94.2 feet. The correct answer is Choice (C).

18. At 3:00 p.m., the angle between the hands of the clock is

(A) 90 degrees

(B) 180 degrees

(D) 360 degrees

At 3:00 p.m., one hand is on the 12, and the other is on the 3. This creates a right angle — a
90-degree angle. The correct answer is Choice (A).

19. 2 3 x2 4 =

(A) 16

(B) 108

(D) 148

2 3 x 2 4 = 2 7 = 2x2x2x2x2x2x2 = 128. Choice (C) is the correct answer.

20. Express 403,000,000,000,000 in scientific notation.

(A) 4.03 x 10 14

(B) 4.03 x lO" 14

(D) 0.43 x 10

The correct way to write the number in scientific notation is 4.03 x 10 14 . When the exponent
is positive, the decimal point moves said number of places to the right. When the exponent

Chapter 9: Brother, Can You Spare an Equation? Arithmetic Practice Questions / Qj

is negative, the decimal point moves said places to the left. The exponent in Choice (A) is a
positive 14, which means you move the decimal point 14 places to the right. Choice (A) is
the correct answer.

21. Simplify Sx 2 - 3x + Axy - 9x 2 -5x- 20xy.

(A) 5x 2 + 9xy

(B) 8x-9x 2

(D) Sx + 9x 2

8X 2 - 3x + Axy - 9x 2 -5x- 20xy = (Sx 2 - 9x t ) + (-3a: - 5x) + (Axy - 20xy) = -x 2 -8x- I6xy. The
correct answer is Choice (C).

22. What's the prime factorization of 90?

(A) 2x3x5

(B) 2 x 3 2 x 5

(D) 2 x 3 x 5 2

When you figure which prime numbers you need to multiply together to get the original
number, you're using prime factorization. Here, 90 = 9xl0 = 3x3x2x5 = 2x3 2 x5. The
correct answer is Choice (B). If you don't know how to solve this problem, you can guess by
finding the value of each answer choice. Choice (A) is 30, (B) is 90, (C) is 36, and (D) is 150.

23 I x 2
£6. 4 X 3

(A)|

0)1

(C)I

CD) I

4 X 3"

2
12

jr. The correct answer is Choice (C).
o

24. A baker has s pounds of sugar to use in baking. After she uses 50 pounds to make donuts,
how much sugar does she have left?

(A) s + 50

(B) 50 -s

(D) s * 50

The variable s stands for the amount of sugar the baker had before she made the donuts.
Taking away 50 pounds, the amount of sugar used, gives you s - 50. Choice (C) is the
correct answer.

/ OU Part " l: Makin 9 the Most of Math: Arithmetic Skills

25. Six pizzas are pepperoni, seven are hamburger, four are cheese, and three are "with every-
thing." What's the probability that a randomly selected pizza is pepperoni?

(A)

1
2

(B)

2
5

(C)

(D)

2
3

There are 20 total pizzas (6 + 7 + 4 + 3). The probability that the one chosen is a pepperoni
pizza is -^r, or ^. The correct answer is Choice (C).

Part IV

The Whole Ball of Facts
Technical Skills

The 5 th Wave

By Rich Tennant

©PL^Ef-^KT

"Sure I vJorK on diesels. "bring her around and vte'll
pui her on the lift.*

In this part . . .

70 get into the military, you have to know how to read
and how to add. But to qualify for certain military
jobs, you also have to understand how the world works.
Several ASVAB subtests test your knowledge of science
and mechanics. Don't worry — I've got you covered.

Part IV helps you review principles of science, auto and
shop information, mechanical comprehension, principles
of electronics, and spatial relationships. If you're not inter-
ested in jobs that require this type of background (for a
list of jobs that do, see Appendix A), you don't need to
score high on these tests. But if you've set your heart on
working on Humvees or F-18 Super Hornets, study this
part to get you started.

Chapter 10

General Science

In This Chapter

Figuring out the scientific method

Grasping measurements

Studying scientific disciplines

Using scientific strategies to improve your score

2M s you study for this subtest, you may feel overwhelmed by facts and figures. General
V \ Science requires a lot of straight-up memorization. You're presented with questions
about facts you probably learned in high school in various science classes, such as health,
Earth science, biology, and chemistry. If you don't know that Earth is the third planet from
the sun, then all the other science knowledge you have won't help you one bit when the
question asks, "What is the third planet from the sun?"

Instead of trying to remember nine million individual facts, spend some time reviewing the
general principles behind the facts. Think about how the facts relate to each other. Looking
at the big picture is an effective learning technique.

You have 11 minutes to answer 25 questions on the paper version of the General Science
subtest, or you have 8 minutes to answer 16 General Science questions on the CAT-ASVAB.
That comes out to about 26 or 30 seconds per question, so there's no time to dilly-dally. For
the most part, you either know the answer or you don't. If you don't know the answer, you
can always guess (check out Chapter 3 for tips on guessing on the ASVAB).

You can relax this time around. The General Science subtest has no bearing on your Armed
Forces Qualification Test (AFQT) score. On the other hand, your score on this subtest is
used to calculate some of the military composite scores that are used for job qualification
purposes (see Appendix A for more information).

Take some time to review the facts in this chapter as a mini science lesson. If the job you
want requires a good score on this subtest, dedicate yourself to the information in this
chapter to boost your General Science score. You may also want to seek additional study
time in these references to boost your science knowledge: Chemistry For Dummies by
John T. Moore, Biology For Dummies by Donna Rae Siegfried, Astronomy For Dummies by
Stephen P. Maran, Weather For Dummies by John D. Cox, and Physics I For Dummies and
Physics II For Dummies by Steven Holzner, Ph.D. (all from Wiley Publishing).

There's a Scientific Method to the Madness

Scientists are pretty skeptical. They don't necessarily believe anything said by anyone else
unless it's been shown to be true (time after time after time) using a process called the sci-
entific method. Scientists know that personal and cultural biases may influence perceptions
and interpretations of data, so they've derived a standard set of procedures and criteria to

108

Part IV: The Whole Ball of Facts: Technical Skills

minimize those influences when developing a theory. Because the scientific method is prev-
alent in all fields of science, you can expect to see a few questions about the process on the
General Science subtest.

Here are the usual steps to solving a problem using the scientific method:

1. Observe some aspect of the universe.

2. Make an educated guess (hypothesis) about why this is happening.

3. Make predictions based on the hypothesis.

4. Experiment and observe to test the predictions.

If the results don't match the predictions, modify the hypothesis.

5. Keep repeating Steps 3 and 4 until there are no discrepancies in experimentation
and observation in relation to the hypothesis.

When developing and testing a hypothesis, scientists are guided by a principle known as
Ockham's razor (sometimes spelled Occam's razor). This rule states, "When given two
equally valid explanations for a phenomenon, one should embrace the less complicated for-
mulation." In other words, all things being equal, the simplest solution tends to be the best
one. At this point, if a hypothesis holds up to repeated testing, it becomes a theory. When a
theory is supported consistently over time, scientists may then consider it as a law, fact, or
principle.

Understanding Forms of Measurement

Because science is based on developing objective facts — evidence and results that are
measurable and experiments that can be reproduced — measurements are an important
part of science. And because this subtest is all about science, you can expect to run into a
few questions about measuring scientifically on the ASVAB.

Doing the metric thing

The metric system (or SI, the International System of Units) is based on a decimal system of
multiples (and fractions) of ten. Scientists almost always use the metric system for precise
measurement. No, they don't use it just to make the ASVAB harder for you; they use this
system so a standard exists among scientists around the world. In fact, the majority of
countries around the globe use the metric system — the United States is in its own world
when it comes to the Imperial (non-metric) system.

Here are some units of measurement you need to know for the General Science subtest of
the ASVAB:

v* The meter (m) is the unit of length.

v* The liter (L) is the unit of volume.

(-" The gram (g) is the unit of mass (similar to weight).

You can attach prefixes to these base units to indicate units that are larger or smaller.
Check out Table 10-1 for metric prefixes and Table 10-2 for some abbreviations of common
metric measurements.

Chapter 10: General Science / QQ

Table 10-1

Metric Prefixes

Prefix

Symbol

What It Means

milli-

One-thousandth (0.001)

centi-

One-hundredth (0.01)

deci-

One-tenth (0.1)

deca-

hecto-

100

kilo-

1,000

mega-

1,000,000

Table 10-2

Common Metric Units and Their

Abbreviations

Length

Liquid Volume

Mass

millimeter (mm)

milliliter

mL)

milligram (mg)

centimeter (cm)

centiliter

(cL)

centigram (eg)

meter (m)

liter (L)

gram(g)

kilometer (km)

kiloliter (kL)

kilogram (kg)

&£$*

Figuring temperature conversions

When you think of temperature, you may think of the Fahrenheit and Celsius scales, which
measure temperatures in degrees. Scientists actually use three different scales to report
temperature:

v* Fahrenheit (°F): This scale is more common in the United States. On the Fahrenheit
scale, water freezes at 32°F and boils at 212°F.

i*" Celsius or Centigrade CQ : This scale is the metric standard worldwide. On the Celsius
scale, the freezing point for water is 0°C, and the boiling point for water is 100°C.

j-" Kelvin (K): Scientists have theorized that the coldest anything can get is -273.15°C.
They believe that at this temperature, molecular motion would stop. That's pretty darn
cold! This temperature, often called absolute zero, is assigned to be on the Kelvin
scale (with the units the same size as degrees on the Celsius scale). On this scale, the
freezing point of water is 273.15 K, and the boiling point is 373.15 K.

The word degrees isn't used when stating temperature in kelvins. Scientists who work
with thermodynamics, such as physicists and astronomers, measure temperature
using kelvins. For instance, the surface temperature of planets is always stated in
kelvins.

An ASVAB question may ask you to convert temperatures from one scale to another, so
here are some formulas to commit to memory (C stands for the temperature in degrees
Celsius, and F is the temperature in degrees Fahrenheit):

u* To convert from Celsius to Fahrenheit, use this formula:

'C + 32

J JO Part IV: The Whole Ball of Facts: Technical Skills

v* To convert from Fahrenheit to Celsius, use the following formula:

C = |(F-32)
J-" To get temperatures in the kelvin scale, add 273.15 degrees to the Celsius temperature:

K=C+ 273.15

To go from kelvins to degrees Celsius, do the opposite: Subtract 273.15 from the kelvin
temperature. Then you can convert the Celsius temperature to Fahrenheit if you like.

Here's a quick temperature conversion system that may be easier to remember (Note: This
process only works with Celsius and Fahrenheit):

1. Add 40 to the temperature you want to convert.

2. Multiply this sum by ^ if converting from Fahrenheit to Celsius or ^ if converting
from Celsius to Fahrenheit.

3. Subtract the 40 you added at the beginning to yield the result.

9 5
An easy way to remember whether to use -=- or ^ in the conversion is to associate the /in

5 9

Fahrenheit with Fraction (^ is a proper fraction); similarly, ■= can be Converted to a mixed

number (1-jh — c is for Convert and Celsius.

Another Day, Another Science: Scientific
Disciplines \lou Should Know

Science is divided into areas of study called disciplines, and most of these disciplines have
subdisciplines. When you take the ASVAB, the General Science subtest may ask you some
definitions of these disciplines. I couldn't possibly list all the scientific disciplines, but
here's a handy list for you to start looking over.

First, here are some popular Earth and space sciences (see the later sections "Where Few
Have Gone Before: Astronomy" and "Down to Earth: Rocking Out with Geology and
Meteorology" for more info on these disciplines):

v* Astronomy: Astronomers (not to be confused with astrologists) study outer space.
They get their jollies examining the existence, locations, orbits, energy, and composi-
tions of planets and other celestial matter.

J-" Geology: Is it a real diamond or just a piece of glass? A geologist can tell you. These
scientists study the dynamics and physical history of the Earth, the rocks of which it's
composed, and the physical, chemical, and biological changes that the Earth has
undergone or is undergoing.

j*" Meteorology: You know that person who gets on the TV each day and tells you

whether your planned outing to the beach is going to be ruined by rain? Meteorologists
study the weather and attempt to predict it.

v* Paleontology: Paleontologists study prehistoric life, including dinosaurs. How cool is
that? The science involves the examination of fossils, including those of plants, ani-
mals, and other organisms.

Biologists love everything to do with living organisms and life sciences. There are more sub-
disciplines of biology than you can shake a stick at. And yes, some biologists study sticks.

Chapter 10: General Science / / /

Other biologists specialize in fish, trees, snakes, insects . . . you get the picture. Here are
some subdisciplines of biology (for further info, check out the next section):

v* Agriculture: An agriculturalist studies farming. This discipline includes studying
methods of cultivating soil, producing crops, and managing livestock.

v* Botany: A botanist studies plant life. This includes everything from flowers to the moss
that grows on the north side of the tree.

j-" Ecology: Ecologists do more than just warn people that they're destroying the ozone
layer. They study all aspects of the environment and how organisms (such as people)
interact with it.

v* Entomology: Entomologists like bugs. Specifically, they like insects (bugs with six
legs). This position isn't to be confused with an arachnologist, who studies spiders and
other critters with eight legs.

J-" Genetics: Geneticists study heredity, especially the aspect that deals with inherited
characteristics, such as eye color. (For details, see the later section "Swimming in the
gene pool: Genetics.")

j-" Ichthyology: This discipline is the branch of zoology (the study of animals) dealing
with fish.

Here are a couple of social sciences:

j-" Archeology: For an archeologist, the older, the better. Archeologists study past human
life and culture. The job requires recovery and examination of material evidence, such
as graves, tools, pottery, and buildings.

J-" Genealogy: If you want to find out where your great, great, great, great, great grandfa-
ther was born and what he did for a living, ask a genealogist. These specialists study
ancestry and family history.

Another large discipline is chemistry, in which people mix things together to see what
happens. These scientists study the structure, properties, composition, and reactions of
matter. I discuss chemistry later in "Chemistry: Not Blowing Up the Lab."

Lastly, don't forget physics. Physics involves the study of matter and its movement. This
includes concepts such as energy, force, and motion. In short, physics is concerned with
the study of the universe's behavior and, in general, how things work in nature. Mechanics,
which plays a big role in the ASVAB's Mechanical Comprehension subtest (see Chapter 12),
is a major topic in physics.

If the ASVAB only asked questions like "What does a chemist do?" the test would be a piece
of organic matter (cake). Unfortunately, it's not that easy. The ASVAB writers expect you to
know a little more than just the definitions of various scientific disciplines. The following
sections detail a few of the main branches of science you see on the ASVAB.

Uncovering Biology, from Big to Small

It would be impossible to cover all the areas of biology in this book, and I'm not going to try.
Luckily, the General Science subtest of the ASVAB measures your knowledge of scientific
disciplines at the average high school level. You remember studying about the Animal
Kingdom and the human body and cell structures in high school, right? If not, the following
sections can serve as a short refresher course.

112

Part IV: The Whole Ball of Facts: Technical Skills

*!*!§?

Relating to your World through ecology

Ecology is the study of the environment — more specifically, the relationship between
organisms and the world around them. All plants and animals are part of an ecosystem (a
community including living things and their environment). Like the economy, an ecosystem
includes producers (which make their own food) and consumers (which eat other things). An
ecosystem also has decomposers, such as bacteria, which break down dead plants, animals,
and the waste of all organisms.

Animals can't produce their own food, so they're consumers, which are classified in three
categories:

i*" Carnivores eat only meat. A few examples include lions, tigers, polar bears, snakes,
crocodiles, hawks, and eagles.

u* Herbivores eat only plants. Cows, moose, giraffes, and elk are herbivores.

v* Omnivores eat both plants and other animals. People are omnivores, and so are pigs,
mice, raccoons, chickens, crows, and foxes.

Conditions in the world either encourage or prevent the establishment of individual ecosys-
tems. For plants (producers) to grow, adequate sunlight, good soil, moderate temperatures,
and water must be part of the environment. If plants aren't around, plant-eating consumers
can't be sustained, which means predators (who eat other animals) can't be sustained,
either. For consumers, mates are as essential as a food supply. Diseases and enemies can
prevent an animal from establishing itself in an ecosystem.

Human actions, such as wasting natural resources and polluting the air, water, or soil, can
disrupt an entire ecosystem.

cJftBEtf

Categorizing Mother Nature

A long time ago, scientists looked at the world, noticed the hundreds of thousands of plants
and animals around them, and decided that all these organisms (living things) needed to be
labeled and grouped. To effectively study and discuss plants, animals, and other living crea-
tures, all scientists needed to use the same names. Thus, a system of scientific classification
was developed.

The most common classification system was created by Swedish botanist Carl Linnaeus,
who published ten editions of his works from 1753-1758. Scientists often refer to this
system as taxonomy. Not only does taxonomy provide official names for every plant and
animal, but it also helps scientists understand how living creatures are related to one
another. Modern day taxonomy has its roots in the Linnaean taxonomic system.

No one is privy to the actual questions asked on the ASVAB (test materials are considered
"controlled items" and are locked up in safes when not in actual use). In this category, ques-
tions can range anywhere from "How many kingdoms are there?" to "What's the genus for
Canis familiarisT

Counting douin the classification system

The scientific classification system notes the relationships and similarities among organ-
isms. It consists of seven main levels:

is* Kingdom: A kingdom is the broadest level, so it contains the most kinds of organisms.
The relationship between organisms in a kingdom is extremely loose, so members
share only a few key characteristics.

Chapter 10: General Science J/j

v* Phylum: Phylum (plural phyla) is the next major taxonomic group. Within the king-
doms, organisms are divided into phyla by general characteristics. For example, in the
Animal Kingdom, animals with backbones (vertebrates) are placed in a separate
phylum from animals without backbones.

J*" Class: Organisms in a phylum are divided into classes. In the Animal Kingdom, for
example, birds, mammals, and fish all go in their own classes. Among plants, all flower-
ing plants comprise the angiosperm class, and all conifers, such as pines and spruces,
comprise the conifer class.

i*" Order: Scientific groupings don't follow hard and fast rules, so when you get to the
order of a living thing, there's disagreement about where it belongs. You may find that
different scientific organizations group creatures in different orders or families.

v* Family: Families further divide organisms of the same class by similar characteristics.
Sometimes, not all scientific organizations agree to the exact family an organism
should be classified in.

v* Genus: Two or more species that share unique body structures or other characteris-
tics are closely related enough to be placed in a single genus. A genus may include only
a single species if no other organism has characteristics similar enough for it to be con-
sidered the same genus.

v* Species: A species is the most specific level, so it contains the fewest types of organisms.
Organisms of the same species have very similar characteristics.

To get a better idea of how the scientific classification system works, consider how a lion is
classified:

&£&>

Kingdom Animalia: This kingdom includes all animals.

Phylum Chordata: All vertebrate animals belong to the phylum Chordata.

Class Mammalia: All mammals belong to this class.

Order Carnivora: All mammals that eat meat belong to the order Carnivora.

Family Felidae: The family Felidae includes all cats.

Genus Panthera: This genus includes all the roaring cats, such as lions, tigers, jaguars,
and leopards.

Species leo: This is just a lion.

Humans belong to the kingdom Animalia, the phylum Chordata, the class Mammalia, the
order Primata, the family Hominidae, the genus Homo, and the species sapiens. You know,
just in case you were wondering.

Visiting the kingdoms

Not every scientist agrees (scientists rarely agree on any subject), but in general, most lab-
coated individuals settle on five as the number of kingdoms. Check out the kinds of organ-
isms that comprise the five kingdoms:

v* Animals: This is one of the two largest kingdoms, and it includes many-celled organ-
isms that, unlike plants, don't have cell walls, chlorophyll, or the capacity to use light
to make energy (photosynthesis). Members of this kingdom can move. The Animal
Kingdom includes more than 1,000,000 species.

v* Plants: Plants are also one of the two largest kingdoms. This kingdom includes organ-
isms that can't move, don't have obvious nervous or sensory systems (the Venus fly-
trap is one exception), and possess cell walls made of cellulose. More than 250,000
species belong to the Plant Kingdom.

Part IV: The Whole Ball of Facts: Technical Skills

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v* Monerans: This kingdom includes bacteria and cyanobacteria (blue-green algae) —
one-celled organisms that don't have a nucleus (see the later section "Thinking small:
Looking at cells"). More than 10,000 species have been discovered and classified in the
Monera Kingdom.

j-" Protists: Protists include one-celled organisms that do have a nucleus, such as the pro-
tozoan, which you may remember from biology class. This kingdom consists of more
than 250,000 species.

v* Fungi: Examples of common fungi are mushrooms and yeast. Fungi don't photosynthe-
size (use light to create energy) like plants, but they do have cell walls made of a car-
bohydrate called chitin. More than 100,000 species belong to the Fungi Kingdom.

Thirty-three phyla make up the Animal Kingdom, and 12 main phyla comprise the Plant
Kingdom. Monerans consist of two phyla; protists have seven phyla, and fungi are made up
of four phyla. Numerous classes, orders, families, genera, and species fall under each
phylum.

Just name it: Showing off your genius about the species

Each organism is given a scientific name that consists of two words (usually derived from
Latin) — the genus and the species of the organism. The genus is the first word, and the
species is the second. Thus, Homo sapiens refers to humans. Canis familiaris is the family
dog, and Canis lupus is the family wolf. Because wolves and dogs share many similarities,
they share the same genus (no, no, not the same genes, the same genus).

When writing a scientific name, the genus name is capitalized, and the species name is all
lowercase. Both names are italicized.

Perusing the human body systems

Your body consists of major systems that work together to keep you alive. (And staying
alive is a good thing, so be sure to thank your circulatory system and all the rest!) These
systems include the ones listed in Table 10-3.

Table 10-3

Five Major Human Body Systems

System

Components

What the System Does

Central nervous
system

Brain, spinal cord,
and nerves

Receives, processes, and responds to all physi-
cal stimuli; for example, if you burn your hand on
the stove, this system prompts you to remove your
hand from the stove

Circulatory system

Digestive system

Heart, blood, and Delivers oxygenated blood from the heart to the

blood vessels rest of the body and returns the blood to the heart

to be oxygenated again

Mouth, esopha-
gus, stomach,
small and large
intestines, rectum,
and anus

Breaks down food into smaller substances that
the body can absorb and process into energy and
eliminates the resulting waste

Chapter 10: General Science J/j

System

Respiratory
system

Components

What the System Does

Musculoskeletal Bones, joints. Bones supportthe body's muscles and organs;

system voluntary and joints allow bones to move; voluntary muscles work

involuntary in pairs to move joints; involuntary muscles, which

muscles you can't control, are found in organs such as the

heart

Nose, nasal cavity,
trachea, lungs,
and blood

Inhales air, uses the oxygen in the airto release
energy, and exhales the carbon dioxide that results
from this process

Thinking small: A took at celts

Living things are made up of cells that share certain characteristics. Cells come in different
sizes and shapes, depending on what they do. In the human body, a muscle cell looks very
different from a brain cell. (Has all this talk of cells caused your brain cells to hurt yet?)
Cells combine to create tissues, which form structures like bones and skin.

Looking at cett structure

A cell has three main parts ■

the nucleus, the cytoplasm, and the cell membrane:

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f Nucleus: The nucleus controls cellular activity. It's like the brains behind the cell, and
it holds the cell's genetic material, such as DNA.

Bacteria are prokaryotes, which means their cells don't have nuclei. Their genetic mate-
rial floats in the cytoplasm instead of being held inside a membrane (nuclear envelope).

v Cytoplasm: The cytoplasm is a gel-like substance, composed mostly of water, that's
inside the cell membrane and outside the nucleus. Cytoplasm contains many chemicals
that carry out the life processes in the cell.

v^ Cell membrane (plasma membrane): This thin membrane holds the cell together,
protecting the nucleus and cytoplasm.

See Figure 10-1 for a description of other cell structures.

Plant cells differ from animal cells in a number of ways:

j"* Plant cells have a firm cell wall that supports and protects the cell. Animal cells don't
have such a structure.

j*"* Plant cells have larger vacuoles (storage areas) than those found in animal cells.

i** Unlike animal cells, many plant cells contain chloroplasts, which contain chlorophyll,
a chemical that helps plants create food with the help of sunlight.

v Animal cells contain centrioles (cylindrical structures involved in cell division). Most
plant and fungi cells don't.

W Animal cells have lysosomes (sacs of enzymes), which aren't found in plant cells.

116

Part IV: The Whole Ball of Facts: Technical Skills

Plant Cell

1. Chloroplast: Contains chlorophyll,

which produces food

2. Cell wall: Protects the cell

3. Nucleus: The "brain" of the cell

4. Chromatin: Thin fibers

containing genes

5. Nucleoplasm: Protoplasm (living

material) in the nucleus

6. Ribosome: Combines amino acids

into proteins

7. Cytoplasm: The cell 's factory

8. Mitochondria: Produce the energy

for cellular activity

9. Cell membrane: Contains the cellular

material within it

10. Vacuole: Storage area

Animal Cell

1. Nucleus

2. Chromatin

3. Nucleoplasm

4. Ribosome

Figure 10-1:

5. Cytoplasm

6. Mitochondria

Basic

7. Cell membrane

structures

8. Vacuole

of plant and

animal cells.

Profiting from ce(( processes

Cells perform various processes in order to function at an optimum level. Here are a few of
these processes:

u* Metabolism: Chemical processes within a cell that are necessary for life to be
maintained

v* Osmosis: Movement of water through the cell membrane

j-" Phagocytosis: Acquisition of particles of material from outside of the cell; it's accom-
plished by surrounding the particles and passing them through the cell membrane

v* Photosynthesis: Conversion of carbon dioxide and water into glucose and oxygen (in
plants); in other words, sunlight is used to create energy

J*" Cellular respiration: Process in which food is broken down, producing energy

Swimming in the gene pool: Genetics

Someday you're going to find yourself acting like your mother or father. Whether you like it
or not, it happens because parents pass their traits on to their offspring. Understanding
genetics — how traits are physically passed from parents to offspring and what happens
when the process goes wrong — helps scientists pinpoint the causes of diseases and disor-
ders and can help them develop treatments and cures.

Chapter 10: General Science / / 7

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In human genetics, a healthy person contains 23 pairs of chromosomes (the structure that
contains the genes). The mother and the father each supply one chromosome per pair.
Genes contained in the chromosomes determine many characteristics of the resulting child.

Copying genes

When body cells multiply to produce tissues and organs (and eventually a complete living
thing), they reproduce their genetic material. Most cells reproduce by mitosis, in which the
nucleus of a cell divides, forming two cells and two identical sets of chromosomes.

However, sex cells (eggs and sperm) reproduce differently. Through meiosis, each cell
divides into four cells, each containing only half the number of chromosomes as a nonsex
cell. This process takes place so that the sex cells of one person (with 23 chromosomes)
can hook up with the sex cells of another person (with 23 chromosomes) to produce 46
chromosomes, or 23 pairs. Otherwise, way too many chromosomes would be floating
around.

Sometimes cells don't copy themselves and divide perfectly, and a genetic mistake is made.
This frequently results in a fetus who doesn't live or in a fetus with a genetic disease or
disorder. For example, Down Syndrome is the result of a fetus's having 47 instead of 46
chromosomes.

determining your gender With Wo tittle tetters

The genes on one pair of chromosomes, called the sex chromosomes, determine whether a
child will be male or female. In females, the two sex chromosomes are alike, and they're
labeled XX. In males, the chromosomes are different and are labeled XY.

*** The child always receives an X chromosome from the mother (who only has XX chromo-
somes). The father (who has XY chromosomes) can contribute either an X or a Y chromo-
some, so Papa actually determines the sex of the child.

Knowing Which genes get passed doWn the f amity tine

Many characteristics that you possess (from the way your nose turns up at the end to the
color of your eyes) are determined by a pair of genes (or multiple pairs of genes). These
two genes may be alike, or they may not.

Some genes are dominant, and some genes are recessive. If you have two unalike genes, the
characteristic that they produce comes from the dominant gene; the gene that doesn't over-
shadow the other is called the recessive gene. If each parent has two unalike genes, both
parents will have the dominant trait, but they can have a child with the recessive trait —
because each parent contributes a gene to the offspring, each parent may contribute a
recessive gene to the child. Whew!

Chemistry: Not Blowing Up the Lab

SpRER

Chemists study matter, and everything that has mass and takes up space — including your
old Chevy that's up on blocks and the mosquito buzzing around the room — is matter. All
matter is made up of basic substances (building blocks) called elements.

Mass isn't the same thing as weight. Weight has to do with the force that gravity exerts on
mass. If you were in a gravity-free zone, you wouldn't weigh anything, but you'd still be
there, so you'd still exist and have mass.

Those mad scientists in the movies always seem to be chemists, but chemistry shouldn't
drive you crazy. Here's a straightforward review of the chemistry you need to know for the
General Science subtest.

118

Part IV: The Whole Ball of Facts: Technical Skills

WER

Understanding the elements, my dear Watson

The atom is the smallest part of an element that still retains the characteristics of that ele-
ment. Every atom has particles — pieces of matter that are very, very small. Electrons are
negatively charged particles that float around the atom's nucleus, or core, which is made up
of neutrons (particles with no charge) and protons (positively charged particles).

Each element has its own atomic number that's equal to the number of protons. If an atom
has one proton in its nucleus, it has the atomic number 1. Hydrogen is the only element
with just one proton in its nucleus. Magnesium, which has 12 protons in its nucleus, is given
the atomic number 12.

Atoms can combine with each other to form molecules. If those atoms are of two or more
different elements, the molecule is called a compound. A compound can have very different
properties from the elements that make it up. For example, table salt, which is mostly harm-
less, consists of two lethal elements — sodium and chlorine. But when combined, these ele-
ments make a compound that people ingest every day.

Sitting down at the periodic table

The periodic table (also known as the table of elements) classifies all elements, because sci-
entists love to classify things. Elements are listed according to their atomic numbers
(number of protons) and are arranged into families of similar elements.

The periodic table lists the atomic number, the abbreviation for each element, and its
atomic weight, which is the average mass of one atom of the element. Looking at Figure 10-2,
you can see that copper (Cu, atomic number 29) has an atomic weight of 63.546, which
means that copper is much, much heavier than helium (He, atomic number 2), which has an
atomic weight of 4.0026.

You don't have to memorize these charts to do well on the ASVAB, but you should know the
atomic numbers for common elements such as hydrogen (1), helium (2), carbon (6), nitro-
gen (7), oxygen (8), sodium (11), iron (26), copper (29), gold (79), mercury (80), lead (82),
uranium (92), and plutonium (94).

Getting physical: Changing states

Particles of matter are always in motion. How much kinetic energy (motion energy) a parti-
cle has determines whether the matter is a solid, liquid, or gas in its normal state. Gas parti-
cles move around very quickly, liquid particles move more slowly, and solid particles move
much more slowly than either of the other two.

When heat or cold is applied to matter, the kinetic energy of the matter changes; therefore,
the nature of the substance can change. Heat applied to water changes the water from a
liquid to a gas (steam), and cold applied to water changes it from a liquid to a solid (ice).
When physical changes occur, the molecule itself remains the same. For example, water is
still made of hydrogen and oxygen, no matter which state it's in.

Chapter 10: General Science / / V

Figure 10-2:

The periodic
table.

1 [vein i«i'ii
1.00797

IIA

IIIA

IVA

VIA

VIIA

Helium
4.0026

Lithium
6.939

Betyllium
9.0122

10.811

Carbon
12.01115

Nitrogen
14.0067

Oxynen
15.9994

Fluorine
18.9984

20.183

Mff

Vlll

Sodium
22.9898

24.312

IIIB

IVB

VB VIB

VIIB

__^v___

IIB

Alumrium
26.9815

Silicon

28.086

Phosphorus
30.9738

32.064

Chlorine
35.453

Aryon
39.948

(-I

w
ft.

Cll

Potassium

Calcium

Scandium

Titanium

Vanadium

l ]in iniium

Hai^'aiH'S!

Iron

Cobalt

Nickel

Copper

Zinc

Gallium

r.ermaniun

Arsenic

Selenium

Bromine

Krypton

39.102

40.08

44.956

47.90

50.942

51.996

54.9380

55.847

58.9332

58.71

63.546

65.37

69.72

72.59

74.9216

78.96

79.904

83.80

At?

Cri

Rubidium

Sti"' Hiliinn

Yttrium

ZiiV' niiiiiii

Niobium

McJybdaium

Technetiun Ruthenium

Rhodium

Palladium

Cadmium

Indium

Tin

Ai it in kit

Tellurium

Iodine

Xenon

85.47

87.62

88.905

91.22

92.906

95.94

(99)

101.07

102.905

106.4

107.868

112.40

114.82

118.69

121.75

127.60

126.9044

131.30

Cesium

Barium

Lanthanum

Hafnium

Tantalum

Tungsten

Rhenium

Osmium

Iridium

Platiium

Gold

Mercury

Thallium

Lead

Bismudi

I'l ] lllilllll

Astatine

Radon

132.905

137.34

138.91

179.49

180.948

183.85

186.2

190.2

192.2

195.09

196.967

200.59

204.37

207.19

208.980

(210)

(222)

104

105

106

107

108

109

Francium

Radium

Actinium

v:l:.':-il"nLui

Dubnium

•■■:■.: H i:--.,i ..;

Bohrium

Hassium

Mi.'iiuiit.un

(223)

(226)

(227)

(261)

(262)

(266)

(264)

(269)

(268)

nthanide Series

Cerium
140.12

140.907

Neodvmium
144.24

I'll 'iiHlkiun
(145)

150.35

II , II c J| lil. LL LI

151.96

1 J.;, i lini.iin
157.25

Terbium
158.924

Jvsprosium
162.50

Holmium
164.930

Erbium
167.26

Thulium
168.934

Vlli 1 1 nun
173.04

Lutetium

174.97

100

101

102

103

Actinide Series

Thorium
232.038

Protactiniun
(231)

Uranium
238.03

Neptunium
(237)

Plutonium
(242)

Americium
(243)

(247)

i'< ij iiiin

(247)

Californium
(251)

l.iiisUiiii'.im
(254)

Fermium
(257)

Md No

VlendefeviLin Nobelium
(258) (259)

Liwtviviun
(260)

Causing a chemical reaction

Unlike physical changes, chemical reactions create new molecules. For example, when iron
rusts, a chemical change occurs. The rust isn't the same molecule as the iron.

In a chemical reaction, two kinds of substances are present:

u* Reactants: The elements or molecules involved in the reaction

v* Products: The elements or molecules that result from the chemical reaction

Where feu) Hatfe Gone Before: Astronomy

Earth's solar system consists of the sun and a number of smaller bodies (such as planets,
the planets' moons, and asteroids) that the sun's mass holds in orbit. The sun's mass cre-
ates gravity, and this gravity controls the movements of the smaller bodies.

Taking a quick glimpse at the sun

The sun is the largest and most important object in the solar system. It contains 99.8 per-
cent of the solar system's mass (quantity of matter). The sun provides most of the heat,
light, and other energy that makes life possible.

/ 20 Part IV: The Whole BaM of Facts: Technical Skills

$££&*

Is Pluto really a planet?

Pluto was referred to as the ninth planet since its dis-
covery in the 1930s. But in August 2006, the International
Astronomical Union (IAU) established a new definition
for the word planet. Pluto has so many unusual features
that it was reclassified as a dwarf planet. For example,
it travels around the sun in an elongated oval path much
differentfrom the nearly circular orbits of the other plan-
ets. And unlike the other outer planets, Pluto is small and

1
solid and contains only— -of the mass of Earth.

Under the new standards, Pluto is no longer consid-
ered a planet but instead is classified as a dwarf planet.
According to the planet definition, the solar system con-
sists of eight planets and three dwarf planets. The defi-
nition doesn't apply outside the solar system and doesn't
include provisions for extra-solar planets. The definition
was a controversial one; it has been both criticized and
supported by different astronomers.

The sun's outer layers are hot and stormy. The hot gases and electrically charged particles
in those layers continually stream into space and often burst out in solar eruptions. This
flow of gases and particles forms the solar wind, which bathes everything in the solar system.

The sun is much larger than Earth. The distance from the sun's center to its surface (the
sun's radius) is about 109 times the radius of Earth. Some of the streams of gas rising from
the solar surface are even larger than the Earth's diameter.

Knowing the planets

A planet is a nonluminous celestial body larger than an asteroid or comet, illuminated by
light from a star that the planet revolves around. The solar system consists of eight known
planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Pluto is no
longer classified as a planet by most scientists. (See the sidebar "Is Pluto really a planet?"
for details.)

The Earth revolves around the sun in an oval-shaped pattern called an ellipse. Every 365)4
days, the Earth completes its orbit around the sun and starts again. The Earth rotates
(spins) on its axis, completing a rotation every 24 hours, but because of the tilt of the Earth,
hours of daylight and darkness aren't equal, except for on two days a year.

The inner four planets consist chiefly of iron and rock. They're known as the terrestrial
(earthlike) planets because they're somewhat similar in size and composition. The outer
planets are giant worlds with thick, gaseous outer layers. Almost all their mass consists of
hydrogen and helium, giving them compositions more like that of the sun than of Earth.
Beneath their outer layers, the giant planets have no known solid surfaces. The pressure
of their thick atmospheres turns their insides liquid, though they may have rocky cores.

Rings of dust, rock, and ice chunks encircle all the giant planets. Saturn's rings are the most
familiar, but thin rings also surround Jupiter, Uranus, and Neptune.

Shooting for the moons

Moons (sometimes called satellites) orbit all the planets except Mercury and Venus. The
moon you refer to as the moon revolves around the Earth. It makes a complete revolution
every 27M days. When the moon moves into the Earth's shadow, a lunar eclipse results — the

Chapter 10: General Science j 2 1

Earth is positioned between the sun and the moon. When the Earth moves into the moon's
shadow, a solar eclipse results — the moon is positioned between the Earth and the sun.

The inner planets have few moons. The giant planets probably have more small moons not
yet discovered. See Table 10-4 for a lineup of the planets and their moons. Although Pluto
is no longer officially considered a planet, you never know what those rascally ASVAB test-
writers will ask, so I've included Pluto in the table.

Table 10-4

The Number of Moons

per Planet in Earth's Solar System

Planet

Number of Moons

Mercury

Venus

Earth 1

Mars

2 tiny satellites

Jupiter

Saturn

Uranus

Neptune

Pluto (dwarf planet)

*£3?fc

Jupiter's four largest moons are known as the Galilean satellites because the Italian astrono-
mer Galileo Galilei discovered them in 1610 with one of the first telescopes. The largest
Galilean satellite — and the largest satellite in the solar system — is Ganymede, which is
even bigger than Mercury and Pluto. The largest of Saturn's moons, Titan, has an atmo-
sphere thicker than Earth's and a diameter larger than that of Mercury or Pluto. Pluto's larg-
est moon, Charon, is more than half the size of Pluto.

sftJTl/*.

Watching for meteors, comets, and asteroids

A meteor is a rock from space that hits Earth's atmosphere and glows as it heats up, result-
ing in a brief streak of light. It's often called a shooting star. When a meteor enters the
Earth's atmosphere, it usually burns up (and that's a good thing). If a meteor actually
strikes the Earth, it's called a meteorite.

Comets are snowballs composed mainly of ice and rock. When a comet approaches the sun,
some of the ice in its nucleus (center) turns into gas. The gas shoots out of the sunlit side of
the comet. The solar wind then carries the gas outward, forming it into a long tail.
Astronomers divide comets into two main types:

I i*" Long-period comets, which take 200 years or more to orbit the sun.
v* Short-period comets, which complete their orbits in fewer than 200 years.

The most famous of all comets, Halley's Comet — also referred to as Comet Halley after
Edmond Halley — is a comet that can be seen every 75 to 76 years, making it a short-period
comet. Halley is the only short-period comet that is visible to the naked eye and will return
within a human lifetime. Its many appearances over the centuries have had a notable effect
on human history. Halley's Comet last appeared in the inner solar system in 1986 and will
next appear in mid-2061.

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Part IV: The Whole Ball of Facts: Technical Skills

Asteroids are sometimes called minor planets because they're small bodies that orbit the
sun. Some have elliptical orbits that pass inside the orbit of Earth or even that of Mercury.
Others travel on a circular path among the outer planets. Most asteroids circle the sun in a
region called the asteroid belt, between the orbits of Mars and Jupiter. The belt contains
more than 200 asteroids larger than 60 miles (100 kilometers) in diameter. Scientists esti-
mate that more than 750,000 asteroids with diameters larger than % mile (1 kilometer) exist
in the belt. There are millions of smaller asteroids, and astronomers have even found sev-
eral large asteroids with smaller asteroids orbiting them.

Dou/n to Earth: Rocking Out With
Geology and Meteorology

The study of the physical makeup of the Earth is often called Earth science. Geology describes
the Earth's physical appearance, and meteorology explains the Earth's atmosphere.

Peeling back the layers of the planet

The Earth is like an onion in that it consists of several layers. The crust is the Earth's sur-
face, and it varies in depth from a few miles to 30 miles. The mantle (including the mantle
and an upper mantle) is the solid rock below the crust, and it makes up most of the mass of
the Earth. The core (including the inner and outer cores) is the Earth's fiery center, with a
temperature estimated to reach as hot as 4,300 degrees Celsius (to see what that is in
Fahrenheit, use the conversion equations in "Figuring temperature conversions" earlier in
this chapter). The mantle accounts for about two-thirds of the Earth's mass.

Sometimes cracks in the Earth's crust, called faults, appear. When the land shifts along
these faults, earthquakes result. Molten rock trapped between the crust and the mantle is
called magma. Magma collects in pockets called magma chambers and forms volcanoes.
When volcanoes erupt, the magma is spewed out as lava.

Outta this World: Checking the atmosphere

The atmosphere contains many layers of air surrounding the Earth's surface. Starting with
the layer closest to the Earth and extending outward, Table 10-5 names those layers.

Table 10-5

Layers of Earth's Atmosphere

Layer Name

Location

Details

Troposphere

Extends
about8
miles above
the Earth

This layer is where the jet stream is located and where almost
all weather changes occur.

Stratosphere

Extends
about 30
miles

A major reported cause of ozone depletion is the presence of
chlorofluorocarbons (CFCs) in the Earth's stratosphere. CFCs
undergo a series of chain reactions, which ultimately leads to
the destruction of the ozone layer.

Chapter 10: General Science / £j

Layer Name

Location

Details

Mesosphere

Extends
about 50
miles

Millions of meteors burn up daily in the mesosphere as a result
of collisions with the gas particles contained there.

Ionosphere Extends This layer reflects most radio waves, making it important to

about 70 communications. Note: Scientists disagree among themselves

miles as to whether the ionosphere is a separate atmospheric layer

or whether it's part of the thermosphere.

Thermosphere Extends The International Space Station has a stable orbitwithin

about 350 the upper part of the thermosphere, between 208 and 285

miles miles.

Exosphere Extends It's only from the exosphere that atmospheric gases, atoms,

about and molecules can escape into outer space. No boundary

40,000 miles exists between the exosphere and space; therefore, exosphere
is sometimes used synonymously with outer space.

Warming up to cold fronts

Temperature affects air density (how closely packed the air molecules are). When the sun
shines, land and water absorb its warmth. Land warms up more quickly than water, so air
over land is warmer than air over water during most of the day. At night, the air over land
cools more quickly than air over water. The angle of the sun also affects air density (the sun
shines directly over the Equator but not the poles).

Cold air is denser than warm air. Because it's denser, cold air has high pressure, compared
to warm air's low pressure. (A barometer measures atmospheric pressure.) Air moves from
areas of high pressure to areas of low pressure, creating wind.

Air masses have certain characteristics depending on where they form:

Ii^ If an air mass forms over land, it's dry, and if it forms over water, it's wet.
i* Air masses formed in Earth's northern and southern regions are cold, and those
formed at the Equator are warm.

When two different air masses meet, they don't mix. They form a boundary called a front.
When cold air meets warm air, a cold front develops. The warm air may be pushed up to
form clouds, causing heavy rain. When a warm air mass meets a cold air mass, a warm front
develops. The warm air passes over the cold air, forming a different kind of cloud, which
causes light rain.

Classifying clouds

Clouds are made of small droplets of water or bits of ice that are spread out from each
other. Rain (or snow) falls when the drops get too big and heavy to stay in the cloud. Clouds
have three main types, and the ASVAB may ask you a question or two about their character-
istics, which are detailed in Table 10-6.

12 It

Part IV: The Whole Ball of Facts: Technical Skills

Table 10-6

Types

of Clouds

Cloud Type

Description

What It Forecasts

Cirrus

Thin, wispy, high clouds

Generally indicate rain or snow

Cumulus

White, puffy pillows, often flat-
bottomed with rounded tops

Common during fair weather, but when
they gather, they cause heavy rains

Stratus

Broad, flat, and low-hanging
(gray blanket)

If close to the ground, they may produce
drizzle

Additionally, a prefix or suffix is frequently given to the cloud name to indicate which level
of the atmosphere it's in or whether it's producing precipitation (rain, sleet, snow, and the
like):

p" Cirro- is the prefix given to high clouds (base above 20,000 feet).

k" Alto- is the prefix given to mid-level clouds (base between 6,000 and 20,000 feet).

v* Nimbo- added to the beginning of a cloud name or -nimbus added to the end means the
cloud is producing precipitation.

Therefore, a cirrocumulus cloud is a white, puffy, flat-bottomed, rounded-topped cloud at
high altitude. Altostratus clouds are gray, broad, flat clouds at mid altitude.

Improving \lour Chances on the
General Science Subtest

Even if you study hard for the General Science subtest, chances are you may come across at
least a couple of questions that you can't answer. That's the nature of this subtest — it
pretty much asks you to know all there is to know about the universe. However, you can use
several strategies to improve your chances of selecting the correct answer.

WER

Using common sense to make educated guesses

If you don't know the answer to a question right off the bat, don't panic. You can often elimi-
nate a few incorrect choices simply by using common sense. Even if you can't determine the
answer, keep in mind that this subtest doesn't penalize you for guessing, so guessing makes
sense — you have a 25 percent chance of guessing the right answer even if you can't elimi-
nate any obviously wrong answers. If you can eliminate just one wrong answer, you improve
your chances to 33 percent.

Most people don't have to rush to finish the General Science subtest, but then again, you
don't have much leisure time to stop and think about all the questions at length, either. So
if you don't know the answer to a question right away, do your best to eliminate wrong
answers quickly, mark your best guess, and move along. (For help on making these eliminat-
ing decisions, check out Chapter 3.)

Chapter 10: General Science J 25

^PLE

Try the process of elimination on the following question:

The knee joint is known as a

(A) pivot joint.

(B) fixed joint.

(D) hinge joint.

Looking at the choices, you can eliminate Choice (B), fixed joint, because your knee isn't
fixed, or not moveable (or if it is, it shouldn't be). Your skull is an example of a fixed joint,
but that's irrelevant to this question. Is your knee a pivot joint? If you think of something
that pivots, you think of it moving in a circular or at least a semi-circular manner. Your knee
doesn't do that either; therefore, you can safely eliminate Choice (A). A ball-and-socket joint
is one that permits limited movement in any direction (your shoulder joint is a ball-and-
socket joint). Your knee doesn't do that, so you can strike off Choice (C) and choose
Choice (D), hinge joint, as the most likely answer. Your knee moves like a door on a hinge.

Now suppose you have a question like this:

The most common gas found in Earth's atmosphere is

(A) oxygen.

(B) nitrogen.

(D) helium.

Eliminate Choice (C) because calcium isn't a gas. You can also cross out Choice (D) because
if helium were the most common gas, everyone would be talking in squeaky voices (you
know, like after sucking helium from a balloon). Eliminating these two answers leaves you
with just two choices, and if you simply guessed, you'd have a 50 percent chance of being
right. Unfortunately, most people would guess that oxygen is the most common gas in
Earth's atmosphere, but they'd be wrong. Nitrogen — Choice (B) — tops the list, making up
78 percent of the atmosphere.

Getting back to your Latin roots

Just when you thought vocabulary study was over, leave it to me to bring it up again. Many
scientific words come from Latin or Greek. If you know the meaning of the Latin or Greek
word, you can often figure out the meaning of the scientific word. Often, a Latin or Greek
root word is used to create a longer, more specific word. (For common word roots, see
Chapter 4.)

For example, the Latin root homo means both human being and same. So Homo sapiens
refers to members of the human species, but homogeneous means "of the same kind." So if
you were to run across the word homologous on the General Science subtest, you'd know
that it has something to do with humans or with things that are the same.

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Part IV: The Whole Ball of Facts: Technical Skills

^PLE

Take a look at the following example question:

Which of the following instruments might an oceanographer be expected to use?

(A) aspirator

(B) hydrophone

(D) centrifuge

Even if you don't have a clue about what any of these instruments do, if you know that
hydro relates to water, you've significantly increased your chances of getting the right
answer, Choice (B).

Chapter 11

Auto and Shop Information

In This Chapter

Looking under the hood of vehicles
Knowing the tools of the trade
Checking out the many uses of fasteners
Driving up your test score

tftBEfl

•^ver wonder why automobile mechanics and carpenters charge you about a billion dol-
•Wlars an hour when you need to hire their services? Because if the jobs were easy, every-
one would do them.

Fortunately, to do well on the Auto & Shop Information (AS) subtest of the ASVAB, you don't
have to get your hands greasy or chance hitting your thumb with a hammer. The questions
on this subtest are pretty basic. Automotive questions usually ask about basic automotive
systems and malfunctions. The shop questions generally ask you to identify a tool or fas-
tener or the purpose of such.

The Auto & Shop Information subtest consists of 25 questions on the paper and pencil ver-
sion. Happily, the ASVAB gurus give you 26.4 seconds to answer each question (11 minutes
total). About half of the questions measure your basic knowledge of automotive principles
and half query you about shop tools and basic shop principles. On the CAT-ASVAB, you
have 7 minutes to answer 1 1 questions on Auto Information and 6 minutes to answer 1 1
questions on Shop Information. Your scores on these subtests are combined to give you a
single Auto & Shop score.

The military uses the Auto & Shop Information subtest only to determine your qualifications
for certain jobs. It's not used in the calculation of your AFQT score. Turn to Appendix A at
the back of this book to find the jobs that require a good score on this subtest. If you don't
need to do well on this subtest to qualify for the kind of job you want, you may be better off
studying for a different part of the ASVAB.

Checking under the Hood

Contrary to what you may think, an automobile is much more than the mechanical monster
you park in your driveway each night. It's actually a complex machine that has undergone
more than a century of evolution. Henry Ford would probably have a stroke if he could see
what his simple horseless carriage evolved into.

The modern car is divided into several primary and secondary systems. I cover these sys-
tems in the next few sections.

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Part IV: The Whole Ball of Facts: Technical Skills

The engine: Different strokes

How does an engine work? You turn the key, and if it doesn't start, you call your mechanic
or your dad, right? Well, not quite. The internal combustion engine burns a mixture of gas
and air. Burning the gas and air (the fuel mixture) makes it expand quickly (explode). The
pressure from this explosion is transferred (via additional systems) to the wheels to make
the car move.

The movement is brought about by a cycle, which your car's engine repeats a zillion and
one times. Here are the four strokes that make up a cycle (Figure 1 1-1 illustrates how this
process works):

1. Intake: The intake valve opens as the connecting rod pulls the piston down, drawing
the gas/air mix into the cylinder.

2. Compression: The valves are closed. The connecting rod pushes the piston up, com-
pressing gas/air mix.

3. Power: The spark plug ignites the gas/air mix, forcing the piston down. That pushes
down on the connecting rod, turning the crankshaft; the crankshaft turns the flywheel,
which keeps the engine going.

4. Exhaust: The exhaust valve opens as the connecting rod moves the piston back up,
pushing out the exploded gases. The valves are timed, of course, using push rods
attached to the camshaft.

Push Rod

Spark Plug

Figure 11-1:

A four-
stroke
engine.

ust Gases
Exhaust Valve

Connecting Rod

Crankshaft

Flywheel

&S&*

Chapter 11: Auto and Shop Information / £y

Generally cars have an even number of cylinders — four, six, or eight. These cylinders are
arranged in a row or rows, which are called inline (one row) or K(two rows), depending on
the arrangement.

Most people refer to their engines as four-cycle engines. This isn't really true. It is a four-
stroke, one-cycle engine. The intake stroke, compression stroke, power stroke, and exhaust
stroke are one engine cycle. When the fourth stroke is completed, the cycle begins again.
Automobile engines do this very fast. When the tachometer (an instrument measuring revo-
lutions per minute [rpm]) on your dashboard shows 4,800 rpm, for example, that means the
engine is performing 4,800 of these cycles every minute.

In order for the cycle to happen at all, fuel must be properly mixed with air and transported
within the cylinder at the proper time. Various components perform this function.
Depending on how old a car is, it may use a carburetor or fuel injectors:

V Carburetors: Carburetors are used on most older cars (pre-1990) to mix the fuel and
air mechanically. As air moves quickly through the carburetor, it creates a vacuum,
which draws more and more fuel into the mixture.

«*" Fuel injectors: Fuel injectors have replaced carburetors on newer cars to perform the
air/fuel mixture function. (Actually, fuel injectors have been around since the late
1950s, but they weren't widely introduced until the late 80s and early 90s.) The fuel
injector acts as the fuel-dispensing nozzle. It injects liquid fuel directly into the engine's
air stream. In almost all cases, this requires an external pump.

A doodad called the EFI computer (electronic fuel injection computer) determines the
amount of fuel entering the engine. The EFI computer receives information from the
sensors in the fuel, air, and exhaust system, and from that information, it determines
how much fuel the engine needs to operate at optimum levels.

A throttle is mechanically connected to the carburetor or electronically connected to the EFI
computer. Advancing (opening) the throttle causes more fuel to be transferred to the carbu-
retor or the fuel injectors. The accelerator (the gas pedal) is connected to the throttle by
mechanical linkages. The harder you push on the gas pedal, the farther the throttle is
advanced (opened). Thus, more fuel is transported to the carburetor or fuel injectors.

Cooling system: Acting coot, staying smooth

Because of the high temperature at which the fuel burns, the engine has a cooling system
(otherwise, the engine would melt). In this system, water jackets surround the parts that
reach the highest temperatures. A water pump circulates water through the jackets. While
the water circulates, it absorbs heat from the engine and then passes through the radiator,
where outside air cools the water.

The water in the system is usually mixed with coolant (antifreeze), which raises the boiling
point of the water (which keeps the water from boiling away) and lowers its freezing point
(which keeps the system from freezing up during cold weather).

In addition, the engine parts must be lubricated to prevent them from breaking down, which
occurs if the metal parts are allowed to rub against each other. An oil pump circulates oil
through the engine; oil flows through the crankshaft and connecting rods, lubricating as it
goes. Lubrication reduces friction, which in turn reduces heat.

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Part IV: The Whole Ball of Facts: Technical Skills

Electrical and ignition systems: Starting up

Your car requires more than just gasoline to operate. It also needs a supply of electricity. In
the old days, automotive electrical systems operated on 6 volts. Shortly after World War II, as
electrical accessories became more prevalent in automobiles, 12 volts became the standard.

An electric motor powered by the battery starts the engine when you turn the key. This
motor is called a starter (for obvious reasons). A gizmo called an alternator sends an electric
current back to the battery to keep the battery charged and also powers the other elec-
tronic gadgets on your car when the engine is running.

The ignition system supplies a high-voltage current to the spark plugs to ignite the fuel mix-
ture in the cylinders. (See the section titled "The engine: Different strokes," earlier in this
chapter.) The system takes the 12-volt current from the battery, steps it up to about 20,000
volts, and then sends the current to the spark plugs.

In older cars, this increase of voltage is accomplished by means of a device called a coil, which
uses electromagnetic induction to step up the voltage. The current then passes through an
electrical/mechanical switching device called a distributor. A rotating shaft and a switch within
the distributor, called breaker points, routes the current through wires to the spark plugs. A
condenser absorbs excess current and protects the breaker points from damage by the high-
voltage surge. The distributor and other devices control the timing of the spark-plug discharges.

In the 1970s, the electronic ignition systems were introduced. In modern ignition systems,
the distributor, coil, points, and condenser have been replaced by solid-state electronics
controlled by a computer. A computer controls the ignition system and adjusts it to provide
maximum efficiency in a variety of driving conditions.

Dri(/e system: Taking it for a spin

Having a working engine is all fine and dandy, but the power of the engine still has to be trans-
ferred to the wheels to make them move. This is the job of the drive system. Cars have drive
systems that run on axles. The axle is the shaft on which the wheels revolve. The universal
joint allows the axle to move up and down without breaking the drive shaft. The drive shaft is
the connecting component that carries torque and transmits rotation. Gears on the axle allow
the vehicle to make turns. Axle shafts turn the wheels. The wheels on vehicles turn in three
different ways:

v* Rear-wheel drive: The rear wheels push the car. The drive shaft extends from the
transmission to the rear axle.

v* Front-wheel drive: The front wheels pull the car. The drive shaft extends from the
transmission to the front axle.

v* All-wheel drive (four-wheel drive): All wheels push and pull the car at the same time.
The drive shaft extends from the transmission to both axles.

Cars also have transmissions. The transmission changes the speed of the engine in relation
to the speed of the rear wheels (in rear-wheel drive), the front wheels (in front-wheel drive),
or all the wheels (in four-wheel or all-wheel drive). Vehicles have two types of transmis-
sions: automatic or manual (stick shift).

The transmission consists of gears in several combinations so that the amount of torque
used can vary according to needs. When the terrain is difficult (as in snow), the wheels
need more torque (the force that produces rotation) in order to move. The transmission
increases torque as needed. In an automatic transmission, this variation is done automatically
by the torque converter. In a manual transmission, the driver shifts the gears by hand. The
clutch is used to facilitate this process by disconnecting the engine from the drive shaft. It's

Chapter 11: Auto and Shop Information / jj

necessary to temporarily disconnect the engine in order to change to a different gear
(torque). The clutch also allows the engine to run when the car isn't moving.

*£S&>

Brake system: Putting out alt the stops

When a vehicle is in motion, you apply brakes to stop that car from moving (a long way
from the time when Fred and Barney stopped their car by dragging their heels). Each wheel
has a brake that applies friction to the wheel to stop its rotation.

A brake system consists of a master cylinder that has brake lines (filled with brake fluid)
running from it. The brake pedal applies pressure to the master cylinder, which sends pres-
sure (and brake fluid) through the lines. What happens next depends on the type of brakes:

v* Drum brakes: In a drum brake, the lines are connected to a hydraulic cylinder on each
wheel. This cylinder contains pistons that move outward and force two brake shoes
against the metal drum that rotates the wheel.

v* Disc brakes: In a disc-brake system, the master cylinder forces a caliper, containing a
piston, with brake shoes on each side, to squeeze against a rotating disc in each wheel,
thus stopping your car by using fluid and releasing hot air.

Most modern cars use both drum brakes and disc brakes. Drum brakes are usually installed
on the rear wheels, and disc brakes are generally installed on the front wheels. A drum
brake system usually consists of a rotating drum with shoes that expand to rub the inside of
a drum. This differs from the disc brake, which uses pads that pinch a rotating disc.

Emissions-control systems:
In layman's terms, fitters

Think of the engine as a giant cigarette and the emissions-control system as a filter. The
exhaust from automobiles emits pollutants, including carbon monoxide. These pollutants
are a result of the combustion process (or they're partially combusted fuel or unburned
fuel). To prevent these pollutants from poisoning the atmosphere, manufacturers place
emissions-control systems on cars. These systems include the following:

v* Positive-crankcase ventilation: An old method (still in use) that forces unburned or
partially burned fuel back into the cylinder so the fuel can be burned

v* Air-injection system: System that forces air into the engine's exhaust system to burn
unburned or partially burned fuel before the fuel comes out the exhaust pipe

J*" Catalytic converter: Oxidizes hydrocarbons and carbon monoxide into water vapor
and carbon dioxide (the same thing people exhale); this system doesn't control other
types of pollutants such as nitrogen oxides

v* Exhaust-gas-recirculation system: Helps control nitrogen-oxide emissions by forcing
some of the gases back into the cylinders

Picking Up the Tools of the Trade

You've probably heard the phrase "the right tool for the right job." This comment is what
Dad used to yell at you when you'd use a Phillips screwdriver to punch holes in oil cans
(thereby getting oil on your shirt). The ASVAB folks also believe in using the right tool for
the right job, and many of the questions on the Auto & Shop Information subtest ask you to
identify the best tool for certain tasks.

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Part IV: The Whole Ball of Facts: Technical Skills

Tools are easiest to understand when you classify them by their function, so the following
sections are divided by function. See Figure 11-2 for an illustration of the various types of
tools covered.

Sliding Calipers

' i ' i ' i ' i ' i ' i ' i ' i ' i ' i ' i ' i ' i ' i ' i '

Scale Locking Device

Ratchet Handle

1 )

6-point 12-point
Socket Socket

Socket
Wrench

Deep
Socket

C-Clamp

Calipers

Butt Chisel

Mortising Chisel

Cold Chisel

Vise Grip Pliers

Handscrew Vise

Flat
Washer

Split Lock
Washer

Shake-proof
Washer

Figure 11-2:

Various

tools you

need to

know for the

ASVAB.

Wing Nut

Cap Nut

Adjustable
Pipe Wrench

Chapter 11: Auto and Shop Information j jj

Striking toots

Striking tools apply driving force to an object. (Watch your fingers!) These tools include
hammers, sledges, and mallets. Here's a brief explanation of the three:

v* Hammer: A hammer is generally made of metal or plastic and consists of a handle, a
head, a face (the part of the hammer that touches the nail or other fastener), a claw (to
pull nails), and a wedge that attaches the head to the handle. The face of a hammer
may be made of steel, brass, or lead.

p" Mallet: A mallet is generally made of metal or plastic but may be made of wood,
rubber, or rawhide. It's used to strike another tool or to strike a surface without dam-
aging it. A mallet doesn't have a claw like its friend, the hammer.

p" Sledge: A sledge is generally made of metal. People use it to drive bolts and chisels and
to break rock. A sledge doesn't have a claw, either.

Fastening toots

Fastening tools apply fasteners, such as screws, to objects. (For more info on fasteners,
check out "Sticking Materials Together with Fasteners," later in this chapter.) Numerous
tools make up the fastening category:

p" Stapler: A stapler is a fastening tool. Heavy-duty staplers can staple roofing felt to a
roof, for instance.

v* Wrenches: Wrenches turn nuts and bolts. The bolt or nut fits between the jaws of the
wrench, and the wrench turns the bolt. Some wrenches have adjustable jaws. Not only
can wrenches be used to turn nuts and bolts, but they may also be used to keep nuts
and bolts stationary.

• Open-end wrenches: These wrenches have open jaws.

• Box wrenches: Box wrenches are closed. Some wrenches have open-end jaws on
one end and a box wrench on the other.

• Socket wrenches: Socket wrenches have box-type sockets of varying sizes that
can be attached to a handle, which in turn can be attached to an extension.

Note: Socket, box, and open-ended wrenches come in set, standard sizes — either
in inches or in millimeters. They're not interchangeable. (Selecting the wrong
socket wrench is how mechanics learn to use cuss words.)

• Torque wrenches: These wrenches apply additional leverage to a fastener. A
torque wrench looks much like a socket wrench but has additional internal mech-
anisms designed to measure and limit the amount of torque (force) being applied.

• Pipe wrenches: Pipe wrenches have serrated jaws and grip round objects.

v* Screwdrivers: A screwdriver, in the shop world, turns screws. (In the civilian world,
it's a yummy drink!) Some special screwdrivers have different blades to fit different
types of screws:

• Standard screwdriver: A standard screwdriver has a flat blade at one end of the
shank (the other end of the shank goes into a handle).

• Phillips screwdriver: Phillips screwdrivers have a blade that is shaped like a
cross; this blade fits into a cross-shaped Phillips screw head.

• Allen wrench: An Allen wrench fits hexagonal screw heads. Nobody knows why
this tool is called an Allen wrench instead of an Allen screwdriver; after all, it's
used on hexagonal screws. That's just one of the mysteries of the shop world.

734

Part IV: The Whole Ball of Facts: Technical Skills

$££&>

The Allen wrench, which was designed in 1943, gets its name from the Allen
Manufacturing Company of Hartford, Connecticut.

• Offset screwdriver: Offset screwdrivers have the shank set at an angle to the
blade to allow the tool to be used in cramped spaces. Offset screwdrivers can
have a standard blade, Phillips blade, or any number of other blades.

k" Pliers: Pliers can be used to fasten and unfasten fasteners, hold objects, and cut mate-
rial. When you squeeze the handles, the jaws of the pliers come together.

• Long-nosed or needle-nosed: Long-nosed pliers, also called needle-nosed pliers,
have tapered jaws that can hold small objects or fit into small spaces.

• Curved-nose: These pliers have curved jaws.

• Slip-joint: These pliers can be adjusted so the handles lock in a certain position.

• Wrench or vise-grip: Wrench pliers, or vise-grip pliers, have serrated jaws that
clamp onto and hold objects of all shapes.

• Cutting: These pliers are used to cut wire.

Cutting toots

Cutting tools use sharp blades to cut through metal, wood, or other materials. Cutting tools
have teeth. The number of teeth per inch (or points per inch) gives an indication of the type
of work the saw can do. Because of the way points and teeth are counted, a saw always has
one more point per inch than tooth per inch. A saw with fewer teeth is used for rough work,
like cutting wood to size. A saw with more teeth cuts more finely and is used for more deli-
cate work, like sawing joints and lightweight pieces of wood. Check out Table 11-1 for a
breakdown of the different cutting tools that may be covered on the ASVAB.

Table 11-1

Cutting Tools

Cutting Tool

Description/Function

Bolt cutters

Heavy-duty shears that produce enough force when the han-
dles are closed to slice through metal bolts or rods

Circle snips

Used to cut curves

Crosscut saw

A type of handsaw that cuts against the grain of the wood; the
shape of the teeth and the angle in which they're set are the
main differences in this type of saw

Coping saw

A type of handsaw that's used to cut curved lines or shapes

Hacksaw

A type of handsaw that's used to cut metal; a hacksaw has
an adjustable frame that holds thin blades of varying length in
place; a handle is set in one end

Pipe cutters and tube cutters

Used to score and cut metal pipes and tubes

Ripsaw

A type of handsaw that cuts with the grain of the wood; the
shape of the teeth and the angle in which they're set are the
main differences in this type of saws

Snips and shears

Snips and shears have two cutting blades that scissor together
when the handles close; the blades can be curved or straight

Chapter 11: Auto and Shop Information J 35

^\NG

Drilling, punching, and gouging toots

No, this section isn't about hand-to-hand combat training from basic training. Masters in the
art of shop often make holes in the material they're working with in order to build that per-
fect birdhouse (or whatever else they're working on). These holes can be made with a vari-
ety of tools, which I cover in the following sections.

Oritts and bits

Twist drills use drill bits, which are round pieces of steel shaped in a spiral, to create holes.
Drill bits are attached to a drill (usually a power drill but sometimes a hand drill operated
by manually turning a crank). The point of the drill bit is sharpened, and the shank is
smooth and fits into the drill.

A countersink is a drill bit that enlarges just the surface of a hole so that a screw head can
be accommodated. A countersink is used to allow the top of the fastener to be set exactly
even with the material to which it's attached. Without a countersink, the fastener slightly
protrudes from the material to which it's been attached.

Auger bits bore larger holes. They're shaped differently from drill bits. They have a long
deep spiral flute for easy chip removal. They're also much larger. Auger bits are most com-
monly used with a brace for drilling holes in wood. Their length varies from 7 to 10 inches.

Punches

Punches have a sharp end that's placed against the material to be punctured; the other end
is struck with a hammer. A center punch is used to mark where a drilled hole is to be
placed; this keeps the drill bit in position and prevents the drill from jumping to another
part of the material.

Using a Phillips screwdriver as a punch is bad form in the shop world because hitting the
handle of a screwdriver with a hammer can damage it (and then you'll get talked about in
serious shop circles).

Chisels

Chisels are made of steel and have a sharp cutting edge. They're used to chip or cut metal
or wood:

-«JNG.

p* Metal-cutting chisels: Chisels that cut metal are usually struck with a mallet to make
the cut. These chisels have different shapes depending on how they'll be used; cold
chisels are flat, and they're used for cutting metals without using heating torches or
forges, whereas round chisels make circular cuts.

v* Wood-cutting chisels: Some wood chisels, called socket chisels, are also struck with a
mallet. Other wood chisels require only the pressure of your hands.

Wood chisels also come in different shapes, depending on what they're used for. A butt
chisel has a short blade and is used for in-close work. A mortising chisel has a narrow
blade made for chiseling out the narrow mortises in joints. A framing chisel has a
heavy, strong blade meant for rough work.

Because you use chisels with other tools and the pressure of your hands, there's a little bit
of a risk involved with this tool. One slip and these instruments can easily cut large chunks
out of your skin, so be careful.

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Part IV: The Whole Ball of Facts: Technical Skills

Finishing toots

Filing and finishing shop tools are used to sharpen the blades of other tools and to smooth
the edges of cut metal objects. Files come in a range of fineness, and the blades can be cut
in different patterns. Files also come in different shapes to finish different kinds of objects.
Here are the different kinds of files:

i*" Single-cut: Single-cut files are used for finishing work and sharpening blades.

v* Double-cut: Double-cut files are used for rough work.

«*" Flat files and half-round: These files are for general purposes.

v* Square and round: These files fit square and round openings.

Planes are a type of finishing tool used to prepare wood for final finishing and to fit doors
and trim. Planes consist of a handle to push with, a knob to guide with, a frame, a sole, and
a mouth (where the blade is). Bench planes are used to smooth surfaces. Longer planes give
a more uniform surface by shaving off a portion of the wood.

Clamping tools

A clamping tool is a device used to hold or fasten objects securely so they won't move while
you're working on them. There are several types of clamping tools available for many differ-
ent purposes:

j-" Pliers: Pliers (discussed in the "Fastening tools" section earlier in the chapter) can be
used to hold objects while you're working on them.

v* Vises: Vises hold material while it's being sawed, drilled, or glued. Here are some differ-
ent types of vises:

• Bench vise: A bench vise has large, rough jaws that keep the material from
slipping.

• Pipe vise: Pipe vises hold round trim or pipes.

• Handscrew vise: A handscrew vise has two hard, wooden jaws connected by two
long screws. The screws are tightened to bring the jaws of the handscrew vise
together.

v* Clamps: Clamps are used when a vise won't work. Vises generally attach to a work-
bench, while clamps generally connect only to the items being worked with. C-clamps
consist of a stationary frame and a screw that moves back and forth to open and shut
the clamp.

Measuring toots

As any shop enthusiast will tell you, the golden rule of shop is to "measure twice and cut
once." It's frustrating to cut a piece of material only to find it's just a little bit too short
to fit in the place you intended. Using measuring tools helps you avoid this embarrassing
situation.

Tape rules, rigid steel rules, steel (or fiberglass) tape rules, and folding rules are all used to
measure material. Calipers are also used for very exact and small measurements. Calipers
can be used with a rule to measure diameter; the legs of a set of calipers curve in to measure
outside curves and curve out to measure inside curves. Slide calipers have the rule built in.

Chapter 11: Auto and Shop Information J j7

Depth gauges measure the depth of holes. Thickness gauges measure the thickness of small
openings. Thread gauges measure the number of threads per inch in threaded fasteners.
Wire gauges measure the thickness of wire.

Leveling and squaring toots

A square is used to check the trueness (accuracy) of an angle. Because most squares have
a rule, they can also be used for measuring (see the preceding section). Squares have two
arms, called the blade and the tongue, that meet at a right angle. A square can be set against
any angle that is supposed to be a 90-degree angle. If a gap exists between the square and
the material, the material isn't true — that is, it's not at the specified angle. A sliding T-bevel
has an adjustable blade so that different angles can be checked.

Levels show whether a surface is true. A basic level has one or more small tubes filled with
a liquid (like alcohol) and an air bubble. If the level is placed on a surface and the bubble
remains exactly in the center of the tube, the surface is level. (This method can't be used to
see if your recruiter is on the level. I tried it. Recruiters simply won't hold still long enough.)

A plumb bob is a heavy weight that's suspended from a line. It indicates vertical trueness.

Sticking Materials Together With Fasteners

Although wood and metal (and other materials) can be held together with glue, straps, duct
tape, and other brilliant fastening methods, people usually fasten these types of materials
with nails, screws, bolts, and rivets. These fasteners offer more strength and stability than the
white glue that you used to fasten painted macaroni noodles onto construction paper in the
first grade.

*£5fe

Mails

Nails are used to hold pieces of wood together. The nail head is flat, and the shank is usu-
ally round. Nail length is designated by the penny system, which is abbreviated with a d. A
ten-penny nail is a lOd nail. Length and thickness generally correspond. Nails that are larger
than 20-penny are called spikes and are measured in inches.

x " The penny system is used in the United States. Penny size indicates the nail's length. The
higher the penny size, the longer the nail. The penny system is derived from the price of 100
nails in the 15th century in England.

Other type of nails include the following:

v* Brads and finishing nails: They have heads that are made to fit flush with or slightly
below the surface of the wood.

i*" Common nails: These nails are the most commonly used nails. (How about that for a
truly difficult vocab word?)

v* Double-headed nails: These have two heads, one lower than the other, and a point on
the other end. The nail is driven to the lower head but can be pulled out of the material
because of the remaining higher head. These nails are used for temporary construction
that will be taken apart.

138

Part IV: The Whole Ball of Facts: Technical Skills

The magic of ABS

In the modern world of cars, most vehicles are equipped
with an antilock brake system (ABS). The ABS is a four-
wheel system (usually) that prevents the wheels from
locking up. The system does this by automatically
adjusting the brake pressure during an emergency stop.
This enables the driver to maintain steering control
and to stop in the shortest possible distance under most
conditions.

The theory behind ABS is simple. If your car isn't
equipped with ABS and you have to stop quickly, your

wheels simply stop turning when you hit the brakes.
If your tires don't have much traction on the road,
your car may continue forward in a skid, even though
the wheels are locked. You don't stop as quickly as
you would with ABS, and you won't be able to steer.
However, with ABS, your wheels are slowed to a stop
as quickly as possible, without locking up, which gives
the driver much better control during an emergency stop
situation.

Screws and bolts

Unlike nails, you can easily take screws and bolts out of the wood without causing addi-
tional damage to the wood (unless, of course, the threads are stripped). These fasteners
also hold more tightly than nails. Screws have flat heads, round heads, or oval heads; and in
addition to this classification, they also have standard heads (for standard slotted screw-
drivers) or Phillips heads (with cross-shape slots). Screw sizes are based on length and the
diameter of the unthreaded part of the screw.

Here's the lowdown on these types of fasteners:

v* Wood screws: Wood screws are used to fasten wood. (Hmm, ingenious!)

j*" Lag screws: Lag screws have square- or hexagon-shaped heads.

j-" Bolts: Bolts don't thread into wood. They have flat ends (as opposed to the pointed
ends of screws). They're held in place by a nut (which is what actually screws into the
threads) and washer. The body of the bolt may have few threads or many.

v* Machine screws: Machine screws are used to fasten metal parts. Machine screws are
sometimes used with nuts. They come in various lengths and widths and have a wide
variety of heads.

Nuts and Washers

Nuts can be square or hexagonal. Cap nuts are rounded and smooth; stop nuts prevent the
screw or bolt from coming loose. Wing nuts have flanges on each side so they can be tight-
ened by hand.

Washers prevent damage to the surface of material by preventing the bolt head from dig-
ging into the material. They also help keep the bolt (or screw) in place. Flat washers, a
simple ring of flat metal, are the most common type of washer. Shake-proof washers have
teeth to prevent them from skipping, while split-lock washers have two ends that dig into the
nut and the material to keep the screw from slipping out.

Chapter 11: Auto and Shop Information / $<)

Rii/ets

Rivets are commonly used to fasten metal parts together, especially when a weld is insuffi-
cient. Standard rivets are driven using a bucking bar. Rivets come in a wide variety of
lengths, diameters, and head shapes. The rivet material should match the material being
fastened. Pop rivets can be driven when only one side of a joint is accessible.

Building a Better Score

If you haven't picked up auto and shop knowledge by this point in your life and want to do
well on this subtest, one thing you can do is get an automotive manual and take your car
apart (hoping that you can get it back together again). Then get a woodworking book and
build some furniture for your mom. (Even if you mess it up, Mom always likes gifts from the
heart.)

Or you can check out your local community college, which may be a more practical solu-
tion. Many community colleges offer basic Auto and Shop classes. You may also want to
take a gander at the following books, all published by Wiley Publishing:

K" Auto Repair For Dummies by Deanna Sclar

u* Woodworking For Dummies by Jeff Strong

v* Home Improvement All-in-One For Dummies by Roy Barnhart, James Carey, Morris
Carey, Gene Hamilton, Katie Hamilton, Donald R. Prestly, and Jeff Strong

On this subtest, you usually either know the answer or you say, "Huh?" However, some
questions you run into can be answered by using the common sense approach. For exam-
ple, say you run into a question on the ASVAB that reads something like the following:

When attaching two pieces of wood together, the most secure bond would be formed by
using:

(A) wood screws

(B) nails

(D) both A and C

If you think about it, screws have threads, which are likely to "grab" wood more securely
than a nail would. Glue would likely strengthen that bond even more. It's obvious that the
common sense answer would be Choice (D).

Try a variation of the same question:

The best fastening method to use when attaching pieces of wood together when time is of
the essence would be

(A) wood screws

(B) nails

(D) both A and C

Part IV: The Whole Ball of Facts: Technical Skills

Making the grade: Octane ratings

Octane ratings measure gasoline's ability to resist
engine knock, a rattling or pinging sound that results
from premature ignition of the compressed fuel-air mix-
ture in one or more cylinders. Most gas stations offer
three octane grades: regular (usually 87 octane), mid-
grade (usually 89 octane) and premium (usually 92 or
93). By federal law, the ratings must be posted on bright
yellow stickers on each gasoline pump.

The octane rating correlates to how much the gasoline
can be compressed before it ignites spontaneously.
When gasoline ignites this way, instead of by the spark
of a spark plug, the engine begins knocking. That's not
a good thing because early ignition can cause engine
damage overtime.

But don't be fooled — that doesn't mean using higher
octane gas is better. In most cases, using a higher

octane gasoline than your owner's manual recom-
mends offers absolutely no benefit. It won't make your
car perform better, go faster, get better mileage, or
run cleaner. The only time you may need to switch to
a higher octane level is if your car engine knocks when
you use the recommended fuel. This happens to a small
percentage of cars. Buying higher octane gasoline is a
waste of money, too. Premium gas costs 1 5 to 20 cents
or more per gallon more than regular. That can add up to
hundreds of dollars a year in unnecessary costs.

How can you tell if you're using the right octane level?
Listen to your car's engine. If it doesn't knock when you
use the recommended octane, you're using the right
grade of gasoline.

In this case, the best answer would be Choice (B), because pounding a nail in with a hammer
is generally faster than waiting for glue to dry or screwing a screw in with a screwdriver
(even in these days of electric screwdrivers).

WER

When all else fails, guessing is okay. If you guess, you have a 25 percent chance of guessing
the right answer. If you leave the answer blank, you have a percent chance. If you're taking
the computerized version of the ASVAB, you don't have a choice, of course, because you
must provide an answer before you're presented with the next question. For general guess-
ing hints, check out Chapter 3.

Chapter 12

Mechanical Comprehension

In This Chapter

Using the forces of physics
Figuring out the principles of work
Manipulating machines to help you work
Jacking up your test score

men

m f your M-16A2 .223 caliber rifle jams on the firing range, knowing how to take it apart and
«S put it back together will benefit you. Of course, your drill sergeant in basic training will
be more than happy to teach you this, but how easily you grasp such tasks depends greatly
on your aptitude for understanding simple mechanical operations. That's the purpose of
the Mechanical Comprehension (MC) subtest of the ASVAB.

The questions on this subtest measure your understanding of simple machines and mecha-
nisms. Many of the questions on this subtest display a diagram, such as a series of gears,
followed by a question, such as which direction the gears turn or how fast they revolve.
This subtest is almost all about mechanical physics, so you may want to review some basic
physics textbooks from your local library.

Only some military jobs require a good score on this subtest. Turn to Appendix A at the
back of this book for information about the subtest scores you need to qualify for specific
military jobs. If you have no interest in taking apart a fighter aircraft or rebuilding a tank,
you're better off reviewing for the Word Knowledge or Arithmetic Reasoning subtests,
which make up part of the core exam (the AFQT; see Chapter 1) that you must do well on
to even qualify for enlistment.

To ace this subtest, you also have to bone up on your mathematical skills. The Mechanical
Comprehension subtest often asks you to make calculations based on formulas to explain
mechanical principles. Don't panic; the formulas are easy to understand, but you do have
to use math to come up with a final answer. See Chapters 7 and 8 for more information on
math. In this chapter, you get the mathematical formulas for commonly asked questions on
the ASVAB, so pay especially close attention to these little beauties. (If the information
probably isn't on the ASVAB, I don't burden you with it here.)

The CAT-ASVAB (computerized test) has 16 Mechanical Comprehension questions that
you're supposed to answer in 20 minutes. For the paper version of the ASVAB, this subtest
has 25 questions. You have 19 minutes to answer the questions, which is enough time for a
mechanically oriented individual to tackle this subtest and put a broken clock back together.
Well, maybe not the whole clock.

Understanding the Forces of the Universe

By applying force (a push or pull), you can open the door or close it, speed it up (slam it) or
slow it down (catch it before it slams), or make it change direction (push it shut when the
wind blows it open).

Part IV: The Whole Ball of Facts: Technical Skills

* In physics, applying force allows changes in the velocity (the speed and direction) of an

object. A change in velocity is known as acceleration. Here's the mathematical formula to
determine force:

Force = Mass x Acceleration

Martial artists use this concept all the time. Although a larger fighter may have more size
(mass), a smaller fighter can usually speed up more quickly (have more acceleration), pos-
sibly resulting in both fighters' applying the same amount of force. This concept is why 110-
pound martial artists can break boards and bricks just as well as 200-pound martial artists.

This section gives you the basics of force that you need to know for the ASVAB.

He hit me first! The basics of action and reaction

Sir Isaac Newton sure was one of the sharpest crayons in the box. His third law of motion
states that for every action (force) in nature, there's an equal and opposite reaction. In
other words, if object A exerts a force on object B, then object B also exerts an equal and
opposite force on object A. Notice that the forces are exerted on different objects.

Take a look at Figure 12-1. As you sit in your chair, your body exerts a downward force on
the chair, and the chair exerts an upward force on your body. There are two forces result-
ing from this interaction: a force on the chair and a force on your body. These two forces
are called action and reaction forces.

Action

Figure 12-1:

An example

of action

and reaction

forces.

Reaction

This force can also be used to describe how a motorboat moves through the water. As the
propellers turn, they push the water behind the boat (action). The water reacts by pushing
the boat forward (reaction).

Equilibrium: finding a balance

Forces are vector quantities. That means that they have both a magnitude (size) and a direc-
tion associated with them. Forces applied in the same direction as other forces increase the
total force, and forces that move in opposite directions reduce the total force. In general, an
object can be acted on by several different forces at any one time.

Chapter 12: Mechanical Comprehension J A3

*jABE*

A very basic concept when dealing with forces is the idea of equilibrium or balance. When
two or more forces interact so that their combination cancels the other(s) out, a state of
equilibrium occurs. In this state, the velocity of an object doesn't change. The forces are
considered to be balanced if the rightward forces are balanced by the leftward forces and
the upward forces are balanced by the downward forces.

If an object is at rest and is in a state of equilibrium, then it's at static equilibrium. Static
means being stationary or at rest. For example, a glass of water sitting on a table is at static
equilibrium. The table exerts an upward force on the glass to counteract the force of gravity.

0m*

Under pressure: Spreading out the force

Pressure is a measurement of force over an area. Pressure is usually measured in pounds
per square inch (psi). The formula for deriving pressure is

Pressure ■

Force (in pounds)
Area ( in inches )

*££&>

If 50 pounds of force is exerted on 10 square inches of surface, the amount of pressure is
5 pounds per square inch (5 = 50 * 10).

Consider this: If you're sleeping in bed, the amount of pressure being exerted per square
inch is much less than when you're standing on your feet. The surface area of the bottoms
of your feet (supporting all that weight) is much less than the surface area of all your body
parts that touch the mattress.

Ever wonder how a person can lie on a bed of nails? The answer involves elementary physics.
His or her body rests evenly on hundreds of nails; therefore, no individual nail exerts a great
amount of pressure against the skin. Have you ever seen someone stand on a bed of nails? It's
unlikely because more pressure is on the feet, and the nails would puncture the feet.

A barometer is a gauge that measures atmospheric pressure. Normal atmospheric pressure
is 14.7 psi. A change in air pressure means the weather is about to change. For more infor-
mation on science and barometric pressure, see Chapter 10.

Looking at kinds of forces

Here are some of the forces that act on objects:

j-" Friction: Resistance to the motion of two objects or surfaces that touch

v* Gravity: The physical property that draws objects toward the center of the Earth (and
other objects that have mass)

p" Magnetism: The property of attracting iron or steel

j*" Recoil: The property of kicking back when released

f Static electricity: The production of stationary electrical charges, often the result of
friction

In this section, I explain a few of these forces in detail.

Friction: Resisting the urge to motfe

When one surface (such as a floor) resists the movement of another surface (the bottom of
a piano), the result is frictional resistance. (This friction isn't like resisting orders to cut the

Part IV: The Whole Ball of Facts: Technical Skills

grass. That type of resistance may cause friction between you and your dad, but I'm talking
about a different kind of resistance here.)

In order to perform work — that is, to get an object to move in the direction you're pushing
or pulling — sometimes you have to overcome friction by applying more force. For example,
when you're moving a piano across a smooth, vinyl floor, little friction is produced, so the
amount of force required to push the piano comes from the piano's weight and the very
minor friction produced by the smooth floor. But when you're moving a piano across a car-
peted floor, more friction is produced, so you have to push harder to move the same piano
the same distance. (See the later section "You Call that Work?!" for more information on
what's considered work in physics terms.)

Rolling friction (like the friction that occurs when you roll a wheel along the pavement) is
always less than sliding friction (which occurs when you shove a piano along the floor). If
you put wheels on a piano, it's much easier to push!

You can decrease friction by using a lubricant. Oil, grease, and similar materials reduce fric-
tion between two surfaces. So theoretically, if you oil the bottom of a piano, it's easier to
move! Note: Oiling the bottom of your piano isn't recommended (for reasons involving the
appearance of your floor and piano).

WER

Gravity: What goes up must come dovin

Sir Isaac Newton invented gravity in 1687 when he failed to pay attention while sitting under
a tree and got bonked on the noggin by an apple. Before that, gravity didn't exist, and every-
one just floated around. Okay, I'm kidding. Isaac Newton didn't invent gravity. But the
famous mathematician was the first to study gravity seriously, and he came up with the
theory (now a scientific law) of how gravity works.

Newton's law of universal gravitation states that every object in the universe attracts every
other object in the universe. The Earth produces gravity, and so do the sun, other planets,
your car, your house, and your body. Even this book you're reading produces gravity. The
amount (force) of the attraction depends on the following:

v* Mass: The force of gravity depends on the mass of (amount of matter in) the object. If
you're sitting in front of your television, you may be surprised to know that the televi-
sion set is attracting you. However, because the mass of the TV is so small compared
to the mass of the Earth, you don't notice the physical "pull" toward the television set.

Note that the force of gravity acting on an object is equal to the weight of the object. Of
course, other planets have lesser or greater masses than the Earth, so the weight of
objects on those planets will be different.

f Distance: Newton's law also says that the greater the distance is between two objects,
the less the objects will attract each other. In other words, the farther away an object
is from the Earth (or any large body), the less it will weigh. If you stand at the top of a
high mountain, you will weigh less than you will at sea level. Don't get too excited
about this weight-loss technique. Gravitational pull isn't the next big diet craze. The
difference is incredibly small. Sorry!

For an object to really lose weight, it must be far away from the Earth (or any other
large body). When an object is far enough away from these bodies that it experiences
practically no gravitational pull from them, it is said to experience weightlessness —
just like the astronauts you see on TV.

Gravity pulls objects downward toward the center of the Earth, so the old saying "what
goes up must come down" is appropriate when discussing gravity. If you fire a bullet
straight up into the air, it will travel (overcoming the force of gravity) until it reaches its
furthest or highest point, and then it will fall.

Chapter 12: Mechanical Comprehension J hjy

Centrifugal force: False gravity

An object traveling in a circle appears to experience a
gravitational force. This isn't really gravity, but instead
it's a concept known as centrifugal force. The amount
offorce depends onthe mass of the object, the speed of
rotation, and the distance from the center:

u* The more massive the object, the greater the force.

j"* The greater the speed of the object, the greater the
force.

C" The greaterthe distance from the center, the greater
the force.

The centrifugal force, or effect, on an object is actu-
ally a fictitious outward force on an object moving along
a curved path, which can be equal to the centripetal

force on an object. Centripetal force points toward the
center of an object's circular path, perpendiculartothe
direction of motion of an object.

If you're riding on a merry-go-round onthe playground
(wee!), you have to exert a constant force to keep from
flying off. This feeling of being pushed outward isn't due
to something actually pushing you in that direction but
to your body's inertia trying to keep you moving in a
straight line. Because one of Newton's laws states that
moving objects tend to want to travel in one direction,
as the merry-go-round turns, your body wants to keep
traveling in one direction (tangentto the circle, if you like
math), so you feel you're being pushed outward.

Applying force to Mo ends: Tension

Tension force is the force transmitted through a rope, string, or wire when force is applied
to both ends. The force is the amount of tension directed along the rope, string, or wire
and pulls equally on the objects at both ends. Tension force is usually measured in either
pounds-force or newtons (N); 4.45 newtons equal 1 pound-force. See Figure 12-2.

Elastic recoil: The trampoline of physics

Liquids and gasses don't have a specific shape, but solid matter does. Solids are perfectly
happy with the way they look and resist changes in shape. If you exert a force on a solid shape,
it responds by exerting a force in the opposite direction. This force is called elastic recoil.

Take a look at Figure 12-3. The cat is standing on a board suspended on two blocks. While
the board bends, the cat can feel the force of the board trying to regain its original shape.
If the cat steps off the board, the board will spring back to its normal state.

Force = 150 pounds-force

Figure 12-2:

An example

of tension

force.

Tension = 150 pounds-force

Weight = 150 pounds

Part IV: The Whole Ball of Facts: Technical Skills

Figure 12-3:

The concept

of elastic

recoil.

\lou Catt That Work!!

*JHBE«

Mechanically speaking, work happens when a force (usually measured in pounds) moving
over a measurable distance (usually measured in feet) overcomes a resistance. In the
United States, the unit of measure for work is often called a foot-pound. One foot-pound of
work occurs when a 1-pound weight is lifted to a height of 1 foot. You can represent this
concept in equation form:

Work = Force x Distance

Work is different from effort; work is the result of effort. You can think of effort as being
force and of work as being what you produce with that force.

Overcoming resistance

The resistance that the work overcomes isn't the same thing as the weight of the object.
(If you've ever tried to put your freaked-out cat in a cat carrier to go to the vet, you know
what I mean.) In other words, if you try to move a 1,200-pound piano, you'll probably notice
a measurable difference between the amount of work it takes to shove it along the floor and
the amount of work it takes to carry it up the stairs. But don't take my word for it — you can
demonstrate this concept at home. First, find a 1,200-pound piano and push it across the
floor. Next, put it on your back and carry it up the stairs. See the difference? (Really, don't
put the piano on your back. I'm just trying to make a point here.)

When you move the piano across the floor, you're really working (pushing) against the fric-
tional resistance (the force that's produced when two surfaces rub together) of the piano
rather than its full weight. Under these circumstances, the frictional resistance of the piano
offers less resistance than its full weight. There are times when an object's full weight is less
than its frictional resistance. Consider trying to push a textbook across a deep-pile carpet.
Picking the book up and carrying it is easier. (For more about friction, see the earlier sec-
tion "Friction: Resisting the urge to move.")

cjABE*

Gaining porter by Working more quickly

Power is the rate of work. If Mary Lou is able to lift more 50-pound sacks of potatoes onto the
truck bed in ten minutes than Joe is, Mary Lou is more powerful than Joe. Mathematically
speaking,

Power =

Work
Time

Chapter 12: Mechanical Comprehension I (l7

cjUBE*

In this formula, work is usually measured in foot-pounds, time is measured in minutes, and
power is measured in foot-pounds per minute. However, the unit of measure for power is
commonly put in terms of horsepower (hp).

Horsepower is derived from the estimate that an average horse can do 33,000 foot-pounds
of work in one minute (according to James Watt). Therefore, 1 horsepower = 33,000 foot-
pounds per minute. One horsepower is also the same as 550 foot-pounds per second.

Reiyinq on Machines to Help \lou Work

Ever since Zog crawled out of his cave and invented the wheel to help him carry fur coats to
his girlfriend, mankind has made use of machines that help him to make work easier.

In addition to increasing efficiency, machines are also used to help with work that couldn't
be done otherwise. Think of the mechanisms and machines you use everyday — from the
simple (like the hinge that allows a door to move easily when you push it open) to the more
complex (like the hydraulic lift that allows you to lift a car up to check its underside). You
could move most doors out of the way without hinges, but you couldn't lift a car over your
head without some help.

<$m

Machines give you the ability to magnify and change the direction of forces. When a
machine multiplies the force you use, it gives you a mechanical advantage. This concept can
be stated as

Mechanical Advantage ■■

Resistance Output Force

Effort

Input Force

Some simple machines may give you a mechanical advantage of only 1 or 2. This means that
they enable you to do one or two times the amount of work by expending the same effort.
But those simple machines are still worth using! Often, even if a machine doesn't multiply
your effort (or doesn't multiply your effort by much), it can at least spread your effort out
and make it more effective.

Machines make work easier by providing some trade-off between the force applied and the
distance over which it's applied. Keep reading to find out more on some basic types of
machines.

Using tetters to qow advantage

You may not think of the seesaw at the neighborhood park as a machine, but it is. It's a
lever. Levers are among the simplest machines used to help increase force.

All levers work by using a fulcrum (point of support) to reduce resistance and multiply the
effect of effort. Resistance is exerted at one end of the lever (the resistance arm) and effort is
exerted at the other (the effort arm). The effort arm moves the resistance arm. See Figure 12-4.

Figure 12-4:

A simple
lever.

Part IV: The Whole Ball of Facts: Technical Skills

To determine how much a lever reduces the amount of effort needed to do work, use the
following formula:

Length of Effort Arm Resistance Force

Length of Resistance Arm Effort Force

*i*!§?

As you can see, the amount of effort needed to move the lever varies depending on how
long the effort arm is and how long the resistance arm is. Keep in mind that a short resis-
tance arm, although easier to move, can't move an object as far through space as a longer
resistance arm can.

The mechanical advantage of using a lever can be stated as

Mechanical Advantage - Effort Arm —
° Resistance Arm

If the effort arm is 6 inches and the resistance arm is 3 inches, the mechanical advantage is 2.
If the effort arm is 6 feet and the resistance arm is 3 feet, the mechanical advantage is still 2.

tfWEK

Ramping up the inclined plane

The inclined plane, also called a ramp, is another very simple machine that makes moving
an object from one point to another easier. The ramp spreads your work out over a longer
distance, so less force is needed to do the work.

For instance, suppose you have to lift a 50-pound barrel to a truck bed that's 3 feet off the
ground. You would have to use 50 pounds of force for 3 feet to move the barrel. But if you
put a 6-foot ramp in place and push the barrel up the ramp, you'd only use half as much
force to get the barrel in the truck (assuming there's no friction) because the mechanical
advantage of such a ramp is 2.

The advantage of using a ramp can be expressed as

Length of Ramp
Height of Ramp

Weight of Object Being Moved
Force Required to Move Object

&M*

Wedges are a form of inclined plane and can multiply your effort in much the same way as a
ramp can. Screws are also inclined planes, only in spiral form. Screw jacks, which you can
use to lift your house up to build a new foundation, are a combination of a lever and an
inclined plane.

Easing your effort: Pulleys and gears

Pulleys and gears are simple machines that can be used to change the magnitude (size) and
direction of force. When you ride in an elevator, step onto an escalator, drive your car, or
wind up your watch, you're using pulleys and gears.

Block and tackle systems

When used in a block and tackle arrangement (see Figure 12-5), pulleys make lifting heavy
objects easier. In block and tackle systems, pulleys can also be used to change the direction
of your pull. If you tie a 200-pound crate to one end of a rope, run the rope through a pulley,
and grab the other end of the rope, you can pull down on the rope to lift the crate up.
Without a pulley, you could pull down on the crate all day, and it wouldn't go up. In this case,

Chapter 12: Mechanical Comprehension J h Q

using a simple pulley, the force of your pull must equal the weight of the object being lifted.
The regular pulley doesn't multiply your force, but it makes the process of lifting easier.

Using a block and tackle allows you to distribute your force more effectively. Instead of
hoisting that entire 200-pound crate in one try, you can pull on a rope to lift it a few inches,
pull on the rope some more to lift it a few more inches, and so on. This makes the work
easier to perform.

A block and tackle system can also be used to reduce effort by magnifying force. To help
understand how this works, look at Figure 12-6:

v* Example 1 shows a 100-pound box secured to the ceiling by a single line. The weight
supported by the line is equal to the weight of the box.

v* In Example 2, the box is secured to the ceiling by using two lines. Each line is support-
ing one-half the weight of the box.

v* In Example 3, a single line is threaded through a pulley. Although the line (as a whole)
is supporting the entire weight of the box, each section of the line is supporting only
one-half of the box's weight, just as in Example 2.

v* In Example 4, a man is using this principle to lift the 100-pound box by applying only
50 pounds of force. In short, this block and tackle system provides the man with a
mechanical advantage of 2. In receiving a mechanical advantage of force, the man must
pull the rope farther than if he weren't using a pulley. In this example, the man would
have to pull 2 feet of rope to raise the box 1 foot.

Additional pulleys can be added to a block and tackle arrangement to further increase the
mechanical advantage. Figure 12-7 shows a couple of examples:

j-" In Example 1, three sections of rope produce a mechanical advantage of 3. Lifting a
weight with this pulley arrangement requires only K of the effort required to lift the
weight directly. However, in order to lift the crate 1 foot, you have to pull 3 feet of rope.

j-" Example 2 illustrates a block and tackle system with six sections of rope. Using this
arrangement provides you with a mechanical advantage of 6, but you have to pull the
rope 6 feet for every foot you want to raise the box.

Figure 12-5:

A pulley

used in

a block

and tackle

system.

Block and tackle
(pulley)

EFFORT

200-pound crate

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Part IV: The Whole Ball of Facts: Technical Skills

100 lbs.

Example 1

Example 2

Figure 12-6:

Reducing

effort by

using a

block and

tackle.

y~s"

100 lbs.

Example 3

Example 4

Figure 12-7:

Two
examples
of a block
and tackle
arrange-
ment.

Example 1

Example 2

$***

Understanding how gears Work

Machines often use gears to transmit motion from one place to another. An additional
advantage of using gears is that they can be used to change direction, increase or decrease
speed, or increase or decrease force.

Gears arranged in a series turn in the opposite direction of each other. If you have an even
number of gears connected in a series, the first and last gear turn in opposite directions. If
you have an odd number of gears aligned in a series, the first and last gear spin in the same
direction. Look at Figure 12-8. Gear 1 is rotating counterclockwise, which causes Gear 2 to
turn clockwise, resulting in Gear 3's spinning counterclockwise, with Gear 4 turning clockwise.

Chapter 12: Mechanical Comprehension /SI

Figure 12-8:

The motion
of gears
with an
even num-
ber of gears
aligned in a
series.

cjftBE/f

The speed at which a gear rotates (in relation to the driving gear connected to it) depends
on the number of teeth. In Figure 12-9, Gear 1 has six teeth, and Gear 2 has eight teeth. This
relation of teeth can be expressed as a ratio of 6:8, which can be further reduced to 3:4.
That means that Gear 1 has to rotate four times in order for Gear 2 to make three revolu-
tions. Or expressed another way, for each rotation made by Gear 1, Gear 2 will make three-
quarters of a revolution.

6 teeth

8 teeth

Figure 12-9:

The ratio

of teeth

between

two gears

affects

rotational

speed.

Ratio :

When gear shafts aren't parallel to one another, bevel gears can be used to connect gears that
have shafts at different angles. The principles of gear rotation remain the same. Figure 12-10
shows an example of bevel gears designed to connect shafts having a 90-degree angle to the
other.

Figure 12-10:

Two bevel

gears meet

at a right

angle.

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Part IV: The Whole Ball of Facts: Technical Skills

PuNey and belt arrangements

In addition to magnifying force as part of a block and tackle system, pulleys have another
use. When connected by a system of belts, pulleys can drive other pulleys.

Like gears, pulleys are used to transmit motion from one location to another. However, the
physical properties of pulleys are different from those of gears:

v* Turning direction: Unless the driving belt is reversed (twisted), pulleys connected in
series rotate in the same direction. Figure 12-11 illustrates this concept with two sets of
pulleys. In the first set of pulleys, all the pulleys turn in the same direction (counter-
clockwise) as the driving pulley. However, in the second set of pulleys, the driving
pulley and the lower pulley are rotating counterclockwise, but the right-hand pulley is
rotating in a clockwise direction because the belt is twisted.

Figure 12-11:

Pulleys
rotate in the
same direc-
tion unless
the belt is
reversed.

Driving
Pulley

i*" Speed of rotation: Although the speed of gear rotation is determined by the number of
teeth, how fast a pulley rotates depends on the diameter of the pulley in relation to the
diameter of the pulley that's driving it. Have a look at Figure 12-12. Pulley A has a diam-
eter of 1 inch, Pulley B has a diameter of 2 inches, and Pulley C measures 4 inches in
diameter. The ratio among the three pulleys is 1:2:4. For every complete revolution
made by Pulley A, Pulley B makes half of a revolution. Each time Pulley B makes a
full revolution, Pulley C makes half of a revolution. Thus, for every full revolution of
Pulley A, Pulley C makes a quarter of a revolution.

Multiplying yow effort: Wheels and axles

The wheel-and-axle machine multiplies the effort you use, producing a greater force. When
you steer a car by using a steering wheel (which is a wheel-and-axle device), a little effort
exerted on the steering wheel turns the wheels of the car in the direction you desire. Turning
your car wheels would be a lot more complicated if you didn't have the steering wheel.

In true wheel-and-axle machines, the wheel and the axle are fixed together and turn at the
same time. This arrangement multiplies the amount of force you can exert by a consider-
able amount.

Chapter 12: Mechanical Comprehension / 3^3

Figure 12-12: [

o S^^*^^

Pulley rota- \

b y^-^-^^^

tion speed

is based on

the pulley's

Pulley A Diameter = 1 inch

diameter.

Pulley B Diameter = 2 inches

Pulley C Diameter = 4 inches

The relationship between the radius of the wheel and the radius of the area to which force
is being applied determines the mechanical advantage you receive by using this piece of
equipment. (Remember, the radius of a circle equals half the diameter; a straight line
extending from the center of the circle to the edge is the radius of a circle.) A hand drill may
apply 200 pounds of force for your 10 pounds of effort. (A hand drill uses a gear to convert
the direction of the force.) See Figure 12-13.

Figure 12-13:

A hand drill.

Force required

to turn handle

IE)

Mechanical advantage of
wheel and axle =

Radius of
wheel's circle

%w~

Width of
drill tip (W)

Resistance
offered by
material (S)

Getting a qxip on things With Vises

Although many mechanisms are designed to transmit motion, some machines have the pur-
pose of keeping things motionless. Vises are very useful because they can close around
items and hold them with great force (much greater force than you could do by holding the
item in your hands). Figure 12-14 shows an illustration of a standard shop vise.

754

Part IV: The Whole Ball of Facts: Technical Skills

Figure 12-14:

A standard
shop vise.

Rotating the handle on the vise causes a screw to turn, which either tightens or loosens the
vise. A screw is a cylinder wrapped in a continuous spiral. The distance between the ridges
of the spiral is called the pitch of the thread. The greater the pitch of the thread, the farther
the jaws of the vice move for each revolution of the handle. However, there's a trade-off.
Larger pitches require more force to rotate the handle than screws with smaller pitches do.

Magnifying your force With liquid: Hydraulic jacks

A hydraulic jack uses a nearly incompressible liquid, such as oil, to exert force in order to
move an object (see Figure 12-15). As the handle moves, it applies pressure to the oil.
Because the oil doesn't compress, the oil transmits whatever force is applied to it to the
work cylinder with no (or little) loss in efficiency. The mechanical advantage is the ratio
between the diameters of the two cylinders.

In the figure, the small cylinder has a diameter of 1 inch and the large cylinder has a diame-
ter of 4 inches. This difference in diameter results in a mechanical advantage of 4. If the
rocks weigh a total of 100 pounds, only 25 pounds of force has to be applied to the piston in
the small cylinder in order to lift the load. However, although the force required is reduced
by a factor of 4, the smaller piston has to move 4 feet for every foot the piston in the larger
cylinder moves.

Force

Figure 12-15:

A hydraulic
jack.

Force

Chapter 12: Mechanical Comprehension / QQ

Working \lour Way to a Better Test Score

When you take the Mechanical Comprehension subtest, you may not know the correct
answer to a question, or you may not know the mechanical principle involved. You may
know the mechanical principle but not remember the formula you need to come up with the
right answer. Never fear — you can still stumble through this test without totally flaming out.

Using yow observations and common sense

Questions on this subtest often include illustrations. The ASVAB test-makers expect you to
look at the illustrated device and guess how it operates. When you run across these types
of questions, make sure that you understand the illustration. Often, parts of the device are
labeled. Make certain you read and understand these labels before you try to answer a
question about the illustration.

Also, try to use a common-sense approach. You may see the following question:

Which of the following controls an automatic sump pump?

(A) mechanical switch

(B) manual switch

(D) float

You may not know the answer to this question, but you can rule out Choice (B), manual
switch, because the question asks you about an automatic sump pump, and anything
manual isn't automatic. Eliminating one choice narrows your chances from one in four to
one in three. Not a bad start, huh?

A sump pump is used to drain water from an area, and if you know that, you have an even
better shot at getting this question right. Think about what type of device detects the pres-
ence of water, and you may guess correctly that Choice (D), float, is the right answer.

You can answer a lot of the questions correctly if you just think about what you've observed
in the world around you. Remember, the Mechanical Comprehension subtest also tests your
knowledge of physical principles of the world around you — questions you may expect to
find on the General Science subtest. For example, a question may ask something like this:

If all the following objects are the same temperature, which one will feel coldest on a
cool day?

(A) a wooden spoon

(B) a plastic spoon

(D) a fiberglass spoon

You don't need to know mechanical or scientific principles to know that a metal spoon will
feel colder than the other spoons. So it makes sense to select Choice (C) as your answer,
even if you can't explain the science behind this correct answer.

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Part IV: The Whole Ball of Facts: Technical Skills

*2£&>

The nerve endings in your skin detect the difference between your inside body temperature
and your outside skin temperature. Metal is an excellent conductor of heat, so heat readily
flows from your hand into the metal. The heat is conducted rapidly away into the bulk of
the metal, leaving your skin surface relatively cool. That's why metal feels cooler than
other, less efficient conductors of heat, such as wood, plastic, or fiberglass.

^PLE

Using the mathematics of mechanics

Mechanical principles are based on mathematical principles. Therefore, a screw making
a complete revolution turns 360 degrees, because a mathematical principle states that
360 degrees are in a circle, a complete revolution. If you have to know the surface area of a
floor in order to determine the pounds per square inch that a ton of tile would put on the
floor, that's a mathematical principle, too (Area = Length x Width).

Suppose you run across this question:

A 3-inch-diameter flanged pipe with six holes is being fitted to a base with six holes. What's
the maximum number of degrees the pipe must be rotated in order to line up the holes?

(A) 120 degrees

(B) 180 degrees

(D) 360 degrees

This isn't really a Mechanical Comprehension question at all — it's a math question. The only
part that requires mechanical knowledge is knowing that the holes are spaced equally distant
from one another on a flanged pipe. The answer is 360 degrees * 6 = 60 degrees, Choice (C).

Guessing With a mechanical mind

Like most of the other subtests on the ASVAB, you can and should guess on the Mechanical
Comprehension subtest when you don't know the answer. Check out these tips to help you
narrow the field:

v* The amount of force needed to move an object (not including friction resistance) is
never greater than the weight of the object. Any answer that includes a force that's
greater than the weight of the object being moved is probably wrong.

j*" The correct answer is a mechanical answer. For example, if the question asks, "What's
the purpose of lubricating oil in an engine?" the correct answer won't be "to make the
parts look shiny." The answer may be "to reduce friction between moving parts."

u* Any change in a mechanical operation almost always has pluses and minuses associ-
ated with it. So when a question proposes a change, the correct answer is probably the
one that specifies the good, the bad, and the ugly. For instance, suppose the question
says, "Enlarging the wheel on a hand drill will . . . ?" The correct answer is the one that
says something like "increase the mechanical advantage and decrease the amount of
effort needed to operate the drill."

For more general tips on guessing on the ASVAB, flip to Chapter 3.

Chapter 13

Electronics Information

In This Chapter

Understanding current, voltage, power, and more
Comprehending electrical flow
Deciphering circuit diagrams
Amplifying your test score

VUBE/?

■ ^^hen I was around 12 years old, I impressed my parents by taking an old television
▼ ▼ set apart and putting it back together. I impressed them right up to the point where
I plugged it in and blew up the garage. But the world of electronics is a bit more complex
than simply plugging something in and seeing whether it works. I (and the garage) learned
this lesson the hard way.

Six years later, when I took the ASVAB, I scored very well on the Electronics Information
subtest. (Go figure!) This subtest is designed to measure your knowledge of the principles
of electricity and how these principles are applied in the real world. You may see questions
about transistors, magnets, engines and motors, and radio and television. (Curiously, there
are no questions on this subtest concerning the impromptu demolition of garages.)

You don't have to be an electronics whiz to score well on this subtest. If you're not familiar
with this information and you want to pursue a military career that requires you to do well on
this subtest, this chapter is calling your name. You also need to have some familiarity with
basic mathematical and algebraic principles (see Chapters 7 and 8 for more information).

Not every military career requires a good score on this subtest. (Turn to Appendix A to find
out which military jobs require a score on this — and other — subtests.) If the military feels
that the Electronics Information subtest is important to your desired career, study inten-
sively for this test. You can even take a course or two at the local community college if you
don't have a strong enough background in this area. If, however, you don't intend to pursue
a career that requires a score on this subtest, spend your time studying for other areas of
the ASVAB.

You have 9 minutes to answer 20 questions on this subtest on the paper version of the
ASVAB and 8 minutes to answer 16 questions on the computerized ASVAB. Although 8 or
9 minutes is sufficient time to answer the questions, it doesn't provide much time for any-
thing else — if you don't know an answer, guess and go.

Uncovering the Secrets of Electricity

One day in 1752, Benjamin Franklin was minding his own business, flying a kite in a storm.
A key was tied to the kite string and when lightning struck the metal key, Ben was struck by
the notion that lightning must be electrified air (well, it happened something like that).

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Part IV: The Whole Ball of Facts: Technical Skills

*J*BEft

■0*5!?

Although electricity was just a hobby for Ben Franklin, he made many important contribu-
tions. As a result of his famous kite flight, he created many of the terms used today when
folks talk about electricity: battery, conductor, condenser, charge, discharge, uncharged,
negative, minus, plus, electric shock, and electrician.

Electricity is a general term for the variety of phenomena resulting from the presence and
flow of electric current. You can't see electricity running through a wire (but you can cer-
tainly feel it). You only know electricity is there when you flip on the light switch and the
light turns on. Even though electricity appears to be pretty mysterious at first glance, scien-
tists understand a great deal about its properties and how it works.

Electricity is measured in three different ways:

j*" Volts: Volts measure the difference of potential between two points.

f Amperes (amps): Amps measure the number of electrons that move past a specific
point in 1 second.

v* Ohms: Ohms measure resistance, including anything that could limit the flow of
electrons.

Here are some other electricity terms that are important for you to know for the ASVAB:

v* Current: Electricity is like water — it flows. Electrical current occurs when electrons
move from one place to another. The use of conductors, such as copper and water,
allows the electrons to move freely. Insulators, such as rubber and wood, discourage
the electric current.

v* Watt: A watt measures power, the rate at which electrical energy is consumed or trans-
formed into another type of energy, such as light or heat.

v* Watt-hour: A watt-hour is the amount of energy used in 1 hour at a rate of 1 watt. Most
electricity is measured in kilowatt-hours, which is how much energy you'd use if you
ran a 1,000-watt (1-kilowatt) device for an hour. For example, 10 kilowatt-hours is
enough energy to run a 10,000-watt speaker system for an hour-long outdoor concert,
or it could run a 5,000-watt air conditioner for 2 hours or a 1,000-watt waffle iron for
10 hours. You find watt-hours by multiplying wattage by time (expressed in hours).

The following sections explain electricity in more detail.

Measuring Voltage: Do you hai/e the potential}

A circuit is just the path of an electrical current. A very simple circuit consists of several
components. For example, it may consist of a battery, one side (terminal) of which is con-
nected by a conductor (a wire) to an on/off switch, which is connected to a lamp (a light
bulb) by another wire, which is then connected back to the other side of the battery. As
long as the switch is off — which means it's set to a position so that there's an open (liter-
ally an open space) in the circuit — current cannot flow. When you flip the switch, there's a
short (meaning the open space has been closed), and current can flow from one side of the
battery, through the closed switch, through the light bulb, and back to the other terminal of
the battery, all by way of the wires connecting the components.

Voltage, which is supplied by the battery in this circuit, is the difference of the pressure
between two points in a circuit. It is sometimes called the voltage drop or difference of poten-
tial. So, for instance, a 9-volt battery supplies 9 volts of electricity. To see what the voltage
is anywhere in a circuit, you have to compare the voltage at that point to ground. Ground is
any part of a circuit (or other object that has electricity running through it) that measures

Chapter 13: Electronics Information J jQ

$mn

volts, such as the case of your radio, the base of a lamp, or the chassis of your car. The
negative terminal of a 9-volt battery is at ground potential, so the voltage from the negative
terminal to ground will measure volts. The voltage from the positive terminal to either
ground or the negative terminal of the battery will measure 9 volts.

To measure voltage in a circuit, you use a voltmeter or a multimeter, which has several
meters in one instrument. A voltmeter has two leads. To measure voltage, you place one
lead somewhere in the circuit and one lead at another location in the circuit. The voltmeter
tells you what the voltage is between those two points.

A cell (a storage compartment for electricity in a battery) has a specific voltage. For exam-
ple, in a particular battery, cells may be 1.5 volts. Therefore, you can figure out the number
of cells a battery has by dividing the voltage of the battery by 1.5. Pretty handy stuff, huh?

Examining the current of the electrical riVer

Electrons are negatively charged, and they attempt to shift from one atom to the next, to the
next, trying to get to a positive charge, such as the positive side of a battery. They're able to
shift if the material is a conductor. But if the material is an insulator, the electrons will be
much, much less able to shift because of the insulating material's molecular structure.

Electrical current is the flow — or, more precisely, the rate of flow — of electrons in a con-
ductor. Current flow can be expressed in terms of coulombs (abbreviated C), which mea-
sure charge. A coulomb is the amount of electricity provided by a current of 1 ampere
flowing for 1 second. It's called a coulomb because a guy named Charles de Coulomb dis-
covered it in the late nineteenth century, and the rules say that if you discover something,
someone will stick your name on it (not sure who made up those rules, though).

If 1 coulomb (about 6,241,500,000,000,000,000 electrons) flows past a specified point in
1 second, that's a flow rate of 1 ampere (amp, abbreviated A). An ampere represents the
strength of a current. For the sake of convenience, electrical currents are measured in
amps. Typically current is tiny, so small that it's measured in milliamperes; 1 milliampere is
one-thousandth of an ampere. Current meters, called ammeters, measure the flow of current
through a circuit.

The amount of voltage (the difference in potential) and the resistance in a circuit determine
the number of amperes along a wire — or whatever you're using to conduct the electricity
from one place to another. More voltage (for instance, a higher-voltage battery) means that
more amps flow in a wire (or conductor). You can read more about this relationship in the
next section, which discusses Ohm's law.

Resistance: Stowing the electrical rii/er

Current doesn't just flow in any properly working circuit unimpeded. Resistance pops up
along the way. If the flow of electricity needs to be regulated, resistance is deliberately set
up in a circuit. If the flow weren't regulated, the motors powering devices like can openers
and microwave ovens would quickly overheat and melt. (But before that happens, hopefully
a fuse would blow or a circuit breaker would trip, halting current flow and saving the equip-
ment.) In a sense, even a wire, such as a filament in a light bulb, is a type of resistance and
is a way to deliberately create circuit resistance.

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Part IV: The Whole Ball of Facts: Technical Skills

Adding or removing resistance

Sometimes a circuit must be opened in order to add or remove resistance. In other words,
the flow of the electricity must be interrupted in order to physically change the resistance.
Using a circuit breaker, which is a device that automatically interrupts the electrical current,
is an example of opening a circuit to control the current. When the circuit breaker trips, the
electrical device can no longer operate.

Some devices use a rheostat, which can vary the resistance without opening the circuit —
the device can continue to work even as the resistance is altered. If an application doesn't
use all the electricity, the rheostat absorbs it. A dimmer switch on a light is an example of a
rheostat. You increase the amount of resistance to dim the light and decrease the resis-
tance to brighten the light.

Ohm's (avi: Relating resistance to current and Voltage

The amount of resistance that interferes with the flow is measured in ohms (pronounced just
like those yoga chants). The symbol for ohm is the Greek letter omega, which looks like an
upside-down horseshoe: Q. Resistance can be measured by dividing the voltage measured at
any given point (the voltmeter reading) by the amount of current at the same point in a cir-
cuit (the ammeter reading). Or you can measure the resistance directly by an ohmmeter.

If you have a current flowing through a wire, three influences are present:

v* The amount of voltage, measured in volts

v* The resistance to the current, measured in ohms

v* The amount of current, measured in amps

These three units are always present in a specific relationship to each other. If you know
the value of any two of the influences, you can find the value of the third. (Yes, this requires
more math. Sorry.)

£jftBE# Ohm's law, which was first stated by Georg Simon Ohm, reads, "The current in a circuit

is directly proportional to the applied voltage and inversely proportional to the circuit
resistance," but it's actually easier to understand in mathematical terms. When stating the
relationship mathematically, abbreviations are used, where / is current, E is voltage, and R
is resistance:

Current (amperes) = „ — . - .- . A , or / = 4r
v v J Resistance (ohms) R

This essentially means that current in a basic circuit is always dependent on the voltage
and resistance in the circuit. If you use a higher-voltage battery (increase E), the resistance
doesn't change, but current in the circuit increases. By the same token, if you leave the
same battery in the circuit but increase the resistance (increase R~), current decreases.

Here are two other ways to write the same formula, solved for voltage and resistance:

Iv* Voltage = Current x Resistance, or E = IR
v* Resistance = p ^-r, or R = 4-

Ohm's law works exactly the same, no matter which format you use.

Chapter 13: Electronics Information / 1

*££&>

Measuring porter

Power is measured in watts. One watt is a very small amount of power. It would require
nearly 750 watts to equal 1 horsepower. One kilowatt represents 1,000 watts.

A kilowatt-hour (kWh) — the amount of electricity a power plant generates or a customer
uses — is equal to the energy of 1,000 watts working for one hour. Kilowatt-hours are deter-
mined by multiplying the number of kilowatts (kW) required by the number of hours of use.
For example, if you use a 40-watt light bulb 5 hours a day, you've used 200 watt-hours, or
0.2 kilowatt-hours of electrical energy.

The term watt was named to honor James Watt, the inventor of the steam engine.

Getting around to circuits

Although this section suggests that electricity flows like water, it actually flows more like
NASCAR. Electricity must be sent along the path of a closed circle (a circuit), just like all
those NASCAR speedsters roaring around the track. The drivers never actually get any-
where; they just keep driving in circles. Electrical charges are a lot like that.

However, electricity does flow like a river in one respect. In general, electricity follows the
path of least resistance. The conventional way in thinking about the electrical flow of cur-
rent is based on that the vacancies left by electrical particles "moving" from the positive (+)
terminal to the negative (-) terminal of a battery. This concept is called conventional cur-
rent. However, the military teaches current flow based on the flow of the electrons, and elec-
trons, no matter how you look at it, flow from the negative terminal to the positive terminal
(see Figure 13-1).

Figure 13-1:

A simple Terminal
electric
current.

If any of the wires leading from one terminal to the other is broken, the circuit is shot — no
more current. Current can't flow because under most circumstances, the electrons can't
bridge the open gap in a conductor (the open gap is basically air, and air is an insulator).

In some cases, current does flow through an insulator — if there's enough difference of
potential (voltage). When lightning bridges an expanse of air from a cloud to ground (or a
tree or a golfer), it's because there is a huge amount of voltage, on the order of 100 million
volts between the source of the lightning and (literally) ground.

Here's another circuit problem that may come up: A short circuit occurs when any wire acci-
dentally crosses over another wire, causing the electricity to bypass the rest of the circuit
and not follow the intended path.

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Part IV: The Whole Ball of Facts: Technical Skills

Magnetic, electric: No, not your personality

Certain magnetic effects always accompany an elec-
tric current, and these effects follow definite laws. In a
wire, the magnetic lines of force (imaginary lines used
to explain magnetic effects) are perpendicular to the
conductor and parallel to each other.

But when you wrap a wire around a core and pass
current through it, the wire forms a coil. As the lines of
force around the core take on a different shape,the field
around each turn of wire links with the fields from the
other turns of wire around it. The combined influence
of all the turns of wire produce a two-pole magnetic
field, very much like the magnetic field of a simple bar
magnet — one end of the coil is a north pole; the other
end is a south pole.

The strength of the magnetic field depends on several
factors. Here are the main ones:

v Number of turns: If you increase the number of
turns, you increase the field strength.

J-" Closeness of the turns: The closer the turns, the
stronger the field.

j-" Amount of current: If you increase current, you
increase field strength.

w Material in the core: Most coils are classified as
either air or soft iron, based on their cores. Air coils
are usually wrapped around a piece of cardboard;
soft-iron coils are wrapped around a piece of iron.
Soft iron offers a better path for magnetic lines of
force because its high permeability offers less
reluctance to magnetic flux, resulting in more lines
of force. (Think of magnetic flux as a measurement
of magnetic strength located on a two-dimensional
surface. A good example of magnetic flux would be
the magnetic strength of one side of a magnet.) The
more lines of force, the strongerthe magnetic field.

Passing a suspended loop of conductive material (wire)
through a magnetic field creates electromagnetic induc-
tion, which is the basic principle behind the electric
generator. When the conductor is standing still, cur-
rent doesn't flow through it. But when the loop starts to
rotate clockwise through the lines of force of the mag-
nets, the lines of force induce free electrons to move
through the wire.

Producing electrical effects

Electric currents can produce different effects. These effects are packaged and sold com-
mercially. The following is a description of effects produced by current and some of their
commercial applications:

v* Chemical effect: Current produces this effect when it passes through a chemical com-
pound and breaks that compound up. Also called electrolytic decomposition, this phe-
nomenon is used in electroplating, a process used to cover objects with a very thin
coating of metal.

J-" Heat effect: Conducting electricity causes wires to become heated. Heat develops
because the current must overcome the resistance of the wire. This heat energy can be
quite obvious or hardly noticeable to touch, depending on the size of the wire and the
amount of current.

v* Magnetic effect: When a wire is introduced into a magnetic field, electricity flows
through the wire and creates a magnetic field that repels a magnet. This effect is used
to create energy through electromagnetic induction, the basic principle behind the
electric generator. If the wire is wrapped around an iron core and a current is sent
through the wire, the iron becomes magnetized. (See the nearby sidebar for more on
the magnetic effect.)

j-" Physiological effect: Current produces this effect when it passes through your bicep
(or any of your muscles for that matter) and causes the muscle to contract. This effect
is used in medicine.

Chapter 13: Electronics Information / Oj

Sitiitchinq Things Up With Alternating
and Direct Current

A current doesn't always flow in one direction. A direct current (DC) does — it only and
always flows in one direction. An alternating current (AC), however, constantly changes
direction in a regular pattern. Higher voltages are easier to obtain with alternating current,
and transferring high voltage down a power line is ultimately cheaper than transferring low
voltage, so most electricity comes in the form of AC. The following sections cover some
important points about alternating and direct current.

sfiLSTl^

WER

Figuring out frequency

The number of times an alternating current changes direction per second is known as its
frequency. Hertz (Hz) is the unit of measurement for frequency. One hertz (Hz) equals one
complete cycle per second. In other words, the current makes two complete alternations of
direction.

The AC (alternating current, not the air conditioner) in your house probably completes
60 alternating cycles per second. Therefore, the AC in your house has a frequency of 60 Hz.
Most electronic devices operate at higher frequencies; therefore, frequencies may be mea-
sured in kilohertz (kHz, 1,000 hertz), megahertz (MHz, 1 million hertz) or even gigahertz
(GHz, 1 billion hertz).

AM radio stations often broadcast in the 530-1,700 kHz range. Television stations may
broadcast at as low as 7 to as high as 1,002 MHz. Radar operates in the 1-40 GHz range.

Impedance: Join the resistance!

Resistance interferes with the flow of current in a circuit. But the flow of current is also
impeded by two properties of alternating currents:

v* Capacitive reactance (capacitance): Capacitance is the storage of energy that occurs
in a nonconductor. This property resists any change in voltage in a circuit.

u* Inductive reactance (inductance): Inductance is the property that causes an electro-
motive force (another way of saying voltage) to be induced in a circuit.

These two types of reactance combine to impede the flow of current. Impedance can be
expressed as the ratio of electromotive force to the current:

Impedance =

Electromotive force
Current

Electronic devices often require a specific capacitive or inductive reactance to work. Capacitors
and inductors are devices used in circuits to provide the type of reactance needed. Capacitors
are rated in microfarads (uF), and inductors are rated in millihenries (mH).

You can relate impedance to Ohm's law in reference to AC circuits. Simply substitute resis-
tance in Ohm's law with impedance and voltage with electromotive force.

/ ()l) Part IV: The Whole Ball of Facts: Technical Skills

Sorting out capacitors and inductors

Capacitors store or hold a charge of electrons. In an AC
circuit, because AC voltage goes positive and negative
in each cycle, the capacitor is constantly charging and
discharging. The rate of the charging and discharging
acts as opposition to the changing AC voltage — as a
resistive effect called capacitive reactance.

Inductors are coils of wire that make use of the proper-
ties of a magnetic field. The property specifically desired
is the flow of current through the wire. With full current.

the magnetic field is at its maximum. However, if you
take away the current, the field doesn't disappear imme-
diately. It decays gradually, and the decay continues to
push electrons in the path they were going. But in an
AC circuit, the current constantly reverses. The rate of
changing current flow and the resulting collapse and
regeneration of the magnetic field in the coil act as
opposition to changing AC current — a resistive effect
called inductive reactance.

Rectifying the situation: Going direct

Certain electronic circuits are engineered to change alternating current to direct current.
The process of making the change is called rectification, and the circuits that perform the
rectification are called rectifiers.

Rectifiers contain semiconductor diodes, a component made of a material with conductivity
somewhere between that of a conductor and an insulator. Diodes conduct electricity in only
one direction. Rectification also often requires inductors and capacitors (see the preceding
section).

Rectification helps appliances run at cooler temperatures and allows them to run at vari-
able speeds. Devices typically need direct current to run properly. The process of rectifica-
tion changes the incoming AC to DC.

Turning up the old transistor radio

A transistor is a semiconductor (an object that conducts electricity poorly at low tempera-
tures) that controls the flow of electricity in a circuit. It's usually made of germanium or sili-
con. This electrical device can amplify a signal, which is why it's used in transistor radios.
Transistors have many properties:

p" Unlike rectifier diodes (see the preceding section), a transistor doesn't require a
vacuum to operate.

f Transistors are small, require little power, and last a long time.

t* A transistor contains at least three terminals:

• The emitter is the voltage output.

• The base acts like a gate, and the voltage at the base controls the flow of current
through the transistor (and therefore the voltage).

• The collector is the voltage input.

Chapter 13: Electronics Information / \)5

Picture It: becodinq Electrical Circuit Codes

Electronic circuits can be combined to create complex systems, such as those required to
operate a stereo system. Block diagrams are used to show the various combined circuits
that form a complex system.

Many of the questions on the Electronics Information subtest require you to identify an
electronic component symbol and know what that component does in an electronic circuit.
Figure 13-2 shows the most common component symbols. The figure's items are grouped
based on similarity of functions. For example, cells, batteries, DC power supplies, and AC
power supplies all have similar functions (they supply power to the circuit).

So, what do all these electronic doodads do when connected in a circuit? I cover each item
in the following list:

v* Wires: Wires are used to pass current from one part of the component to another.
Wires that are connected to each other are indicated by a dark circle and are called
joined wires. Sometimes in complex circuit diagrams, it's necessary to draw wires
crossing even though they aren't connected. In this case, the dark circle is omitted, or
a hump symbol is drawn to make it clear the wires aren't connected — this is called
unjoined wires.

e* Cell: A cell supplies electrical current. Some call this a battery, but technically a battery
is more than one cell. The large terminal (on the left side of the cell image in Figure 13-2)
is positive.

v* Battery: A battery is two or more cells. The large terminal is positive.

i*" DC power supply: A DC power supply provides direct current. Direct current always
flows in one direction.

(-" AC power supply: An AC power supply provides alternating current. Alternating cur-
rent constantly changes direction at a specific frequency.

j*" Fuse: A fuse is a safety device that blows (melts) if the current flowing through it
exceeds a specified value.

v* Transformer: A transformer consists of two coils of wire linked by an iron core.
Transformers are used to step up (increase) and step down (decrease) AC voltages.
No electrical connection exists between the coils. Energy is transferred between the
coils by the magnetic field in the core.

i*" Ground: A ground is a connection to the earth.

v* Transducer: A transducer is a device that converts energy from one form to another.
Here are various types of transducers:

• Lighting lamp: Converts electrical energy to light, such as in a light bulb or auto-
mobile headlight

• Indicator lamp: Converts electrical energy to light for such uses as a warning
light on a car's dashboard

• Motor: Converts electrical energy to kinetic energy (motion)

• Heater: Converts electrical energy to heat

• Bells and buzzers: Convert electrical energy to sound

• Microphone: Converts sound to electrical energy

• Earphones and speakers: Convert electrical energy to sound

/ 66 Part IV: The Whole BaM of Facts: Technical Skills

Wire

Joined Wires Unjoined Wires

Cell

H ► I

Battery

DC Power Supply AC Power Supply

Fuse

Transformer

Inductor

2-Way Switch

Ground

fun-
Heater

Push Switch

Dual On/Off Switch

Lighting Lamp Indicator Lamp

Bell

Push-to-Break
Switch

I f ONO

Relay

X] X3 id

Buzzer Microphone Earphone Speaker

On/Off Switch

-AWW 1 1—

Resistor Resistor

Rheostat

Potentiometer

Figure 13-2: Po | arized Capacitor Variable Capacitor

Symbols in

electronic

circuit

diagrams.

^^^^^^^ m Transistor Amplifier

Preset Variable
Resistor

— D+

Diode

Antenna

Capacitor

Light-Emitting Diode
(LED)

p* Inductor: An inductor is a coil of wire that creates a magnetic field when current passes
through it.

p" Switch: Here are several types of switches:

• Push switch: A push switch allows current to flow only when the button is
pressed, such as in a doorbell.

• Push-to-break switch: With this switch, the circuit is normally closed (the device
is on), and the circuit is open (device is off) only when the button is pressed.

• On/off switch: An on/off switch allows current to flow only when it's in the closed
(on) position.

• Two-way switch: A two-way switch directs the flow of current to one of two
routes, according to its position.

• Dual on/off switch: This type is often used to switch main electricity because it
can isolate both the live and neutral connections.

• Relay (relay switch): A relay is an electrically operated switch that may operate
multiple switches at one time. Current flowing through a coil sets up a magnetic
field, which causes the lever(s) to move, effectively changing the (relay) switch's
position(s).

Chapter 13: Electronics Information J 07

v* Resistor (nonvariable): There are two different versions of the basic resistor symbol.
Resistors restrict the flow of electric current. Resistors are rated in ohms and have a
color code on them to indicate their value, tolerance, and sometimes quality. The band
code is as follows:

• Black is

• Brown is 1

• Red is 2

• Orange is 3

• Yellow is 4

• Green is 5

• Blue is 6

• Violet is 7

• Gray is 8

• White is 9

The first and second bands on the resistor are the first two digits in the resistor's
value. The next band indicates the multiplier (number of zeros after the first two num-
bers). So if the first band is red, the second is yellow, and the third band is orange, the
resistor's value is 24,000 ohms. A gold or silver band after the first bands indicates tol-
erance, and a quality band may follow the tolerance band.

v* Variable resistor: Variable resistors also restrict the flow of electric current. There are
several symbols in use in circuit diagrams for standard variable and preset variable
resistors. Types of variable resistors include the following:

• Rheostat: A type of variable resistor with two contacts, usually used to control
current; examples of controlling current would be adjusting lamp brightness or
adjusting motor speed

• Potentiometer: A type of variable resistor with three contacts that's used to con-
trol voltage

• Preset variable resistor: A device that operates with a small screwdriver or simi-
lar tool; it's designed to be set when the circuit is made and then left without fur-
ther adjustment

j*" Capacitor: Capacitors store electric charge. They're used with resistors in timing cir-
cuits because it takes time for a capacitor to fill with charge. They're also used in filter
circuits because capacitors easily pass AC (changing voltage) signals but they block
DC (constant voltage) signals. Two types of capacitors include the following:

• Polarized capacitors must be connected the correct way in circuit.

• Variable capacitors are used most often in radio tuning circuits.

«*" Diode: Diodes allow electricity to flow in only one direction. The arrow of the circuit
symbol shows the direction in which the current can flow. Diodes are the electrical
version of a valve, and early diodes were actually called valves. Light-emitting diodes
(LEDs) emit light when an electric current passes through them. Specialized diodes,
called Zener diodes, do allow current in the opposite direction after a threshold is met.

168

Part IV: The Whole Ball of Facts: Technical Skills

v* Transistor: Transistors amplify current. For example, they can be used to amplify the
small output current from a logic chip so it can operate a lamp, relay, or other high-
current device.

i*" Amplifier: An amplifier isn't actually an electronic component but instead is a complex
circuit. The block diagram symbol shows where an amplifier circuit would be con-
nected. Amplifier circuits are used to magnify power, current, or voltage.

v* Antenna: An antenna is a device designed to receive and/or transmit radio signals.

Circuit diagrams show how electronic components are connected together. These diagrams
show the connections as clearly as possible with all wires drawn neatly as straight lines.
The actual layout of the components is usually quite different from the circuit diagram,
however. Circuit diagrams are useful when testing a circuit and for understanding how it
works. Figure 13-3 shows a diagram of an adjustable timer circuit. See how many compo-
nents you can identify.

Adjustable Timer Circuit

Figure 13-3:

An adjust-
able timer [
circuit.

Eyeinq Some Electronic Information Test Tips

When it comes to the electronics test, don't feel like you have to know as much as Ben
Franklin to get a passing score. Just use your common sense. If a question asks, "What's the
safest way to run an extension cord to a reading light?" the answer "across the middle of
the floor" is probably going to be wrong.

You can also figure out quite a few answers if you remember these units of measure:

f Current: Amperes (or amps)

v* Voltage: Volts

i*" Resistance: Ohms

v* Power: Watts

i*" Energy: Watt-hours

Chapter 13: Electronics Information j Q Q

**!!?

Memorizing simple principles

If you commit the following principles to memory, you'll have an easier time succeeding on
the Electronics Information subtest:

n" Ohm's law: Current =

Voltage

Resistance

j-" Power (watts) = Voltage (volts) x Current (amperes), or P = EI

p" Current flows from a negative pole to a positive pole.

V A closed circuit must exist for electricity to flow. (Think NASCAR.)

p" Alternating current (AC) changes direction constantly at a constant rate. The number
of times a current completes two alternations of direction per second is known as its
frequency; the unit of measurement for frequency is the hertz (Hz).

p" Electronic devices operate at very high frequencies.

p" Electronic devices often require a specific capacitive or inductive reactance to work.
Capacitors and inductors are devices used in circuits to provide the type of reactance
needed.

n" Devices that change alternating current to direct current are called rectifiers.

v A transistor can amplify a signal.

If you need a good score on this subtest to get your military dream job or you want to
rebuild that old television set without sacrificing your garage, you may want to check out
Electronics For Dummies by Gordon McComb and Earl Boysen (Wiley) for additional help.

Playing the guessing game

The Electronics Information subtest is the type of test where you either know the answer or
you don't. But if you don't know the answer, you should still guess. Remember, you don't
have a lot of time to ponder the answer choices. Guess and move on. To increase your
chances of guessing correctly, you can often eliminate an incorrect answer.

Sometimes one answer is obviously wrong, or one answer is more obviously right than
another. The electronics answer is usually the right answer. Therefore, an answer that has
to do with how much something costs or how pretty it looks will probably be wrong.

Not all questions are specifically electronics questions. You may be asked, "A mil measures
what quantity?" Think about how you've seen that prefix used before, such as in the word
millimeter. A millimeter, you may remember, is one-thousandth of a meter. So you may be
safe in assuming that a mil is one-thousandth of an inch. For additional guessing help, flip
back to Chapter 3.

170

Part IV: The Whole Ball of Facts: Technical Skills

Chapter 14

Assembling Objects

In This Chapter

Checking out the newest ASVAB subtest
Connecting the dots and putting the pieces together
Getting your test score into shape

^M lthough much of the ASVAB measures academic knowledge at the high school level,
¥ \ Assembling Objects is a subtest that probably doesn't resemble any of your high
school classes (unless your high school offered a course in Jigsaw Puzzles 101).

The Assembling Objects subtest is designed to measure your ability to look at pieces of an
object and determine how those pieces should fit together (technically called visualizing
spatial relationships'). Spatial skills, which help people figure out maps and interpret techni-
cal drawings, are important to everyday living as well as for performing well in school and
on the job. Society today places greater demands on spatial skills, such as interpretation of
graphs, maps, architectural drawings, and X-rays.

The Assembling Objects subtest of the CAT-ASVAB consists of 16 graphical problems that
must be solved in 15 minutes; the paper version of the ASVAB has 25 questions to be solved
in 16 minutes. That gives you a little less than a minute for each question (not counting any
time you take out to scratch your head). That's plenty of time to finish if you're good at
jigsaw puzzles.

Getting the Picture about Assembling Objects

The Assembling Objects subtest is relatively new to the ASVAB. It was added when the
ASVAB was last revised, when the Numerical Operations and Coding Speed subtests were
deleted. First it was added only to the computerized version of the ASVAB, and then it was
added to the paper enlistment version about a year later. If you're taking the high school
version of the ASVAB or the in-service version (Armed Forces Classification Test), you
won't see this subtest.

At the time of this writing, only the Navy uses the score from the Assembling Objects sub-
test for job qualification purposes. Additionally, only a handful of ratings (what the Navy
calls jobs) require a score in this area. The other branches don't use the results of this sub-
test at all, but they may in the future. For details about which Navy enlisted jobs require a
score in this area, see Appendix A.

The upshot is that unless you're planning to join the Navy, in one of only a handful of Navy
enlisted jobs, you can safely ignore this entire chapter. Don't say I never gave you a gift.

172

Part IV: The Whole Ball of Facts: Technical Skills

Adopting the AO subtest

It's interesting that the Navy is the only service to use
scores from the Assembling Objects subtest, because it
was an Army study that brought this subtest to life. Way
back in 1994, the Army concluded a study called Project
A. (Kind of makes you wonder if the people in charge
of naming military projects were on vacation that week,
doesn't it?) Project A was all about trying to improve
the selection and classification of enlisted personnel.
The Assembling Objects subtest was a major product
of this effort. The U.S. Army Research Institute for the
Behavioral and Social Sciences found Assembling

Objects questions to be an excellent measure of both
overall spatial ability and complex problem-solving skills.

The Army developed two types of Assembling Objects
questions and tested them under field conditions for a few
years. A mere ten years later, the Department of Defense
incorporated the subtests into the ASVAB. (You just got
to love the speed at which the military makes changes.)
By that time, the Army had decided that they really didn't
need to use this new subtest at all. But the Navy said,
"Hey, that looks pretty cool. .. let's give it a try!"

Tu/o Types of Questions for the Price of One

The Assembling Objects subtest has two types of questions, both of which consist of five
separate drawings. In the first drawing, you see a picture with various disassembled parts,
followed by four drawings that show the parts assembled or connected. Your task is to
choose the drawing that shows what the parts may actually look like after they're assem-
bled or connected properly.

*3*BE*

Both types of Assembling Objects problems require you to perform mental rotation —
a process through which you predict what an array of objects would look like if they were
rotated or turned by some number of degrees.

Putting slot A into tab B: Connectors

The first type of problem presents you with simple geometric figures such as stars, cloud
shapes, letter shapes, circles, and triangles. In the first drawing, you can see shapes and
lines labeled with dots and the letters A and B. These letters and dots indicate points of
attachment.

The next four drawings show possible solutions of what the shapes would look like if con-
nected at designated points by the line. The shapes may be reoriented or rotated from what
you observe in the first drawing. The correct solution shows the line connected correctly to
reflect the points shown in the first drawing.

Look at Figure 14-1 and see whether you can solve it. In the first drawing, you see a star and
a sort of lopsided T. There's a small dot on the short appendage of the T, labeled A, and a
dot on one of the points of the star, labeled B.

Figure 14-1:

Identifying

points and

shapes.

g|T*t tl/

Chapter 14: Assembling Objects j 7j

In Figure 14-1, Choice (A) is the correct solution. Choices (B) and (C) include shapes that
aren't included in the first drawing, so they're obviously incorrect. Although Choice (D) has
the correct shapes, they aren't connected at the same points depicted in the first drawing.

Okay that sounds simple, doesn't it? Don't worry; it gets more complicated (sorry to burst
your bubble). Figure 14-2 shows the same problem but with a different twist.

Figure 14-2:

Rotated

shapes

make the

problem

harder.

•T"i

J 1

Choice (A) is the correct solution for the problem in Figure 14-2. In this case, the two shapes
have been repositioned and rotated.

jttNG/

On the flip side: Avoiding mirrors

Mirroring (or flipping or reflecting) isn't the same as rotation, as Figure 14-3 illustrates. The
shape in Box B isn't the same as the shape in Box A. It's a mirror image. No matter how you
rotate the shape in Box A, it will never look like the shape in Box B. Think of it this way —
although you can turn a jigsaw puzzle piece upside down so the picture side is facing the
table, it may fit, but that's not the proper method of putting the puzzle together. (It wouldn't
look very pretty, either). The Assembling Objects subtest is the same way. The possible
solutions may include shapes that are reflections of a shape shown in the first drawing, but
they'll never be the correct solution.

Figure 14-3:

Figuring out

mirrored

shapes

(AandB)

and rotated

shapes.

**BE»

Crossing ot/er the right places

If a shape in the first drawing shows a line that goes through any part of the shape, the cor-
rect solution must also reflect the same line-shape relationship. Check out Figure 14-4. In
the first drawing, Point B is in the center of the star. But note the line intersects the star at
one of its indentations and not one of its points. That means the correct solution shows the
same intersection.

Figure 14-4:

Line-shape
relation-
ships.

•T'i

•4

17 It

Part IV: The Whole Ball of Facts: Technical Skills

In this example, Choice (B) is the correct solution. At first glance, Choice (C) looks like it
could be correct. Can you spot the reason it's not the correct solution? Right! The lopsided
T shape in the image is a reflection of the shape shown in the first drawing.

Putting it all together

You're starting to see the shape of things! (I'm sorry, but these little zingers just keep pop-
ping out.) Try a couple more, just to get into shape. Look at Figure 14-5.

Figure 14-5:

Another
example of
spatial rela-
tionships.

<2.

A-

In Figure 14-5, did you select Choice (C) as the correct answer? If so, good job! Choice (A) is
incorrect because the line intersects the triangle at the wrong point and conection point A
is misplaced. Choice (B) is incorrect because the weird shape is actually a mirror image of
the shape shown in the first drawing. Choice (D) is incorrect because the points don't corre-
late to the points depicted in the first drawing.

Now try Figure 14-6. The first drawing includes a shape that kind of looks like a Y and a
shape that looks like the letter C.

Figure 14-6:

shapes to

test your

spatial skills.

B^ §Ki §hJ l^@ ^

The correct answer for the problem shown in Figure 14-6 is Choice (B). Choice (A) is incor-
rect because the Y shape is a mirror image of the shape shown in the first drawing, and the
connection points don't correspond to the first drawing's points. Choice (C) is incorrect
because the Y shape is a mirror image of the shape shown in the first drawing. Choice (D) is
incorrect because the Y shape is a different shape (the stem is much shorter) than the
shape shown in the first drawing and because the connection dot on the C shape is in the
wrong location.

Solving the jiqsaW puzzle: Shapes

Many people may find the second type of Assembling Objects problem easier than the con-
nection problems. This type of problem is very much like a jigsaw puzzle, except it doesn't
result in a picture of the Statue of Liberty or a map of the United States. Also, there's a heck
of a lot fewer pieces than that 1,000-piece puzzle your parents kept insisting on buying you.
The difficulty lies in the fact that you can't use your hands to twist the pieces around on the
table in order to see how they fit. You have to rotate and move the pieces mentally.

Chapter 14: Assembling Objects j (5

In Figure 14-7, the solution is pretty straightforward.

Figure 14-7:

A simple

jigsaw

example.

By mentally sliding the shapes in the first drawing together, it's easy to see that they fit
together to form the picture shown in Choice (A). Look at Figure 14-8.

Figure 14-8:

Putting
the pieces

together

with

rotation.

Choice (A) is the correct answer. The figure shown in Choice (A) is the same as the figure
depicted in Choice (A) of Figure 14-7, except it's been rotated.

The previous two figures were warm-up exercises — the questions on the ASVAB are harder.
Check out Figure 14-9 for a better representation of the types of questions on the ASVAB.

Figure 14-9:

A harder

example of

spatial

problems.

Pay attention to the curve of the leaf shape inside the square. It's not bowed out as in
Choice (B) — the edges have more of a wave shape. Choice (C) has that shape too thin. If
you selected Choice (D) as the correct solution, give yourself a pat on the back. Examining
spatial relationships can help locate the correct answer with ease. Try a couple more exam-
ples to see if you've gotten the hang of it. Check out Figure 14-10.

Figure 14-10:

Practice

mentally

rotating and

relocating

pieces of
puzzles.

176

Part IV: The Whole Ball of Facts: Technical Skills

In Figure 14-10, Choice (B) is the correct answer. Mentally rotate and relocate the pieces in
the first picture until you can see how they fit together to form the shape in Choice (B). In
the puzzle, three pieces have both a curved edge and a single straight edge. Practice elimi-
nating choices that lack these characteristics. Choice (A) lacks these shapes, so you can
discount it right away. Notice the curved pieces are all different sizes. Visualize fitting these
pieces of the puzzle in your mind and compare the sizes and differences. Now try Figure 14-11.

Figure 14-11:

Putting the

pieces of

-A

1(\

the puzzle

together

l/&n

with your
mental spa-
tial skills.

In Figure 14-11, Choice (A) is the correct answer. If you didn't get this one quite right, head
to Chapter 15 for additional practice and Chapters 16, 18, and 20 for practice examinations.

Tips far the Assembling Objects Subtest

In following sections, I offer some tips for improving your score on the Assembling Objects
subtest. I offer strategies for eliminating wrong answers during the test, and I name some
ways you can improve your spatial skills in general (which may come in handy the next time
you have to read a map, too).

*>*!!?

Comparing one piece or point at a time

On the Assembling Objects subtest, you can sometimes improve your odds of getting the
answer right if you select just one shape from the first drawing and then quickly look at
each of the choices to see whether that shape is represented there but in a different orien-
tation. This process can help you quickly eliminate answer choices that are obviously
wrong.

On connection-type problems, note the position of the dot on one of the shapes in the first
drawing and then quickly scan the possible answers, eliminating any choice that depicts the
dot in a different location or that shows the line passing through the shape at a different
point than shown in the first drawing.

Remember to be aware of mirror images — shapes that are reflected (instead of rotated)
from the image shown in the first drawing. The tricky test-makers often make use of such
mirror representations to see whether they can trick your eyes.

Chapter 14: Assembling Objects J 77

Visualizing success: Practicing
spatial skills ahead of time

Researchers at the University of Chicago have determined that your basic foundation for
spatial skills is established at a very early age, perhaps as young as age 4 or 5. But don't
worry. That doesn't mean all is lost if your parents never got you that model rocket kit you
wanted. The same research has concluded that you can still improve spatial skills by engag-
ing in activities that are spatially orientated. Some of those activities include the following:

j"* Practicing reading maps: Map reading can help you develop the ability to gauge scales
of size and direction between related objects (roads, rivers, towns, cities, and so on).

v^ Putting together jigsaw puzzles: This way is an obvious form of practice for improving
your spatial perceptions.

j*"* Playing puzzle games online: Many puzzle games at free online game sites exercise
the skill of identifying spatial relationships and visual similarities.

j*"* Playing graphical computer games: Computer games may help you to improve your
spatial skills. A study conducted in the United Kingdom showed that children who
played computer games consistently scored higher on spatial aptitude tests than chil-
dren who didn't play the games.

c" Sketching: Look at an object or a picture and attempt to sketch it as viewed from a dif-
ferent view. This exercise can help you to improve your ability to mentally visualize
angles.

178

Part IV: The Whole Ball of Facts: Technical Skills

Chapter 15

Facing the Facts: Technical
Skills Practice Questions

In This Chapter

Taking a stab at General Science questions
Getting a handle on Auto & Shop Information
Practicing your Mechanical Comprehension knowledge
Tuning in to the Electronics Information section of the ASVAB
Building a better score on an Assembling Objects practice test

m t's time to see a few examples of what the ASVAB technical skills questions look like.

«C None of these subtests are used in calculating your AFQT score (the score used to deter-
mine your general qualification to join the military), but they may be used in computing the
line score you need to get the military job you want. See Appendix A to determine whether
you need to do well on any of these subtest areas for the job that you want.

On the actual paper version of the ASVAB (and on the full-length practice tests in the
following chapters), you get 25 General Science questions, 25 Auto & Shop questions,
25 Mechanical Comprehension questions, 20 Electronics Information questions, and
16 Assembling Objects graphical problems. The CAT-ASVAB gives you 16 General Science
questions, 16 Electronics Information questions, 11 Auto Information questions, 11 Shop
Information questions, 16 Mechanical Comprehension Questions, and 16 Assembling
Objects questions. I don't want you to tire out too quickly, so in this chapter, you get only
eight sample questions in each area.

General Science Practice Questions

General science is a hard topic to study for because the field is so broad. To score well on
this subtest, you pretty much have to wade through the textbooks and memorize the facts.
You can also check out Chapter 10 for additional help. See how well you do on the following
eight practice questions.

1. If the temperature in Fahrenheit is 212 degrees, the temperature in Celsius is

(A) degrees.

(B) 32 degrees.

(D) 106 degrees.

Measured in Celsius, the boiling point of water is 100 degrees. If you don't have this
memorized, you can calculate it. To convert from Fahrenheit to Celsius, use the formula
C = jy(F- 32). The correct answer is Choice (C).

/ 80 Part IV: The Whole BaM of Facts: Technical Skills

2. A cell nucleus is often referred to as the

(A) control center.

(B) cytoskeleton.

(D) chromosome.

The nucleus contains most of the cell's genetic material and is often referred to as the control
center of the cell, so the correct answer is (A).

3. The human circulatory system

(A) uses air to release energy.

(B) processes food and eliminates waste.

(D) controls movement of joints.

The respiratory system uses air to release energy, the digestive system processes food and
eliminates waste, and the musculoskeletal system controls the movement of joints. The cor-
rect answer is Choice (C).

4. Compasses work by

(A) measuring heat in the air.

(B) reacting to magnetic fields.

(D) magic.

A compass is a device that takes advantage of the Earth's magnetic field. Choice (B) is the
correct answer.

5. If an atom has one proton and one electron, the atomic number is

(A) 2

(B) 10

(D) 1

The atomic number refers to the number of protons an atom has in its nucleus. Choice (D) is
the correct answer.

6. The element with the lowest atomic number is

(A) hydrogen.

(B) helium.

(D) uranium.

Hydrogen has an atomic number of 1. The atomic numbers for the other elements listed are
2 (helium), 3 (lithium), and 92 (uranium). The correct answer is Choice (A).

Chapter 15: Facing the Facts: Technical Skills Practice Questions / $ j

7. Absolute zero is equivalent to

(A) degrees Kelvin.

(B) kelvins.

(D) -273.15 kelvins.

Absolute zero is -273.15 degrees Celsius, which is equivalent to kelvins. Temperatures
stated in the Kelvin scale are measured by using units of kelvins, not degrees. The correct
answer is Choice (B).

8. A comet's tail is visible when

(A) the metal alloys react to the atmospheric change.

(B) the ice and rock collide.

(D) the comet passes the Kuiper Belt.

Comets are balls composed mainly of ice and rock. The comet's tail is formed when the ice
turns into gas from the heat of the sun; therefore, the comet must be closer to the sun for
the tail to be visible. The correct answer is Choice (C).

Auto & Shop Information Practice Questions

If you like to tinker with cars and your idea of a fun weekend is to rebuild the engine, you
should do well on this subtest without too much additional study. If your idea of fixing your
car involves calling that guy down the street, a little extra study may be in order. Check out
Chapter 1 1 for help with this area.

9. A two-penny nail is

(A) thicker than a lOd nail.

(B) shorter than a lOd nail.

(D) harder than a lOd nail.

Penny, abbreviated d (for the ancient Roman denarius coin), indicates length; a 2d nail is
shorter than a lOd nail. Choice (B) is the correct answer.

10. A carburetor has the same function as a/an

(A) distributor.

(B) fuel-injection system.

(D) exhaust system.

The alternator, exhaust system, and distributor all have very different purposes from the
carburetor, which combines the fuel and air mixture and sends it to the engine, just as the
fuel-injection system does. Therefore, Choice (B) is the correct answer.

/ 82 Part IV: The Whole BaM of Facts: Technical Skills

11. An engine's rotational energy is stored by using which mechanical device?

(A) connecting rod.

(B) rear axle.

(D) cylinder.

The flywheel accelerates a rotor to a high speed and uses rotational energy to maintain and
store the energy to keep the engine speed constant as the flywheel and rotor work together.
The correct answer is Choice (C). As for the other devices, the drive shaft turns the rear
axle. The cylinder contains the piston that moves the connecting rod that's connected to
the crankshaft, which turns the flywheel.

12. A hacksaw is used to cut

(A) with the grain of wood.

(B) against the grain of wood.

(D) metal.

The hacksaw has a blade specifically designed to cut metal, not wood. Choice (D) is the cor-
rect answer.

13. To drive a cold chisel, the best object to use would be

(A) a frozen hammer.

(B) a warm sledge.

(D) your foot.

A hammer has a smaller, harder striking surface than a mallet. A mallet won't damage the
chisel (or the object being chiseled, should the mallet slip off the chisel). A sledge is excep-
tionally large and heavy and is therefore inappropriate for this use. Temperature of the
striking object is irrelevant. Choice (C) is the correct answer.

14. Which of the following is NOT normally part of an automotive tune-up?

(A) Replace the air filter.

(B) Replace the spark plugs.

(D) Check the fluids.

A general automotive tune-up consists of checking/replacing the following: air and fuel filter,
belts, spark plugs, distributor cap, battery, clutch (if it's manual), engine timing, fluids, igni-
tion timing, and valves. You can also change the positive crankcase ventilation valve and
change the points and condenser if you have an older vehicle. Replacing the CV (constant
velocity) axles is something that is accomplished when they become worn. Choice (C) is the
correct answer.

Chapter 15: Facing the Facts: Technical Skills Practice Questions f OD

15. Antifreeze is used to

(A) prevent the engine from overheating.

(B) prevent water in the cooling system from freezing.

(D) all of the above

Antifreeze raises the boiling point of water and lowers the freezing point. This process
keeps the water in the cooling system from boiling away or freezing. Either condition can
cause damage to the engine. The correct answer is Choice (D).

16. The best tool for cutting curves or shapes in wood is a

(A) ripsaw.

(B) crosscut saw.

(D) pliant saw.

Coping saws have thin blades with many teeth and are specifically designed to cut curves
and shapes in wood. The correct answer is Choice (C).

Mechanical Comprehension Practice Questions

Mechanical comprehension is all about figuring out how machines and mechanical mechanisms
operate. A solid background in mechanical physics is a big advantage in scoring well in this
area. You can flip back to Chapter 12 if you need additional help with mechanical info. Basic
math skills are also a plus in this area. Test yourself with the next several questions.

17. The moisture that forms on the inside of a window on a cold day is called

(A) condensation.

(B) distillation.

(D) tarnation.

Distillation is the process of extracting or refining a substance using both boiling and con-
densation. Evaporation is the process of removing moisture from the surface of a liquid —
the water molecules escape the surface and assume gas form. Tarnation is an interjection
used to express anger. The correct answer is Choice (A), condensation.

18. If a 200-pound barrel must be lifted 4 feet to the bed of a box truck, an inclined plane will
reduce the amount of effort required to move the barrel by half if the inclined plane is

(A) 2 feet long.

(B) 6 feet long.

(D) 9 feet long.

The formula used for determining how an inclined plane reduces effort is Length of Ramp *
Height of Ramp = Weight of the Object * Force, or x ± 4 = 200 * 100. The amount of force
needed to lift the object is equivalent to the object's weight, but the question wants to
reduce that amount of force to half, so half of the object's weight is 100. Now do the math:
Xt4x4 = 2x4;x=8. The correct answer is Choice (C).

/ SI) Part IV: The Whole BaM of Facts: Technical Skills

19. Two people are carrying a 100-pound crate on a 2- x 8- x 12-foot board. To distribute the
load evenly between the two people, the crate should be placed

(A) 2 feet from the end of the board.

(B) in the middle of the board.

(D) The load can't be evenly distributed.

If the weight is placed closer to one person or the other, that person would carry more of
the load, so the weight should be placed in the middle. Choice (B) is the correct answer.

20. Wheel A has a diameter of 9 feet. Wheel B has a diameter of 12 feet. If both wheels revolve at
the same rate, Wheel B will cover a linear distance of 24 feet

(A) at the same speed as Wheel A.

(B) more slowly than Wheel A.

(D) more quickly than Wheel A.

Because Wheel A has a smaller circumference, it covers a shorter linear distance than
Wheel B when turning at the same rate. Thus, Wheel B covers the distance of 24 feet faster
than Wheel A. Choice (C) is inaccurate because the diameter of Wheel A is not exactly half
the diameter of Wheel B. If both wheels revolve at the same rate, then Wheel A turns 25%
more slowly than Wheel B, because wheel A's diameter is three-quarters of wheel B's.
Choice (D) is the correct answer.

21. Not including friction, a stationary single pulley gives a mechanical advantage of

(A) 2.

(B) 4.

(D) 1.

A stationary single pulley allows you to change the direction of force but doesn't result in
an increased mechanical advantage. The correct answer is Choice (D).

22. Four gears are connected in a series. If Gear #1 is turning clockwise, Gear #4 will turn

(A) clockwise.

(B) counterclockwise.

(D) more slowly than Gear #1.

Gears connected in series turn in opposite directions of each other. Gears 1 and 3 rotate
clockwise, and Gears 2 and 4 rotate counterclockwise. The size of gears is unknown, so
there isn't enough information to determine whether (C) or (D) is correct. The correct
answer is Choice (B).

Chapter 15: Facing the Facts: Technical Skills Practice Questions f OD

23. The sideways force one feels when a car turns sharply is often called
A) thrust force.

(B) angle force.

(D) positive force.

Although commonly referred to as centrifugal force, this property isn't actually a force at all
but is rather a property of inertia, one of Newton's laws of motion. As the car turns, your
body is trying to continue traveling in a straight line. The correct answer is Choice (C).

24. When two or more forces act to balance each other out, the condition is called

(A) equilibrium.

(B) static recoil.

(D) concurrent forces.

When two or more forces interact so that their combination cancels the other(s) out,
there's a state of equilibrium. In this state, the velocity (speed and direction) of an object
doesn't change. Choice (A) is the correct answer.

Electronics Information Practice Questions

The questions in this section measure your knowledge of basic electronics principles.
Chapter 13 contains a more in-depth discussion of electronics if you need some help.
For now, give these questions a try.

25. What does the abbreviation DC stand for?

(A) duplicate charge

(B) direct charge

(D) diode current

DC stands for direct current. I made up the other choices. The correct answer is Choice (C).

26. Which of the following is the ohm symbol?

(A) Z

(B) A
(C)O

(D) n

Remember, the upside-down horseshoe (the Greek letter omega) is the symbol for ohm, the
measure of electrical resistance. The correct answer is Choice (D).

/ 86 Part IV: The Whole BaM of Facts: Technical Skills

27. Which of the following has the least resistance?

(A) iron

(B) rubber

(D) wood

Silver is the best conductor of electricity of those listed here. Therefore, it offers the least
resistance to an electric current. The correct answer is Choice (C).

28. What is the point at which electrical connections (such as two wires) are made?

(A) terminal

(B) trigger

(D) transformer

A terminal is a device that connects electrical circuits together, a trigger initiates a circuit
action, a transmitter is a device used to achieve transmission, and a transformer is an induc-
tor with two or more windings. Windings are magnetic wires that are coated with enamel
and wrapped around the core of a transformer. The primary winding is driven by transis-
tors, and the secondary winding is driven by the core's magnetic field, produced by the pri-
mary winding. Choice (B) is the correct answer.

29. A device used to amplify a signal is called a

(A) diode.

(B) transformer.

(D) transistor.

A diode is a semiconductor that conducts electricity in one direction only; a transformer is a
device that changes voltage (either "transforming" low voltage to high voltage or high volt-
age to low voltage); a rectifier is a circuit that changes alternating current to direct current.
Choice (D) is the correct answer.

30. The amount of electrical power is measured in units called

(A) volts.

(B) amperes.

(D) ohms.

A watt measures the amount of power, the rate at which energy is produced or used. The
correct answer is Choice (C).

Chapter 15: Facing the Facts: Technical Skills Practice Questions I $7

31. Components designed to store electrical charge are called

(A) capacitors.

(B) transformers.

(D) transistors.

Capacitors store electric charge. They're used with resistors in timing circuits because it
takes time for a capacitor to store voltage (to become charged). The correct answer is
Choice (A).

32. In an electronic circuit diagram, the symbol used to show wires' connecting is a/an

(A) X symbol.

(B) dot.

(D) T symbol.

Wires connected to each other are indicated by a darkened circle. The correct answer is
Choice (B).

Assembling Objects Practice Questions

Assembling Objects questions measure your spatial skills. There are two types of questions:
connecting questions and putting-pieces-together questions. The first type presents you
with simple geometric figures such as stars, cloud shapes, letter shapes, circles, and trian-
gles. Your task is to choose the answer that shows the shapes properly connected together
at the designated points. The second type of question is similar to putting a jigsaw puzzle
together. Choose the answer that best shows what the shapes in the first drawing would
look like if assembled together. See Chapter 14 for a complete explanation and illustrated
examples.

33.

CL^

£S

Note that the bottom figure in the first drawing has a line that intersects the short side of
the trapezoid shape, so (C) and (D) are wrong. Connection point A is at the tip of the mitten
shape, so (A) is wrong as well. The correct answer is Choice (B).

34.

«J

Mentally rotate and reposition the shapes in the first drawing until you can see how they fit
together to form the shape shown in Choice (C) — the correct answer. In first drawing,
notice that the shape at the upper right resembles a shark fin — it has two sharp points,
and the third point is curved. Choice (C) is the only image that contains this shape (it's at
the bottom).

/ 88 Part IV: The Whole BaM of Facts: Technical Skills

35.

1^ A T

O !

«*

®Tt

0— 0-

36.

37.

38.

39.

40.

If you selected Choice (A), you were fooled. The arrow shape shown in Choice (A) is a
mirror of the shape depicted in the first drawing. The correct answer is Choice (D).

Mentally rotate and reposition the shapes in the first drawing until you can see how they fit
together to form the shape shown in Choice (A) — the correct answer. If you had trouble
with this one, notice that the piece in the center of the upside-down heart should have a
corner that dips a bit on the left. Choice (C) has the dip in the center, and Choice (D) has it
on the right, so these answers are wrong. Choice (B) has only three pieces.

Note that both shapes in the first drawing have lines that intersect the shapes at designated
points. If you selected Choice (B), your eyes were fooled by mirror images. The correct
answer is Choice (D).

Mentally rotate and reposition the shapes in the first drawing until you can see how they fit
together to form the shape shown in Choice (B) — the correct answer. Here, you can take a
mental snapshot of the largest shape and look for it in the answers — (B) is the only choice
that has it. Verify that this is the right answer by recognizing that (B) is also the only
answer that contains a segment of a circle, at the top.

Don't be fooled by the mirror shape in Choice (B), because the correct answer is
Choice (A).

Mentally rotate and reposition the shapes in the first drawing until you can see how they
fit together to form the shape shown in Choice (C), which is the correct answer. Here, you
may note that the first drawing contains two shapes that resemble triangles with one side
curved inward. Choice (C) is the only image that contains those shapes.

PartV

Practice ASVAB Exams

The 5 th Wave

By Rich Tennant

PfcWB*.iN4MT

RECRUITER

"Excuse we. Vm a dog. Can I still take
tke CAT-ASVA^?'*

In this part . . .

m Boing well on the ASVAB requires an effective study
♦i^plan. You want to concentrate your study time on
subject areas you may be having problems with. The prac-
tice examinations in this part are great tools to enhance
and plan your study program.

Take the first test in this section to determine your
strengths and weaknesses. Concentrate most of your
study efforts on subject areas that are hard for you. When
you think you've got it down, take the second test to mea-
sure your improvement. Take the third test right before
you're ready to take the actual ASVAB to brush up on your
test-taking skills.

In this part, you also find a bonus Armed Forces
Qualification Test (AFQT) practice exam. This practice
test includes only the four ASVAB subtests that are used
to make up your AFQT score — the score that determines
whether you can even join the military branch of your
choice.

Not only does taking the sample tests help you understand
what you need to study, but it also gets you into the test-
taking mindset. By taking the tests, you get used to the
format of each subtest. Trust me — these sample tests will
give you confidence on test day.

Chapter 16

Practice Exam 1

7 his sample test features nine subtests, just like the ASVAB. As you may have guessed,
the sample tests in this book are paper-based tests. (Yes, I'm a master of the obvious.)
When you take the actual ASVAB, it may be a paper-based or a computer-based exam. The
computer version basically has the same subtests as the paper version, but it follows a dif-
ferent time format and has a different number of questions.

Another difference with the computer-based test is that you can't skip a question and go
back to it, and you can't change an answer after you enter it into the computer. Check out
the computer-based test in greater detail in Chapter 3, and experience computer-based
practice tests on the CD-ROM.

To get the most out of this sample test, take it under the same conditions as the real ASVAB:

v* Allow yourself about 3 hours to take the entire exam, and take the whole thing at one
time.

i*" Find a quiet place where you won't be interrupted.

c" Bring a timer that you can set for various lengths of time, some scratch paper (you get
two pieces during the exam, but you can get more; just ask for it as needed), and a
pencil.

J-" At the start of each subtest, set your timer for the specified period of time. Don't go on
to the next section until the timer has gone off, and don't go back to a previous section.
If you finish early, check your work for that section only.

J-" Use the answer sheet that's provided.

J-" Don't take a break during any subtest. You can take a short one- or two-minute break
between subtests if you need it.

After you complete the entire sample test, check your answers against the answers and
explanations in Chapter 17.

Your primary goal with this sample test is to determine your strengths and weaknesses. If
you miss only one question on the Word Knowledge subtest but you miss 15 on Arithmetic
Reasoning, you know where to spend your study time. If you're not going to pursue a career
that requires a score on a particular subtest or the type of knowledge a subtest covers,
don't worry about your score there. (See Appendix A for information on the subtests that
various careers require good scores on.)

192

Part V: Practice ASVAB Exams

Answer Sheet for Practice Emm 1

Subtest 1: General Science

1®®©® 6®®©® 11®®©® 16®®©® 21®®©®

2®®©® 7®®©® 12®®©® 17®®©® 22®®©®

3®®©® 8®®©® 13®®©® 18®®©® 23®®©®

4®®©® 9®®©® 14®®©® 19®®©® 24®®©®

5®®©® 10®®©® 15®®©® 20®®©® 25®®©®

Subtest 2: Arithmetic Reasoning

1®®©® 7®®©® 13®®©® 19®®©® 25®®©®

2®®©® 8®®©® 14®®©® 20®®©® 26®®©®

3®®©® 9®®©® 15®®©® 21®®©® 27®®©®

4®®©® 10®®©® 16®®©® 22®®©® 28®®©®

5®®©® 11®®©® 17®®©® 23®®©® 29®®©®

6®®©® 12®@©@ 18®®©® 24®®©® 30®®©®

Subtest 3: Word Knowledge

1 ®@©@ 8 ®@©®

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2 ®@©® 9 ®®©®

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3®®©® 10®®©®

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4®®©® 11®@©@

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5®®©® 12®@©@

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6®®©® 13®@©@

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7®®©® 14®®©®

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Subtest 4: Paragraph Comprehension

1 ®@©® 4 ®@©®

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2 ®®©® 5 ®®©®

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3 ®@©® 6 ®@©@

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Subtest 5: Mathematics Knowledge

1 @®©@ 6 ®®©®

®@©®

2 ®@©@ 7 ®®©®

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3 ®®©® 8 ®®©®

®®©®

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4 ®®@® 9 ®@©@

®@©@

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®®©@

5®®©® 10®®©®

®@©®

®®©®

Subtest 6: Electronics Information

1 ®®©® 5 ®@©®

®@©®

®®©®

2 ®@©@ 6 ®®©®

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®®©@

®@©@

3 ®@©® 7 ®®©®

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4 ®®©® 8 ®@©®

®@©®

®®©®

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Subtest 7: Auto & Shop Information

1 ®®©@ 6 ®@©®

®@©®

®®©®

®@©@

2 ®@©@ 7 ®®©®

®®@®

®®©@

®@©@

3 ®@©® 8 ®®©®

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4 ®®©® 9 ®@©@

®@©®

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5®®©® 10®®©®

®®©®

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®®©®

Subtest 8: Mechanical Comprehension

1®®©® 6®®©® 11®®©® 16®®©® 21®®©®

2®®©® 7®®©® 12®®©® 17®®©® 22®®©®

3®®©® 8®®©® 13®®©® 18®®©® 23®®©®

4®®©® 9®®©® 14®®©® 19®®©® 24®®©®

5®®©® 10®@©@ 15®®©® 20®®©® 25®®©®

Subtest 9: Assembling Objects

1®@©@ 6®®©® 11®®©® 16®®©® 21®@©@

2®®©® 7®®©® 12®®©® 17®®©® 22®®©®

3®®©® 8®®©® 13®®©® 18®®©® 23®®©®

4®®©® 9®®©® 14®®©® 19®®©® 24®®©®

5®®©® 10®@©@ 15®®©® 20®®©® 25®®©®

Chapter 16: Practice Exam 1 f 9j

Subtest 1: General Science

Time: 11 minutes for 25 questions

Directions: This subtest tests your knowledge of general science principles usually covered in high
school classes. Pick the best answer for each question and then mark the space on your answer
sheet that corresponds to the letter indicating your choice.

1. Which planet is named after the Greek god
who personified the sky?

(A) Earth

(B) Mars

(D) Uranus

2. An animal that eats only meat is called a(n)

(A) omnivore.

(B) herbivore.

(D) voracious.

3. The chemical process in which electrons
are removed from a molecule is called

(A) respiration.

(B) recreation.

(D) metabolism.

4. What is a single unit of quanta called?

(A) quantum

(B) quantumonium

(D) quanfactorial

5. Light waves travel at a rate of about

(A) 186,000 miles per hour.

(B) 186,000 miles per minute.

(D) 186,000 miles per second.

6. The largest planet in the solar system is

(A) Earth.

(B) Mars.

(D) Jupiter.

7. The intestines are part of the

(A) circulatory system.

(B) nervous system.

(D) digestive system.

8. Joints that hold bones firmly together are
called

(A) hinge joints.

(B) ball and socket joints.

(D) pivot joints.

9. Of the levels listed, the top or broadest
level of the classification system for living
organisms is called the

(A) class.

(B) phylum.

(D) genus.

10. Which planet is the brightest object in the
sky, aside from the sun and moon?

(A) Saturn

(B) Pluto

(D) Mercury

11. The human heart includes

(A) 2 chambers.

(B) 3 chambers.

(D) 5 chambers.

Go on to next page

196

Part V: Practice ASVAB Exams

12. White blood cells

(A) produce antibodies.

(B) fight infections.

(D) both A and B

13. A measureable amount of protein can be
found in all of the following foods EXCEPT

(A) eggs.

(B) meat.

(D) apples.

14. What is the most abundant element, by
mass, in the Earth's crust?

(A) carbon

(B) oxygen

(D) salt

15. Osmosis is

(A) diffusion of water.

(B) transfer of oxygen.

(D) protein.

16. A meter consists of

(A) 10 centimeters.

(B) 100 millimeters.

(D) 10 millimeters.

17. One light-year is

(A) the distance traveled by light in one
year.

(B) the brightness of light at 30,000 miles.

(D) Spock's birthday.

18. Electrons are particles that are

(A) positively charged.

(B) neutral.

(D) negatively charged.

19. The asteroid belt is located

(A) around Mercury.

(B) between Mars and Jupiter.

(D) There is no such thing as an asteroid
belt.

20. The atomic number of an atom is deter-
mined by

(A) the size of its nucleus.

(B) the number of protons.

(D) its location in the periodic table.

21. The "control center" of a cell is called the

(A) nucleus.

(B) compound.

(D) atom.

22. How many planets in the solar system have
rings?

(A) one

(B) two

(D) four

23. The temperature at which a substance's
solid and liquid states exist in equilibrium
is its

(A) melting point.

(B) boiling point.

(D) concentration point.

Go on to next page

Chapter 16: Practice Exam 1 f Qjy

24. The atmosphere of Mars is composed
mostly of

(A) oxygen.

(B) carbon dioxide.

(D) Mars has no atmosphere.

25. Not counting the sun, the closest star to
the Earth is

(A) Rigel.

(B) Proxima Centauri.

(D) Betelgeuse.

STOPI

DO NOTTURNTHE PAGE UNTILTOLDTO DO SO.
DO NOT RETURN TO A PREVIOUS TEST.

196

Part V: Practice ASVAB Exams

Subtest 2: Arithmetic Reasoning

Time: 36 minutes for 30 questions

Directions: This test contains questions about arithmetic. Each question is followed by four possi-
ble answers. Decide which answer is correct and then mark the space on your answer sheet that
has the same number and letter as your choice. Use scratch paper for any figuring you want to do.
A calculator is not allowed.

If a car is towed 12 miles to the repair shop
and the tow charge is $3.50 per mile, how
much does the tow cost?

(A) $12.00

(B) $3.50

(D) $100.00

The sum of two numbers is 70. One number
is 8 more than the other. What's the
smaller number?

(A) 31

(B) 33

A sales manager buys antacid in bottles by
the gross. If he goes through 3 bottles of
antacid every day, how long will the gross
last?

(A) 144 days

(B) 3 days

(D) 48 days

Jenny's test grades are 93, 89, 96, and 98. If
she wishes to raise her average to 95, what
does she need to score on her next test?

(A) 100

(B) 99

5. A waitress earns an average tip of 12% of
the cost of the food she serves. If she
serves $375 worth of food in one evening,
how much money in tips will she earn on
average?

(A) $37

(B) $45

(D) $420

6. How many square feet of carpeting are
needed to carpet a 12-foot x 12-foot room?

(A) 24

(B) 120
(C)48
(D) 144

7. Carpet stain protector costs $0.65 per
square yard to apply. How much will it cost
to apply the protector to a 16-foot x 18-foot
carpet?

(A) $187.20

(B) $62.40

(D) $96.00

8. A printing plant that produces baseball
cards has a monthly overhead of $6,000. It
costs 18 cents to print each card, and the
cards sell for 30 cents each. How many
cards must the printing plant sell each
month in order to make a profit?

(A) 30,000

(B) 40,000

(D) 60,000

Go on to next page

Chapter 16: Practice Exam 1 /v7

9. Joe received an hourly wage of $8.15. His
boss gave him a 7% raise. How much does
Joe make per hour now?

(A) $0.57

(B) $8.90

(D) $13.85

10. Alice leaves her house, driving east at 45
miles per hour (mph). Thirty minutes later,
her husband Dave notices she forgot her
cell phone and sets off after her. How fast
must Dave travel in order to catch up with
Alice 3 hours after he leaves?

(A) 49 mph

(B) 50.5 mph

(D) 54 mph

11. A baker made 20 pies. A Boy Scout troop
buys one-fourth of his pies, a preschool
teacher buys one-third of his pies, and a
caterer buys one-sixth of his pies. How
many pies does the baker have left?

( A ) |
(B)15
(9 12
CD) 5

12. Miriam bought five cases of motor oil on
sale. A case of motor oil normally costs
$24.00, but she was able to purchase the oil
for $22.50 a case. How much money did
Miriam save on her entire purchase?

(A) $7.50

(B) $1.50

(D) $22.50

13. A security guard walks the equivalent of six
city blocks when he makes a circuit around
the building. If he walks at a pace of eight city
blocks every 30 minutes, how long will it take
him to complete a circuit around the building,
assuming he doesn't run into any thieves?

(A) 20.00 minutes

(B) 3.75 minutes

(D) 7.5 minutes

14. The population of Grand Island, Nebraska,
grew by 600,000 people between 1995 and
2005, one-fifth more than the town council
predicted. The town council originally pre-
dicted the city's population would grow by

(A) 400,000

(B) 500,000

(D) 100,000

15. Joan is taking an admissions examination. If
she has to get at least 40 of the 60 questions
right to pass, what percent of the questions
does she need to answer correctly?

(A) 30%

(B) 40%

(D) 66|%

16. A teacher deposits $3,000 in a retirement fund.
If she doesn't add any more money to the
fund, which earns an annual interest rate of
6%, how much money will she have in 1 year?

(A) $180

(B) $3,006

(D) $6,000

17. The high school track measures one-
quarter of a mile around. How many laps
would you have to run in order to run three
and a half miles?

(A) 12

(B)14

CD) 18

18. Karl is driving in Austria, where the speed
limit is posted in kilometers per hour. The
car's speedometer shows that he's travel-
ing at a rate of 75 kilometers per hour. Karl

knows that a kilometer is about -^ of a mile.

Approximately how many miles per hour is
Karl traveling?

(A) 47

(B) 120

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198

Part V: Practice ASVAB Exams

19. A carpenter earns $12.30 an hour for a
40-hour week. His overtime pay is 1-4 times
his base pay. If he puts in a 46-hour week,
how much is his weekly pay?

(A) $602.70

(B) $492.00

(D) $110.70

20. An office building has 30 employees and
provides 42 square feet of work space per
employee. If five more employees are hired,
how much less work space will each
employee have?

(A) 6 square feet

(B) 7 square feet

(D) 36 square feet

21. Stan bought a monster truck for $2,000
down and payments of $450 a month for
five years. What's the total cost of the mon-
ster truck?

(A) $4,250

(B) $29,000

(D) $34,400

22. Darla spent $120.37 on groceries in
January, $108.45 in February, and $114.86
in March. What was the average monthly
cost of Darla's groceries?

(A) $343.68

(B) $110.45

(D) $114.56

23. Keith is driving from Reno to Kansas City to
meet his girlfriend. The distance between
the two cities is 1,650 miles. If Keith can
average 50 miles per hour, how many hours
will it take him to complete his trip?

(A) 8 hours

(B) 30 hours

(D) 82 hours

24. Michael needs 55 gallons of paint to paint
an apartment building. He would like to
purchase the paint for the least amount of
money possible. Which of the following
should he buy?

(A) two 25-gallon buckets at $550 each

(B) eleven 5-gallon buckets at $108 each

(D) fifty-five 1-gallon buckets at $23 each

25. As a member of FEMA, you're required to
set up a contingency plan to supply meals
to residents of a town devastated by a tor-
nado. A breakfast ration weighs 12 ounces
and the lunch and dinner rations weigh

18 ounces each. Assuming a food truck can
carry 3 tons and that each resident will
receive 3 meals per day, how many resi-
dents can you feed from one truck during
a 10-day period?

(A) 150 residents

(B) 200 residents

(D) 300 residents

26. A train headed south for Wichita left the
station at the same time a train headed
north for Des Moines left the same station.
The train headed for Wichita traveled at

55 miles per hour. The train headed for Des
Moines traveled at 70 miles per hour. How
many miles apart are the trains at the end
of 3 hours?

(A) 210 miles

(B) 165 miles

(D) 375 miles

27. A carpenter needs to cut four sections,
each 3 feet, 8 inches long, from a piece of
molding. If the board is only sold by the
foot, what's the shortest length of board
she can buy?

(A) 15 feet

(B) 14 feet

(D) 12 feet

Go on to next page

Chapter 16: Practice Exam 1 f QQ

28. Kiya had only one coupon for 10% off one
frozen turkey breast. The turkey breasts
cost $8.50 each, and Kiya wanted to buy
two. How much did she pay?

(A) $16.15

(B) $17.00

(D) $7.65

29. A recruiter travels 1,100 miles during a

2
40-hour workweek. If she spends £ of her

time traveling, how many hours does she
spend traveling?

(A) 22

30. Your car uses gasoline at the rate of 21

miles per gallon. If gasoline costs $2.82 per
gallon and you drive for 7 hours at a speed
of 48 miles per hour, how much will you
pay for gasoline for the trip?

(A) $38.18

(B) $45.12

(D) 59.27

(B)5

(9 16

(D)8

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200

Part V: Practice ASVAB Exams

Subtest 3: Word Knortiedqe

Time: 11 minutes for 35 questions

Directions: This test is about the meanings of words. Each question has a word underlined. You
may be asked to decide which one of the four words in the choices most nearly means the same
thing as the underlined word or which one of the four words means the opposite. If the underlined
word is used in a sentence, decide which of the four choices most nearly means the same thing as
the underlined word, as used in the context of the sentence. Mark the corresponding space on your
answer sheet.

1. Tim promised to meet us at the apex .
(A) top

(B) bottom

(D) river

2. Assimilate most nearly means

(A) absorb.

(B) react.

(D) lie.

3. Brittle most nearly means

(A) soft.

(B) fragile.

(D) hard.

4. Datum most nearly means

(A) fiscal year date.

(B) congruence.

(D) positive result.

5. The exchange student was proficient in
French, German, and English.

(A) poor

(B) knowledgeable

(D) exacting

6. The judge imposed a severe penalty due to
Tom's actions.

(A) scheduled

(B) made an example of

(D) questioned

7. Mary went to the store and bought peanuts
galore .

(A) abundant

(B) salty

(D) roasted

8. He ran headlong into the fight.

(A) headfirst

(B) reluctantly

(D) recklessly

9. Frugal most nearly means

(A) quiet.

(B) amazing.

(D) economical.

10. The word most opposite in meaning to
stimulate is

(A) support.

(B) arrest.

(D) dislike.

Go on to next page

Chapter 16: Practice Exam 1 2 v /

11. Licit most nearly means

(A) historical.

(B) lawful.

(D) willfully.

12. Vacate most nearly means

(A) crawl.

(B) impel.

(D) leave.

13. The sergeant gave his reasoned opinion.

(A) irate

(B) logical

(D) uninformed

14. Tacit most nearly means

(A) loud.

(B) understood.

(D) transparent.

15. The brass was not burnished .

(A) yellow

(B) dull

(D) polished

16. The commodity was sold.

(A) product

(B) stock

(D) table

17. Her motives were contrived .

(A) premeditated

(B) emotional

(D) amusing

18. Supplicate most nearly means

(A) make superior.

(B) to be unnecessary.

(D) to be expansive.

19. The word most opposite in meaning to
hypocrisy is

(A) honesty.

(B) happy.

(D) threatening.

20. Bob found the peaches to be extremely
succulent .

(A) large

(B) tasteless

(D) juicy

21. The Army soldiers were ordered to
immediate garrison duty.

(A) field

(B) combat

(D) fort

22. Furtherance most nearly means

(A) advancement.

(B) finance.

(D) destruction.

23. Domicile most nearly means

(A) office.

(B) shopping.

(D) vacation.

24. Abrogate most nearly means

(A) recover.

(B) aid.

(D) abolish.

Go on to next page

202

Part V: Practice ASVAB Exams

25. Compensation most nearly means

(A) religion.

(B) commission.

(D) shower.

26. He gave a brusque account of the events.

(A) passionate

(B) lengthy

(D) concise

27. The vote resulted in the demise of the
proposed new law.

(A) passage

(B) death

(D) abatement

28. We commemorated our veterans during
the ceremony.

(A) denied

(B) remembered
(C) thanked

(D) took pictures of

29. Bore most nearly means

(A) deepen.

(B) hide.

(D) jump.

30. That custom still prevails .

(A) angers

(B) persists

(D) excites

31. Defray most nearly means

(A) invade.

(B) obstruct.

(D) reverse.

32. Chasm most nearly means

(A) abyss.

(B) sky.

(D) valley.

33. Fundamental most nearly means

(A) radical.

(B) religious.

(D) excessive.

34. Susceptible most nearly means

(A) travel.

(B) resistant.

(D) vulnerable

35. Emblem most nearly means

(A) symbol.

(B) picture.

(D) religion.

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Chapter 16: Practice Exam 1 203

Subtest %: Paragraph Comprehension

Time: 13 minutes for 15 questions

Directions: This test contains items that measure your ability to understand what you read. This
section includes one or more paragraphs of reading material followed by incomplete statements or
questions. Read the paragraph and select the choice that best completes the statement or answers
the question. Mark your choice on your answer sheet, using the correct letter with each question
number.

An important stage of personal time manage-
ment is to take control of appointments.
Determined by external obligation, appointments
constitute interaction with other people and an
agreed-on interface between your activities and
those of others. Start with a simple appointment
diary. List all appointments, including regular
and recurring ones. Now, be ruthless and elimi-
nate the unnecessary. There may be committees
where you can't productively contribute or
where a subordinate may be able to participate.
Eliminate the waste of your time.

1. Effectively managing your appointments
allows you to

(A) spend more time with your
subordinates.

(B) delegate responsibility to subordinates.

(D) attend only the most important
meetings.

The U.S. Congress consists of 100 senators
and 435 representatives. Two senators are
elected from each state. The number of
representatives from each state is based on pop-
ulation, although each state has at least one rep-
resentative. Senators serve six-year terms, and
representatives serve two-year terms.

2. According to this passage,

(A) there are equal numbers of senators
and representatives.

(B) the number of representatives from
each state is decided by a lottery.

(D) senators and representatives have
different term lengths.

Indo-European languages consist of those
languages spoken by most of Europe and in
those parts of the world that Europeans have
colonized since the 16th century (such as the
United States). Indo-European languages are also
spoken in India, Iran, parts of western
Afghanistan, and in some areas of Asia.

3. The author of this passage would agree that

(A) Indo-European languages are spoken in
areas all over the world.

(B) Indo-European languages include all
the languages spoken in the world.

(D) Indo-European language speakers can
easily understand one another.

In privatization, the government relies on
the private sector to provide a service. However,
the government divests itself of the entire process,
including all assets. With privatized functions, the
government may specify quality, quantity, and
timeliness requirements, but it has no control over
the operations of the activity. Also, the govern-
ment may not be the only customer. Whoever the
government chooses to provide the services
would likely provide the same services to others.

4. This paragraph best supports the state-
ment that

(A) the government must closely supervise
privatized functions.

(B) privatized functions consist of a mix-
ture of government employees, military
personnel, and private contractors.

(D) privatized functions provide essential
services to the government.

Go on to next page

20U

Part V: Practice ASVAB Exams

The success or failure of a conference lies
largely with its leader. A leader's zest and enthu-
siasm must be real, apparent, and contagious.
The leader is responsible for getting the ball roll-
ing and making the attendees feel as if the meet-
ing is theirs and its success depends on their
participation. A good, thorough introduction
helps establish the right climate.

5. A good title to this paragraph would be

(A) "Lead by Example."

(B) "The Importance of Proper Introductions."

(D) "Conference Participation Basics."

Cloud seeding is accomplished by dropping
particles of dry ice (solid carbon dioxide) from a
plane onto super-cooled clouds. This process
encourages condensation of water droplets in
the clouds, which usually, but not always, results
in rain or snow.

6. From this passage, it's reasonable to
assume that

(A) cloud seeding could be used to end a
drought.

(B) cloud seeding is prohibitively expensive.

(D) cloud seeding can be accomplished by
using regular ice.

To write or not to write — that is the ques-
tion. If assigned a writing task, there's no option.
However, if someone is looking for a specific
answer, find out if they need a short answer or a
detailed one. Can the requirement be met with a
telephone call, e-mail, or short note, or is some-
thing more necessary? A former CEO of a major
corporation once commented that he had looked
at 13,000 pieces of paper in a 5-day period. Think
how much easier and more economical it would
be if people would use the telephone, send an
e-mail, or write a short note.

7. The main point of this passage is that

(A) written records are important because
they provide detailed documentation.

(B) more businesspeople should invest time
and energy improving their writing skills.

(D) it's pointless for businesspeople to
spend time improving their writing skills.

The transistor, a small, solid-state device
that can amplify sound, was invented in 1947. At
first, it was too expensive and too difficult to
produce to be used in cheap, mass-market prod-
ucts. By 1954, though, these cost and production
problems had been overcome, and the first tran-
sistor radio was put on the market.

8. According to this passage,

(A) there was no market for transistors
before 1954.

(B) when transistors could be produced
cheaply and easily, the transistor radio
was put on the market.

(D) transistors are still expensive to produce.

I returned from the City about three o'clock on
that May afternoon pretty well disgusted with life. I
had been three months in the Old Country and was
fed up with it. If people had told me a year ago that
I would've been feeling like that I should've laughed
at them; but there was the fact. The weather made
me liverish, the talk of the ordinary Englishman
made me sick, I couldn't get enough exercise, and
the amusements of London seemed as flat as soda
water that had been standing in the sun.

9. The author is speaking of his travels in

(A) Spain.

(B) Great Britain.

(D) Scotland.

Surveys show that the average child under
the age of 18 watches four hours of television
per day. Although some of the programming may
be educational, most isn't. Spending this much
time watching television interferes with a child's
ability to pursue other interests, such as reading,
participating in sports, and playing with friends.

10. The author of this passage would agree that

(A) television viewing should be restricted.

(B) parents who let their children watch
this much television are neglectful.

(D) adults over 18 can watch as much tele-
vision as they want.

Go on to next page

Chapter 16: Practice Exam 1 203

Questions 11 and 12 are based on the following
passage.

Questions 13 through 15 are based on the
following passage.

High school and college graduates attempt-
ing to find jobs should participate in mock job
interviews. These mock interviews help students
prepare for the types of questions they'll be
asked, make them more comfortable with
common interview formats, and help them cri-
tique their performance before facing a real
interviewer. Because they're such a valuable aid,
schools should organize mock job interviews for
all of their graduating students.

11. The above passage states that mock job
interviews

(A) frighten students.

(B) should be offered to the best students.

(D) should be organized by students.

12. From the above passage, it is reasonable to
assume that

(A) mock interviews can increase a stu-
dent's confidence when he or she goes
into a real job interview.

(B) mock interviews are expensive to
organize.

(D) students don't need job interview
preparation.

Due process, the guarantee of fairness in the
administration of justice, is part of the 5th
Amendment to the U.S. Constitution. The 14th
Amendment further requires states to abide by
due process. After this amendment was enacted,
the U.S. Supreme Court struck down many state
laws that infringed on the civil rights guaranteed
to citizens in the Bill of Rights.

1 3. According to the above passage, due process

(A) is an outdated concept.

(B) guarantees fairness in the justice system.

(D) is the process by which winning lottery
tickets are selected.

14. According to the above passage, it's rea-
sonable to assume that the 5th Amendment

(A) is about taxes.

(B) guarantees due process in all criminal
and civil cases.

(D) should never have become part of the
Bill of Rights.

15. The author of the above passage would
agree that

(A) without the passage of the 14th
Amendment, many laws restricting civil
rights would still exist in various states.

(B) the Supreme Court overstepped its
jurisdiction when it struck down laws
infringing on citizens' civil rights.

(D) the 14th Amendment was opposed by
all states.

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206

Part V: Practice ASVAB Exams

Subtest 5: Mathematics Knowledge

Time: 24 minutes for 25 questions

Directions: This section tests your ability to solve general mathematical problems. Select the cor-
rect answer from the choices given, and then mark the corresponding space on your answer sheet.
Use scratch paper to do any figuring.

If x = 8, what's the value of y in the equation

x 3 • x 4 =

y = (x 2 * 4) - 2?

(A) x 12

(A) 14

(B) 2x 7

(B)16

(0)18

(D)x 7

(D)20

(x + 4)(x + 2) =

The cube of 5 is

(A) x 2 + 6x + 6

(A) 125

(B) x 2 + 8x + 8

(B) 25

(D) x 2 + 6x + 8

(D)50

1.5 x 10 3 =

2.5 x 3 3 =

(A) 45

(A) 22.5

(B) 150

(B) 75.0

(D)15

(D) 675.0

10.

Which of the following is a prime number?

The fourth root of 16 is

(A) 27

(A) 4

(B)ll

(B)l

(D)4

(D)2

11.

What's the mode of the following series of

What's the equation of a line that passes

numbers? 4 4 8 8 8 10 10 12 12

through points (0, -1) and (2, 3)?

(A) 9

(A)y = 2x-1

(B)8

(B) y = 2x + 1

(9 11

(C)x = 2y-1

(D)10

(D) x = 2y + 1

12.

If a = 4, then a 3 * a =

(12 yards + 14 feet) * 5 =

(A) 4

(A) 12 feet

(B)12

(B) 5^ feet

(Q64

(D)16

(D) 2^ yards

Go on to next page

Chapter 16: Practice Exam 1 207

13.

14.

15.

16.

17.

18.

19.

Solve: 5!

20.

If a circle has a radius of 12 feet, what's its

(A) 25

circumference most nearly?

(B) 125

(A) 24 feet

(B) 72 feet

(D)15

(900 x 2) * 6 =

(A) 30

(B) 300

21.

(D) 36 feet

An aquarium measures 16 inches long x
8 inches deep x 18 inches high. What's its
volume?

(A) 2,304 cubic inches

(D) 3,000

(B) 128 cubic inches

If x - 2, then x x (x) =

(A) 8

(D) 288 cubic inches

(B) 2x x

22.

Triangle ABC is a(n)

(D)6

If (5 + 1)(6 * 3)(8 - 5) =

i- 3)x, then x =

/3\

(A) 12

/ \

(B)3

/ \

Xl 2 X

749x^/64 =

(A) right triangle.

(A) 56

(B) obtuse triangle.

(B)15

(D) isosceles triangle.

(D) 3,136

23.

The sum of the measures of the angles of a

Which of the following

fractions is the

trapezoid is

largest?

(A) 360 degrees.

(A)|

(B) 540 degrees.

(B)|

(D) 720 degrees.

^>TO

CD) ||

If 2 + x > 4, then x >

(A) 6

(B)2

(D).

Go on to next page

208 Part V: Practice ASVAB Exams

24. Angles 1 and 2 are

(A) supplementary.

(B) complementary.

(D) both right angles.

25. Convert 24% to a fraction.
6

(A)
(B)
(C)
(D)

_6_

J_
24

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Chapter 16: Practice Exam 1 20 z)

Subtest 6: Electronics Information

Time 9 minutes for 20 questions

Directions This test contains questions to challenge your knowledge of electrical, radio, and elec-
tronics information. Select the correct response from the choices given and then mark the corre-
sponding space on your answer sheet.

Ohm's law states 6.

(A) Voltage = Current x Resistance

(B) Amperes = Current x Resistance

(D) Ohms = Current * Voltage

A resistor's first three color bands are

brown, black, and red. What is its value? 7.

(A) 1,000 ohms

(B) 500 ohms

(D) 50 volts

In the U.S., all metal equipment, electrical
or not, connected to a swimming pool
must be

(A) freestanding.

(B) bonded together.

(D) none of the above

Voltage can also be expressed as

(A) watts. 9 -

(B) amps.

(D) electrical potential difference.

Newer cell phones contain a removable
memory card, which is often called a

(A) SIM card.

(B) DIM chip. 10.

(D) PIN chip.

Made from a variety of materials, such as
carbon, this inhibits the flow of current.

(A) resistor

(B) diode

(D) generator

This is a type of semiconductor that only
allows current to flow in one direction. It is
usually used to rectify AC signals (conver-
sion to DC).

(A) capacitor

(B) inductor

(D) transformer

Radar can operate at frequencies as high as

(A) 100,000 Hz.

(B) 100,000 kHz.

(D) 500,000 MHz.

What do AC and DC stand for in the electri-
cal field?

(A) amplified capacity and differential
capacity

(B) alternating current and direct current

(D) none of the above

Changing AC to DC is called what?

(A) capacitance.

(B) impedance.

(D) induction.

Go on to next page

210

Part V: Practice ASVAB Exams

11. A 5,000 BTU air conditioner can efficiently
cool up to 150 square feet, or a 10-foot x
15-foot room. What does BTU stand for?

(A) basic thermal unit

(B) basic temperature unit

(D) none of the above

12. Which is the most correct definition of
current?

(A) the measure of electrical pressure

(B) the amount of electricity used in a
heater

(D) the presence of electron flow

13. A device that transforms energy from one
form to another is called

(A) a capacitor.

(B) a transducer.

(D) magic.

14. Which one of the following is an active
element?

(A) 15 kQ resistor

(B) 10 mH inductor

(D) 10 V power supply

15. A light bulb is 60 watts. Operated at 120
volts, how much current does it draw?

(A) 0.5 amperes

(B) 5.0 amperes

(D) 7,200 amperes

16. A number-12 wire, compared to a number-6
wire,

(A) is longer.

(B) is shorter.

(D) is larger in diameter.

17. A fuse with a higher-than-required rating
used in an electrical circuit

(A) improves safety.

(B) increases maintenance.

(D) is less expensive.

18. Neutral wire is always

(A) whitish or natural.

(B) black.

(D) blue.

19. To measure electrical power, you would
use a(n)

(A) ammeter.

(B) ohmmeter.

(D) wattmeter.

20. What will happen if you operate an incan-
descent light bulb at less than its rated
voltage?

(A) The bulb will burn brighter and last
longer.

(B) The bulb will burn dimmer and last
longer.

(D) The bulb will burn dimmer but won't
last as long.

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Chapter 16: Practice Exam 1 211

Subtest 7: Auto & Shop Information

Time: 1 1 minutes for 25 questions

Directions: This test is about automobiles, shop practices, and the use of tools. Pick the best
answer for each question and then mark the corresponding space on your answer sheet.

1. Overheating the engine can cause all of the
following problems EXCEPT

(A) burned engine bearings.

(B) enlarged pistons.

(D) improved fuel efficiency.

2. The device that converts an automobile's
mechanical energy to electrical energy is
called the

(A) converter.

(B) alternator.

(D) brakes.

3. A primary advantage of the electronic igni-
tion system over conventional ignition sys-
tems is that

(A) the electronic ignition system is less
expensive to repair.

(B) the electronic ignition system requires
a lower voltage to provide a higher
voltage for spark

(D) all of the above

4. The primary purpose of piston rings is to

(A) seal the combustion chamber and
allow the pistons to move freely.

(B) connect the piston to the crankshaft.

(D) provide lubrication to the piston cylinder.

5. The crankshaft typically connects to a

(A) flywheel.

(B) fuel pump.

(D) battery.

6. What component allows the left and right
wheels to turn at different speeds when
cornering?

(A) differential

(B) camshaft

(D) battery

7. If a car's ignition system, lights, and radio
don't work, the part that's probably mal-
functioned is the

(A) cylinder block.

(B) water pump.

(D) battery.

8. A good tool to cut intricate shapes in wood
would be a

(A) ripsaw.

(B) hacksaw.

(D) pocket knife.

9. A two-stroke engine will normally be
found on

(A) small cars.

(B) large diesel trucks.

(D) snowmobiles, chainsaws, and some
motorcycles.

10. A belt sander would best be used to

(A) cut wood.

(B) finish wood.

(D) keep your pants up.

Go on to next page

212

Part V: Practice ASVAB Exams

11. A car equipped with limited-slip differential

(A) can be readily put into all-wheel (four-
wheel) drive.

(B) won't lock up when the brakes are
applied steadily.

(D) is rated for off-road driving.

12. Big block engines generally have

(A) more than 5.9 L of displacement.

(B) better gas mileage than small block
engines.

(D) air conditioning.

13. A good tool for spreading and/or shaping
mortar would be a

(A) cement shaper.

(B) hammer.

(D) broom.

14. Plumb-bobs are used to

(A) clean pipes.

(B) check vertical reference.

(D) carve stones.

15. Rebar is used to

(A) measure the depth of concrete.

(B) reinforce concrete.

(D) smooth concrete.

16. Annular ring, clout, and spring head are
types of

(A) hammers.

(B) saws.

(D) screwdrivers.

17. A ripsaw cuts

(A) against the grain of the wood.

(B) with the grain of the wood.

(D) only plastic.

18. A cam belt is also known as a

(A) piston.

(B) timing belt.

(D) lug nut.

19. To check for horizontal trueness, the best
tool to use is a

(A) steel tape rule.

(B) plumb bob.

(D) sliding T-bevel.

20. A bucking bar is used to

(A) pull nails.

(B) pry wood apart.

(D) drive screws.

21. Washers that have teeth all around the cir-
cumference to prevent them from slipping
are called

(A) shake-proof washers.

(B) jaw washers.

(D) split-lock washers.

Go on to next page

Chapter 16: Practice Exam 1 213

22. The tool below measures

24. The tool below is used to

(A) an inside curve.

(B) an outside curve.

(D) the thickness of wire.

23. The object below is a type of

(A) finish concrete.

(B) spread joint compound.

(D) dress wood.

25. The chisel used to cut metal is

(D) C ^^<^

(A) nut.

(B) washer.

(D) bolt.

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Part V: Practice ASVAB Exams

Subtest 8: Mechanical Comprehension

Time: 19 minutes for 25 questions

Directions: This test is about mechanical principles. Many of the questions use drawings to illus-
trate specific principles. Choose the correct answer and mark the corresponding space on the
answer sheet.

1. An induction clutch works by

(A) magnetism.

(B) pneumatics.

(D) friction.

2. If a first-class lever with a resistance arm
measuring 2 feet and an effort arm measur-
ing 8 feet are being used, what's the
mechanical advantage?

(A) 2

(B)4

(D)l

3. The bottoms of four boxes are shown
below. The boxes all have the same
volume. If postal regulations state that the
sides of a box must meet a minimum
height, which box is most likely to be too
short to go through the mail?

10"

No. 1

No. 2

No. 3

(A) No. 4

(B) No. 2

(D) No. 3

No. 4

Looking at the figure below, when Anvil B
lands on the seesaw, Anvil A will

Anvil B

Anvil A

(A) remain stationary.

(B) hit the ground hard.

(D) enter the stratosphere.

Air pressure at sea level is about 15 psi.
What's the amount of force exerted on the
top of your head, given a surface area of
24 square inches?

(A) 360 pounds

(B) 625 pounds

(D) 180 pounds

The force produced when a boxer's hand
hits a heavy bag and "bounces" off it is
called

(A) response time.

(B) bounce.

(D) gravity.

Go on to next page

Chapter 16: Practice Exam 1 213

10.

In the figure below, if Gear 1 has 25 teeth
and Gear 2 has 15 teeth, how many revolu-
tions does Gear 2 make for every 10 revolu-
tions Gear 1 makes?

11. When Cam A completes one revolution, the
lever will touch the contact point

(A) about 16|
(B)12

(D) about 20

A cubic foot of water weighs about
62.5 pounds. If an aquarium is 18 feet long,
10 feet deep, and 12 feet wide, what's the
approximate pressure in pounds per square
inch (psi) on the bottom of the tank?

(A) 2 psi

(B) 4 psi

(D) 7 psi

Springs used in machines are usually
made of

(A) plastic.

(B) bronze.

(D) steel.

A clutch is a type of

(A) universal joint.

(B) coupling.

(D) cam follower.

Contact point

Lever arm B

(A) once.

(B) never.

(D) twice.

12. A single block-and-fall is called a

(A) fixed pulley.

(B) gun tackle.

(D) sheave.

13. In the figure below, if the fulcrum support-
ing the lever is moved closer to the anvil,
the anvil will be

fulcrum

(A) easier to lift and will move higher.

(B) harder to lift but will move higher.

(D) harder to lift and will not move as high.

Go on to next page

216

Part V: Practice ASVAB Exams

14. The mechanical advantage of the block-
and-tackle arrangement shown below is

15.

Upper
Block

Lower
Block

'load

(A) 2
(B)4
(C)6
(D)l

In the figure below, if the cogs move up the
track at the same rate of speed, Cog A will

(A) reach the top at the same time as
Cog B.

(B) reach the top after Cog B.

(D) have greater difficulty staying on track.

16. If a house key, a wooden spoon, a plastic
hanger, and a wool jacket are all the same
temperature. On a cool day, which one
feels the coldest?

(A) key

(B) spoon

(D) jacket

17. In the figure below, assume the valves are
all closed. To fill the tank but prevent it
from filling entirely, which valves should be
open?

Water
Supply

Valve 1

Valve 3

Valve 2

Drainage

Valve 4

Valve 5

(A) 1 and 2 only

(B) 1,2, and 3 only

(D) 1, 2, 3, and 5 only

18. If Gear A is turned to the left,

(A) Gear B turns to the right and Gear C
turns to the left.

(B) Gear B turns to the left and Gear C
turns to the left.

(D) Gear B turns to the left and Gear C
turns to the right.

Go on to next page

Chapter 16: Practice Exam 1 217

19. If Gear 1 moves in a clockwise direction,
which other gears also turn clockwise?

20.

(A) 3 and 5

(B) 3, 4, and 5
(C) 2 and 5
(D) 3 and 4

The pressure gauge in the figure below
shows a reading of

21. A way to determine the amount of power
being used is to

(A) multiply the amount of work done by
the time it takes.

(B) multiply the distance covered by the
time it takes to move a load.

(D) divide the amount of work done by the
amount of time it takes.

22. A wood tool, a silver tool, and a steel tool
are placed in boiling water for cleaning.
Which tool will get the hot the fastest?

(A) steel

(B) wood

(D) All three are equally hot.

23. A runner is being used in the figure shown.
How much effort is the boy who's lifting the
50-pound anvil using? Disregard friction,
wind resistance, and the weight of the
pulley and the rope.

(A) 15.0

(B) 19.5

(D) 23.0

50 pounds

(A) 50-pound effort

(B) 100-pound effort

(D) 10-pound effort

Go on to next page

2 J 8 Part V: Practice ASVAB Exams

24. In the figure below, at what point was the
ball traveling most slowly?

25. In the figure below, which angle is braced
most solidly?

B C

Brace

(A) A
(B)B
(C)C
(D) All are braced equally solidly.

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Chapter 16: Practice Exam 1 £ly

Subtest 9: Assembling Objects

Time: 15 minutes for 25 questions

Directions: The Assembling Objects subtest consists of questions that measure your ability to men-
tally picture items in two dimensions. Each question is comprised of five separate drawings. The
problem is presented in the first drawing, and the remaining four drawings are possible solutions.
Determine which of the choices best solves the problem shown in the first picture and then mark
the corresponding choice on your answer sheet.

|Sa a

\®

L it! B

-X

10.

ii. rxK:

12.

ABCD ABCD

13.

p. !

14.

v ol

7. e? A s

B C

15- ^A i

T^ B

ABCD

16.

Go on to next page

220 Part V: Practice ASVAB Exams

17.

£3

22.

\3 A A

is. n^A *

F A

23.

19.

24 "• i<§u<n. <§u

20.

Ai) *

G 1

25.

21.

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Chapter 17

Practice Exam 1:
Answers and Explanations

MM/ ith the first practice test out of the way, you're probably anxious to see how well
▼ ▼ you did. Use the answer keys in this chapter to score yourself on each of the nine
subtests. Remember, your scores on this practice exam don't equate to scores on the actual
ASVAB. That's because on the enlistment ASVAB, you get more points for answering harder
questions correctly than you do for easier questions. The test is scored by comparing your
raw score to the scores of other people, which produces a scaled score, so missing 20 out
of 225 questions doesn't mean that your score is 205. The practice exam, however, is a valu-
able tool for determining which subject areas you need to brush up on. (Turn to Chapter 1
to find out how the ASVAB is scored.)

Subtest 1: General Science Answers

The General Science subtest tests your knowledge of science facts. If you missed a few ques-
tions, reread the questions and try to figure out where you went wrong. If you missed more
than a few questions, review Chapter 10.

General Science is a broad field, but some of the following books may help you: Chemistry
For Dummies by John T. Moore, Biology For Dummies by Donna Rae Siegfried, Astronomy For
Dummies, 2nd Edition, by Stephen P. Maran, Weather For Dummies by John D. Cox, and
Physics I For Dummies by Steven Holzner. You can find additional practice questions in
Chapter 15.

l.D 4. A 7. D 10. C 13. D 16. C 19. B 22. D 25. B

2. C 5. D 8. C 11. C 14. B 17. A 20. B 23. A

3. C 6. D 9. C 12. D 15. A 18. D 21. A 24. B

Subtest 2: Arithmetic Reasoning Answers

Arithmetic Reasoning is one of the four ASVAB subtests that make up your Armed Force
Qualifying Test (AFQT) score, which determines whether you qualify to join the service
branch of your choice (check Appendix A to see whether the jobs you're interested in
require a score in this subtest). If you missed more than five or six questions, dig out
that old high school math textbook and wrap your brain around some math problems.
Chapters 7 and 8 may also help you out.

222 Part V: Practice ASVAB Exams

Some books that may help you score better on the Arithmetic Reasoning subtest include
Basic Math & Pre-Algebra For Dummies by Mark Zegarelli, Algebra For Dummies and Algebra II
For Dummies by Mary Jane Sterling, and Geometry For Dummies by Mark Ryan, as well as the
related workbooks. You can also check out Mark Zegarelli's SAT Math For Dummies and Scott
and Lisa Hatch's SAT II Math For Dummies for some math test practice. Also see Chapter 9 for
additional practice questions.

1. C. Multiply 12 miles by $3.50 per mile: 12 x $3.50 = $42.00.

2. A. Let x equal the smaller number and x + 8 equal the larger number. Because the sum of
the two numbers is 70, you can express this mathematically as x + x + 8 = 70. Now all you
have to do is solve for x. Combine the like terms: 2x + 8 = 70. Then subtract 8 from both
sides of the equation: 2x + 8 - 8 = 70 - 8, or 2x = 62. Divide both sides of the equation by 2,
and you find that x is equal to 31.

3. D. 144 bottles are in a gross, and 144 + 3 (bottles per day) = 48 days.

4. B. To determine Jenny's average, add the test scores and divide the sum by the number of
tests she took. You want to know what she needs on the next test to achieve an average of
95, so let x equal the unknown score. Set up the equation as (93 + 89 + 96 + 98 + x) + 5 = 95.
Combine the like terms: (376 + x) ± 5 = 95. Multiplying both sides by 5 results in 376 + x = 475,
so x = 99.

Choice (A) is very close to the correct answer, but it isn't the best answer. If Jenny's next
test score is 100, her average would be raised to 95.2.

5. B. Multiply the total amount spent on drinks, $375, by 12% (or 0.12) to determine the
amount of tips: $375 x 0.12 = $45.

6. D. You determine square footage by multiplying length by width: 12x12= 144.

7. C. First determine the number of square feet of carpet you want to protect: 16 ft. x 18 ft. = 288 ft. 2
The carpet stain protector is priced by the square yard, so divide 288 by 9 to convert
square feet to square yards (because 1 yd. 2 = 3 ft. x 3 ft. = 9 ft. 2 ): 288 ft. 2 * 9 ft. 2 /yd. = 32 yd. 2

Multiply the number of square yards by the cost of protection per square yard, $0.65, to
get the correct answer: 32 yd. 2 x $0.65/yd. 2 = $20.80

8. C. Let x equal the number of cards printed and sold each month. Each card costs $0.18 to
print and sells for $0.30. Therefore, the cost is equal to 6,000 + 0.18x, and revenue is equal
to 0.30x. You're looking for the point where revenue is greater than the cost (revenue >
cost). The inequality is 0.30x > 6,000 + 0.18x.

Now solve for x. Subtract 0.1 8x from both sides of the inequality and then divide both
sides by 0.12:

0.12x> 6,000

x > 50,000

The printing plant would have to print and sell at least 50,000 cards per month to make a
profit.

9. C. Joe gets a 1% raise. To calculate the new wage, start off by multiplying $8.15 x 0.07 =
$0.57. Then add that number (the amount of Joe's raise) to his original hourly wage. Joe's
new hourly wage is $8.15 + $0.57 = $8.72.

10. C. To find distance, you multiply speed by time. First find how far Alice travels before Dave
catches up with her. By the time Dave leaves, Alice has already been traveling for half an

hour. Three hours later, she would've been traveling for 3-^ hours at 45 mph, or 157.5 miles:

3.5 hr. x 45 mph = 157.5 mi. Dave has three hours to cover this distance. Now find his speed.
To travel 157.5 miles in 3 hours, Dave would have to travel at 52.5 mph: 157.5 mi. * 3 hr. =
52.5 mph.

Chapter 17: Practice Exam 1: Answers and Explanations 223

11. D. To find the amount of pie purchased (which, by the way, does not give you the final
answer), you have to add the fractions. But first the fractions need to have a common
denominator. The denominators (4, 3, and 6), all divide evenly into 12, so use 12 as the
common denominator.

To convert the fractions to the least common denominator of 12, do the following:

Iv3__3_
4 3" 12

I X 4_A
3 4" 12

I x 2__6_
6 2 "12

Now you can add the fractions together:

3.4,2 _ 3 + 4 + 2 _ 9
12 + 12 + 12~ 12 "12

Nine-twelfths of 20 pies is the same thing as ^, or 75%, of the 20 pies. That equals 15 pies.

But that's not what the question asks. One more step: Subtract the pies sold (15) from the
original 20, leaving 5 pies, which makes Choice (D) correct.

12. A. Subtract the sale price from the regular price to find how much she saves on each case:
$24.00 - $22.50 = $1.50. Multiply the answer by the total number of cases to get your final
answer: $1.50 x 5 = $7.50.

13. C. Divide 30 by 8 to determine how long the security guard takes to walk one city block:
30 * 8 = 3.75 minutes. Then multiply 3.75 by 6, the number of blocks it takes to complete
the circuit. The answer is 22.50 minutes.

14. B. Let x equal the original number of how much Grand Island would grow. An additional -^

6
would make the population growth ^, or 120%, of x. You can express the equation as

\.2x = 600,000. To solve for x, divide both sides of the equation by 1.2, which gives you
x = 500,000.

15. D. Divide the number of questions she has to get right (40) by the total number of ques-

9
tions (60) to reach 66^%.

16. C. The interest formula says that interest equals principal times rate times time, or / = Prt.
To determine the amount of interest earned, multiply the principal ($3,000) by the interest
rate (6%) and the number of years interest accrues (1 year): $3,000 x 0.06 x 1 = $180. Add
the interest earned to the principal to show how much total money the teacher would
have: $180 + $3,000 = $3,180.

17. B. Recognize that if the track is a quarter mile long, then 1 mile equals four laps. Therefore,
multiply 4 times 3.5 miles; the answer is 14 laps.

5 5

18. A. One kilometer is approximately % of 1 mile, so you can multiply 75 x -5-: 75x5 =375, and

375 * 8 equals about 46.8. Therefore, Karl was traveling at 47 miles per hour.

19. A. You need to add the carpenter's base pay and overtime pay to find his total pay for the
week. First find his base pay per week: $12.30/hr. x 40 hr. = $492. Then find his overtime

rate per hour, which is 1-4 times his base pay: $12.30/hr. x 1.5 = $18.45. Multiply this rate by

the number of hours of overtime to find his overtime pay: $18.45/hr. x 6 hr. = $110.70.
Finally, add his base pay and overtime pay to find his total pay for the week: $492.00 +
$110.70 = $602.70.

20. A. The office has 1,260 square feet of space (multiply 42 square feet by 30 employees).
With 35 employees, each employee will have 36 square feet of work space (1,260 * 35),
which is 6 square feet less than originally.

221)

Part V: Practice ASVAB Exams

21. B. The total cost is the down payment plus 5 years' worth of monthly payments. Five years
contain 60 months, so multiply $450 (monthly payment) x 60 = $27,000 (total payments).
Then add $27,000 (total payments) + $2,000 (down payment) = $29,000 (total cost).

22. D. Add the three monthly amounts to determine the total amount Darla spent on groceries:
$120.37 + $108.45 + $114.86 = $343.68. Divide the total by 3 to determine the average
monthly cost: $114.56.

23. C. Distance equals speed times time, so divide the total distance by Keith's average speed
to find how long the trip took: 1,650 mi. * 50 mph = 33 hr.

24. B. Choice (A) doesn't provide enough paint (2 x 25 gal. = 50 gal.), so it's wrong. Now deter-
mine the cost of each of the other options:

Choice (B): 11 x $108 = $1,188

Choice (C): 6 x $215 = $1,290

Choice (D): 55 x $23 = $1,265

The lowest price is $1,188, Choice (B).

25. B. First find how many ounces of rations each truck can hold. One ton is 2,000 pounds, so
one truck can carry three times that, or 6,000 pounds. There are 16 ounces in a pound, so
one truck can carry 96,000 ounces: 6,000 lbs. x 16 oz. = 96,000 oz.

Then figure out how many daily rations are in a truckload. The total daily ration for each
resident is 12 ounces + 18 ounces + 18 ounces, or 48 ounces. You can express the number
of daily rations supplied as 96,000 oz. + 48 oz./daily ration = 2,000 daily rations. These
rations need to last 10 days. Dividing 2,000 by 10 days results in 200 residents who can be
fed by one truck during this 10-day period.

26. D. The train headed for Wichita traveled 55 miles/hour x 3 hours =165 total miles. The
train headed for Des Moines traveled 70 miles/hour x 3 hours = 210 total miles. Adding the
distances together gives you the number of miles apart the two trains are after three
hours: 210 + 165 = 375. Another option: You can add the two rates of speed (55 + 70) and
multiply the sum by 3 hours (125 x 3 hours = 375).

27. A. Convert the mixed number to inches: 3 feet, 8 inches equals 44 inches (12 in. /ft. x 3 ft. =
36 in., and 36 in. + 8 in. = 44 in.). Forty-four inches (length each section needs to be) x 4
(number of sections needed) = 176 inches (total molding needed). To find the amount of
molding needed in feet, convert 176 inches into feet by dividing 176 inches by 12 inches.

You get 14-o feet, so the shortest board length necessary is 15 feet.

28. A. One turkey breast costs $8.50 minus 10% of $8.50 (which is $0.85), or $8.50 - $0.85 =
$7.65. The other turkey breast is full price, so add the two costs: $7.65 + $8.50 = $16.15.

29. C. Don't let the number of miles traveled confuse you. You don't use them to solve the
problem. Finding # of a 40-hour work week is the same thing as multiplying 40 times 2,
which is 80, and then dividing 80 by 5, which equals 16 hours the recruiter travels weekly.

30. B. Your first step is to determine the number of miles traveled. Multiply the rate of travel
by the time: 48 x 7 = 336 mi. The amount of gas used is the total miles driven divided by
the number of miles per gallon: 336 + 21 = 16 gal. used. At the price of $2.82 per gallon, you
spent $45.12 for gas: $2.82 x 16 = $45.12.

Subtest 3: Word Knowledge Answers

The Word Knowledge subtest is nothing more than a vocabulary test. However, it's very
important because it's another one of the four subtests used to make up your AFQT score.
If you find you need to improve your vocabulary, see Chapter 4.

Chapter 17: Practice Exam 1: Answers and Explanations 22.2

A couple of other great study references are Vocabulary For Dummies by Laurie E. Rozakis
(Wiley) and SAT Vocabulary For Dummies by Suzee Vlk (Wiley). Additionally, see Chapter 6
for more practice questions.

l.A

6. C

11. B

16. A

21. D

26. D

31. C

2. A

7. A

12. D

17. A

22. A

27. B

32. A

3. B

8. D

13. B

18. C

23. C

28. B

33. C

4. C

9. D

14. B

19. A

24. D

29. C

34. D

5.C

10. B

15. B

20. D

25. B

30. B

35. A

Subtest %: Paragraph Comprehension Answers

Like Word Knowledge, your Paragraph Comprehension score goes toward your AFQT score,
so pay special attention if you've missed more than a couple of these answers — you need
some study time (see Chapter 5). Remember that rereading the paragraph several times to
make sure you have the right answer is perfectly fine. You can find additional practice ques-
tions in Chapter 6.

1. C. Effective appointment management eliminates the waste of your time, as the last sen-
tence of the passage explains.

2. D. The passage gives the numbers of senators and representatives, so Choice (A) is incor-
rect. The passage states that each state's population determines the number of represen-
tatives a state has, so Choice (B) is incorrect. As the passage states, each state has at least
one representative, so Choice (C) is incorrect.

3. A. Many languages are excluded from the Indo-European language group, so Choice (B) is
incorrect. Indians, Iranians, Asians, and Afghans aren't Europeans, so Choice (C) is incor-
rect. The passage gives no evidence to support Choice (D), which isn't true.

4. D. Privatized functions operate independently of the government, making Choices (A) and
(B) incorrect. The passage states that privatized functions may sell goods and services to
other customers as well as the government, so Choice (C) is also incorrect. Choice (D) is
the correct answer, because privatized functions do perform essential services to govern-
ment agencies.

5. C. Choice (A) — "Lead by Example" — is a good philosophy but isn't pertinent to the main
point of the passage. Choices (B) and (D) are subpoints, which support the main point of
the passage, which is how to lead a successful conference (C).

6. A. You can assume that causing rain or snow would end a drought, Choice (A). Nothing in
the passage has to do with expense, so Choice (B) is incorrect. The passage says nothing
about how frequently the process is used, so Choice (C) is incorrect. The passage specifies
that dry ice (solid carbon dioxide) is used; regular ice (solid water) is a different sub-
stance, so Choice (D) is wrong.

7. C. Choices (A) and (B) may be true in certain situations, but they're not the point of this
particular paragraph. The passage doesn't say anything about working to improve writing
skills being a waste of time, so Choice (D) is incorrect. The main point of the paragraph is
that writing may not be the most efficient way of communicating, depending on the situation.

8. B. Products with transistors weren't widely sold before 1954 because of the expense and
difficulty of production, not because markets didn't exist, so Choice (A) is incorrect.
Choice (C) has the right date, but the passage doesn't say who invented the transistor,

226

Part V: Practice ASVAB Exams

so it's wrong as well. Choice (D) is wrong because the passage states that the problem of
transistors' being expensive to produce was solved by 1954. The last sentence notes that
the first transistor radio went on the market after cost and production problems were
overcome, so (B) is the right answer.

9. B. The words London and Englishman make it clear that the author is speaking of his trav-
els in England, which is part of Great Britain.

10. A. The author makes no reference to parents in the passage, so Choice (B) is incorrect.
The author doesn't imply anything about all these interests requiring equal time, so
Choice (C) is incorrect. The passage is about children under 18; you can't draw a conclu-
sion about what the author thinks people over 18 should do, so Choice (D) is incorrect.

11. C. The passage doesn't say anything about mock job interviews being frightening, so
Choice (A) is wrong. The passage says that mock job interviews should be available to all
students, so Choice (B) is wrong. The passage says that schools, not students, should
organize mock interviews, so Choice (D) is incorrect.

12. A. Choices (B), (C), and (D) are the opposite of what the paragraph states and implies.

13. B. Nothing in the paragraph supports Choice (A), which is incorrect. When an amendment
is passed, it becomes part of the Constitution, so Choice (C) is incorrect. The passage
doesn't support Choice (D), because the passage doesn't mention anything related to lot-
tery tickets. The passage defines due process as " the guarantee of fairness in the adminis-
tration of justice," so (B) is correct.

14. C. Because the 14th Amendment guarantees due process in states' laws, the 5th Amendment
must guarantee due process only in federal law, which makes Choice (C) right. Nothing in
the passage implies that the 5th Amendment is about taxes, so Choice (A) is wrong. Because
the passage states that the 14th Amendment had to be enacted to require states to abide by
due process, Choice (B) is incorrect. Choice (D) is neither stated nor implied in the passage.

15. A. Because the Supreme Court struck down many state laws after the 14th Amendment
was enacted, it's probably true that these laws would still exist if there'd been no 14th
Amendment. The passage doesn't support Choices (B), (C), or (D).

Subtest 5: Mathematics Knortiedqe Answers

This subtest is also used to calculate your AFQT score, so it's important. If you miss more
than four or five, consider brushing up on your basic math skills. Chapter 8 can help with this.

The following books may also be of some help: Algebra For Dummies and Algebra II For
Dummies by Mary Jane Sterling, Geometry For Dummies and Calculus For Dummies by
Mark Ryan, and SAT II Math For Dummies by Scott Hatch (all books published by Wiley).
Chapter 9 also has some additional practice questions.

1. A. Substitute 8 for x in the equation and then solve fory:

y = (x 2 + 4) - 2
= (8 2 * 4) - 2
= (64 * 4) - 2
= 16-2
= 14

2. A. The cube of 5 is 5 3 , which is 5 x 5 x 5 = 125.

Chapter 17: Practice Exam 1: Answers and Explanations 22 7

3. C. Because of the order of operations, you need to find 3 3 first and then multiply by 2.5:

2.5 x 3 3

= 2.5(3 x 3 x 3)
= 2.5x27
= 67.5

4. D. Because 2 4 = 16, the fourth root of 16 is 2.

5. A. To get the equation of the line, you need to know the line's slope and y-intercept. The
slope of the line is equal to the change in y values divided by the change in x values. The

change in y values is 3 - (-1) = 4. The change in x values is 2 - = 2. Thus, the slope is % = 2.
The line passes through the point (0, 1), so to find the intercept, substitute for x and
-1 for y in the equation y = 2x + b:

-1 = 2(0) + b

b = -\

Therefore, b = -1, so the full equation is y = 2x- 1.

6. C. Do what's in parentheses first. You need consistent units of measurement, so convert
12 yards to feet; then add 14 feet:

(12 yd. x 3 ft./yd.) + 14 ft.

= 36 feet + 14 feet

= 50 feet

The original problem asks for (12 yards + 14 feet) * 5, so divide by 5 as instructed:
50 feet -5 = 10 feet.

7. D. If two powers have the same base, you multiply them by keeping the base the same and
adding the powers together: x 3 ■ x 4 = x 3 + 4 = x 1 ,

8. D. To find (x + A)(x + 2), you need to multiply every term in the first set of parentheses by
every term in the second set and then add the results. The acronym FOIL (First, Outside,
Inside, Last) can help you keep track of which terms you're multiplying:

v* First: Multiply the first variable in the first set of parentheses by the first variable in the
second set of parentheses: x(x) = x 2 .

V Outside: Next, multiply the first variable in the first set of parentheses by the second
number in the second set of parentheses: x(2) = 2x. So far, the results are x 2 + 2x.

v* Inside: Now multiply the second number in the first set of parentheses by the first vari-
able in the second set of parentheses: A(x) = Ax.

v* Last: Next, multiply the second number in the first set of parentheses by the second
number in the second set of parentheses: 4(2) = 8.

The solution is x 2 + 2x + Ax + 8. Combining the like terms results in x 2 + 6x + 8.

9. C. You need to do powers (exponents) first, so find 10 3 and then multiply by 1.5:

1.5 xlO 3

= 1.5x(10xl0x 10)

= 1.5x1,000

= 1,500

228

Part V: Practice ASVAB Exams

10. B. A prime number is a number that can be divided evenly by itself or by 1 but not by any
other number. Choices (A), (C), and (D) can all be divided evenly by other numbers.

11. B. The mode of a series of numbers is the number that appears in the series the most fre-
quently. In this case, it's 8.

12. D. Substitute 4 for all a's in the problem and then solve, doing the powers first:

43 + 4

= (4 x 4 x 4) * 4
= 64*4
= 16

13. C. The factorial (!) of a number is the number multiplied by the next-smallest whole
number, then by the next smallest whole number, and so on down to 1:

51 = 5x4x3x2x1 = 120

14. B. Do what's in parentheses first:

(900 x2)*6 = 1,800*6 = 300

15. A. Substitute 2 for all x's in the problem and then solve, starting with the powers:

2 2 (2) = 4(2) = 8

16. D. The problem asks you to solve (5 + 1)(6 + 3)(8 - 5) = (3 + 3)x for x. Solve the first half of
the equation, finding the values in parentheses first:

(6)(2)(3) = 36

Therefore, the whole equation becomes 36 = (3 + 3)x, which turns into 36 = 6x. Isolate x:
36 * 6 = 6x * 6
6 -x
To check your answer, substitute 6 for x.

17. A. The square root of 49 is 7; the square root of 64 is 8. And 7 x 8 = 56.

18. D. Find a common denominator for the fractions. In this case, 80 works for all the fractions.
Convert all the fractions using the following method:

2 Y 16_32
5 16 " 80

3 V 10_30
8 10 ~ 80

X v 8_56
10 8 " 80

13 Y 5_65
16 5 " 80

Comparing the fractions, you can see that ^jy or li is the largest fraction.

19. B. Solve as you would solve for any unknown:

2 +x>4
2+x-2>4-2

Therefore, x > 2. To check your answer, substitute 2 for x: 2 + 2 > 4. That's true, so the
answer is correct.

Chapter 17: Practice Exam 1: Answers and Explanations ££y

20. C. Circumference equals n x diameter, and diameter is equal to two times the radius (or
mathematically, C =nd and d = 2r).For this problem, C = nx24.lt you round n to 3.14, the
answer is about 75.36, or about 75 feet.

21. A. Volume equals length x width x height (V - Iwti), so plug in the numbers and solve:
16x8x18 = 2,304 in. 3

22. C. In an equilateral triangle, all sides are equal and all angles are equal.

23. A. All quadrilaterals (four-sided figures) have angles that total 360 degrees.

24. B. If the sum of two angles equals 90 degrees, they're called complementary angles.

25. A. 24% = T^Jou further reduce this fraction to -^ by dividing the numerator and

iuu zo

denominator by 4.

Subtest 6: Electronics Information Answers

The Electronics Information subtest is important only if you plan on a career that requires a
solid score in this area (check Appendix A to see whether the jobs you're interested in
require a score in this subtest). Otherwise, spend your time studying for the math- and
word-related ASVAB subtests. If you do need to score big on this test and you missed more
than five answers, start brushing up. Start by reviewing the corresponding chapter in this
book (Chapter 13).

If you need even more study, check out Electronics For Dummies by Gordon McComb
(Wiley) or consider enrolling in a quick course at a community college. You can also find
additional practice questions in Chapter 15.

1. A. Ohm's law states that Voltage (E) = Current (I) x Resistance (R). All other answer are
incorrect expressions of this law.

2. A. You read a resistor's color bands from left to right. The first band denotes the first digit,
the second band denotes the second digit, and the third band denotes the subsequent
number of zeros. In this example, brown is one, black is zero, and red means there are two
additional zeros.

3. B. Heaters, pumps, stairs, diving boards, railings, and rebar, among other things, must be
bonded together by a minimum #8 wire for safety purposes.

4. D. Voltage is commonly used as a short name for electrical potential difference, and it is
measured in volts.

5. A. SIM stands for Subscriber Identity Module. The card contains information such as your
phone number, your billing information, and your address book. The card makes it easier
to switch from one cell phone to another.

6. A. A resistor is so named because it resists (or inhibits) the flow of current.

7. C. A diode has two terminals, the anode and the cathode, which is why it's called a diode.
It restricts current flow to only one direction.

8. C. Radar can operate as high as 100,000 MHz (megahertz).

9. B. Current is the flow of charged particles. The difference between alternating current (AC)
and direct current (DC) is that the electrons in an AC circuit regularly reverse their direc-
tion. In a DC circuit, electrons always flow in the same direction.

10. C. Changing AC to DC is a process called rectification.

11. C. A British thermal unit (BTU) is a measure of heat energy.

230

Part V: Practice ASVAB Exams

12. D. Current is the presence of electron flow.

13. B. Transducers, which transform energy, can be switches, strain gauges, temperature sen-
sors, or inductive switches.

14. D. Active elements are electronic devices that can create energy (such as voltage supplies
and current supplies). Passive elements are electronic devices that cannot create energy.

15. A. Power = Current x Voltage or, written another way, Current = Power * Voltage. Plug in
the numbers and do the math: 60 watts + 120 volts = 0.5 amperes.

16. C. The larger the number, the smaller the diameter of the wire.

17. C. Because fuses are designed to prevent current overload at a specific level, a fuse with a
high rating may allow a higher current to flow through a circuit not designed to work at
that higher current, possibly causing damage to the circuit.

18. A. Neutral wire is always whitish or natural colored.

19. D. Electrical power is measured in watts, so you use a wattmeter. An ammeter measures
amps (current). An ohmmeter measures ohms (resistance). A voltmeter measures volts
(voltage).

20. B. The bulb will burn dimmer because its full potential isn't used; it'll last longer for the
same reason.

Subtest 7: Auto & Shop In formation Answers

The Auto & Shop Information subtest is fairly straightforward. You either know the informa-
tion or you don't. Not knowing the info may not matter to you as long as the career you
want doesn't require a subtest score in this area (check the Appendix to see whether the
jobs you're interested in require a score in this subtest). But if you do need to do well on
this subtest and you've missed more than five answers, review the material in Chapter 11.

Reviewing Auto Repair For Dummies by Deanna Sclar (Wiley) may also help you score better
on this subtest. Home Improvement All-in-One For Dummies by Roy Barnhart, James Carey,
Morris Carey, Gene Hamilton, Katie Hamilton, Donald R. Prestly, and Jeff Strong (Wiley) can
help you get a better handle on basic tools and their uses. You may even want to take a
class at a nearby community college or at least hang out at the garage and help some
mechanics for a couple of weeks. See Chapter 15 for some more practice questions.

l.D 4. A 7. D 10. B 13. C 16. C 19. C 22. B 25. A

2. B 5. A 8. C 11. C 14. B 17. B 20. C 23. A

3. B 6. A 9. D 12. A 15. B 18. B 21. A 24. D

Subtest 8: Mechanical Comprehension Answers

The Mechanical Comprehension subtest is important only if you want to pursue a military
career that requires a good score on this subtest (check Appendix A to see whether the
jobs you're interested in require a score in this subtest). Otherwise, spend your time study-
ing more important areas of the ASVAB. If you're considering a military job that requires a
high mechanical aptitude and you missed more than four or five questions on this subtest,
give Chapter 12 another once over.

Chapter 17: Practice Exam 1: Answers and Explanations 23 7

1. A. An induction clutch is a magnetic clutch. When a conductor (wire) is wrapped around a
core and electricity is passed through the wire, it sets up a magnetic field. The same wire
also acts as an inductor, which produces inductance, during AC current flow. It's similar to
resistance in a resistor in that it "resists" current flow, but the value of inductance is based
on the value of the inductor (written as L) and the frequency of the AC current. Therefore,
an induction clutch uses magnetism to operate.

2. B. You can calculate mechanical advantage as Length of Effort Arm + Length of Resistance
Arm. Simply plug in the numbers: MA = 8-^2 = 4.

3. D. The box with the largest area on the bottom will have the shortest sides. If Length x
Width x Height = Volume and all the boxes have equal volume, then the sides must be
shortest on the box with the largest area on the bottom. Calculate the area of each box
bottom:

No. 1 = 20 square inches

No. 2 = 35 square inches

No. 3 = 48 square inches

No. 4 = 27 square inches

No. 3, which has the largest area, will have the shortest sides.

4. C. Anvil B's landing on the seesaw will propel Anvil A into the air.

5. A. Pressure equals force divided by area in square inches (P = F '+ A). You can also state
this formula as F= A x P. Substitute the known quantities: F = 15 x 24 = 360 pounds.

6. C. Recoil occurs when an object producing a force is kicked back.

7. A. To determine the answer, multiply the number of teeth Gear 1 has (D) and the number
of revolutions it makes (R). Divide that number by the number of teeth Gear 2 has (d) to
determine the number of revolutions Gear 2 makes (r). Because the gears are proportional,
this formula shows you the ratio of teeth to revolutions.

r-DR

r ~ d
r _ 25x10
15

r _250_50_ 1fi 2
15 " 3 -1D 3

8. B. You can determine the pressure of all that water by multiplying the volume of the
aquarium by the weight of the water. Volume = Iwh. The bottom of the tank is 18 feet long
by 12 feet wide by 10 feet high for a total volume of 2,160 cubic feet: 18 x 12 x 10= 2,160 ft. 3
A cubic foot of water weighs approximately 62.5 pounds, so multiply the volume of water
by 62.5: 2,160x62.5= 135,000.

That gives an approximate pressure on the bottom of the tank of about 135,000 pounds
over the entire surface area. The surface area of the bottom of the tank is length x width.
Convert feet to inches and then find the area: A = (18 ft. x 12 in./ft.) x (12 ft. x 12 in./ft.) =
216 in. x 144 in. = 31,104 in. 2 .

Dividing the pressure of 135,000 by the number of square inches of surface area gives an
approximate psi of 4.

9. D. Machine springs are usually made of steel, although sometimes they're made of brass or
other metal alloys.

10. B. Clutches connect and disconnect parts, so they're a type of coupling.

232

Part V: Practice ASVAB Exams

11. D. When the high point of the cam connects with the lever arm, the lever arm will touch
the contact point. Two high points on the cam mean the lever arm will touch the contact
point twice with each revolution of the cam.

12. C. A single block-and-fall is a way to get mechanical advantage by threading a rope through
a pulley or stationary point, the load being attached to the end of the rope, and you pulling
on the other end of the rope, hoisting the load. The device is also called a runner.

13. C. If the fulcrum is moved closer to the anvil, the length of the effort arm of the lever will
be increased, making the anvil easier to raise, but the height to which the anvil can be
raised will be reduced.

14. A. Because this block-and-tackle arrangement merely changes the direction of the pull, it
has a mechanical advantage of only 2.

15. C. The larger cog (Cog A) covers a greater linear distance in a given period of time, so Cog A
reaches the top first.

16. A. The key will feel coldest because metal is a better conductor than the other materials.

17. D. All but Valve 4 should be open. Opening Valves 1 and 2 allows water to enter the tank.
Opening Valves 3 and 5 prevents water from filling the tank entirely. Opening Valve 4
allows water to leave the tank.

18. A. Gears with their teeth together in mesh turn in opposite directions. Gear A turns Gear B
in the opposite direction (right), and Gear B turns Gear C in the opposite direction (left).

19. A. Gears with their teeth together in mesh turn in opposite directions. Gear 1 turns clock-
wise. Gear 2, in mesh with Gear 1, turns counterclockwise. Gear 3, in mesh with Gear 2,
turns clockwise. Gear 4, in mesh with Gear 3, turns counterclockwise. Gear 5, in mesh with
Gear 2, turns clockwise.

20. C. The gauge shows a reading of 21.

21. D. The formula for determining power is Power = Work * Time.

22. C. Silver is the best conductor, so it will become hotter faster than the other objects
because heat transfers faster into materials with greater conductivity than with those with
lower conductivity.

23. A. Stationary pulleys give no mechanical advantage, so effort equals the weight of the
crate, or 50 pounds.

24. C. At the height of the arc, the ball has no upward momentum, so it goes the slowest at
that point.

25. A. The brace on Angle A covers more area of the angle, so it's more solidly braced.

Subtest 9: Assembling Objects Answers

If you plan on enlisting in the Navy, check Appendix A to see whether the jobs you're inter-
ested in require a score in this subtest. For more information about the Assembling Objects
subtest, see Chapter 14. For additional practice questions, see Chapter 15.

25. C

l.C

4. D

7. C

10. B

13. D

16. A

19. C

22. D

2. A

5. A

8. D

11. A

14. C

17. B

20. A

23. B

6. A

9. B

12. D

15. B

18. B

21. B

24. C

Chapter 18

Practice Exam 2

■ Ve designed the second practice test so you can see how much you've improved. This
«S exam is exactly like the first one from Chapter 16, except (of course) the questions are
different. I hope you used the results from the first practice exam to determine your weak
areas and spent some time hitting the ol' books and recharging your thinking cap.

To get the most out of this practice exam, take it like you'd take the real ASVAB under the
same conditions:

v* Allow yourself about three hours to take the entire exam, and take the whole thing at
one time.

j*" Find a quiet place where you won't be interrupted.

i*" Bring a timer that you can set for various lengths of time, some scratch paper, and a
pencil.

i*" At the start of each subtest, set your timer for the specified period of time. Don't go on
to the next section until the timer has gone off, and don't go back to a previous section.
If you finish early, check your work for that section only.

i*" Use the answer sheet that's provided.

j*" Don't take a break during any subtest. You can take a short one- or two-minute break
between subtests if you need it.

After you complete the entire sample test, check your answers against the answer explana-
tions and key in Chapter 19.

23U

Part V: Practice ASVAB Exams

Answer Sheet for Practice Emm 2

Subtest 1: General Science

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2®®©® 7®®©® 12®®©® 17®®©® 22®®©®

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4®®©® 9®®©® 14®®©® 19®®©® 24®®©®

5®®©® 10®®©® 15®®©® 20®®©® 25®®©®

Subtest 2: Arithmetic Reasoning

1®®©® 7®®©® 13®®©® 19®®©® 25®®©®

2®®©® 8®®©® 14®®©® 20®®©® 26®®©®

3®®©® 9®®©® 15®®©® 21®®©® 27®®©®

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5®®©® 11®®©® 17®®©® 23®®©® 29®®©®

6®®©® 12®@©@ 18®®©® 24®®©® 30®®©®

Subtest 3: Word Knowledge

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2 ®@©® 9 ®®©®

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Subtest 4: Paragraph Comprehension

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2 ®®©® 5 ®®©®

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Subtest 5: Mathematics Knowledge

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2 ®@©@ 7 ®®©®

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4 ®®@® 9 ®@©@

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Subtest 6: Electronics Information

1 ®®©® 5 ®@©®

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2 ®@©@ 6 ®®©®

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3 ®@©® 7 ®®©®

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4 ®®©® 8 ®@©®

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Subtest 7: Auto & Shop Information

1 ®®©@ 6 ®@©®

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2 ®@©@ 7 ®®©®

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Subtest 8: Mechanical Comprehension

1®®©® 6®®©® 11®®©® 16®®©® 21®®©®

2®®©® 7®®©® 12®®©® 17®®©® 22®®©®

3®®©® 8®®©® 13®®©® 18®®©® 23®®©®

4®®©® 9®®©® 14®®©® 19®®©® 24®®©®

5®®©® 10®@©@ 15®®©® 20®®©® 25®®©®

Subtest 9: Assembling Objects

1®@©@ 6®®©® 11®®©® 16®®©® 21®@©@

2®®©® 7®®©® 12®®©® 17®®©® 22®®©®

3®®©® 8®®©® 13®®©® 18®®©® 23®®©®

4®®©® 9®®©® 14®®©® 19®®©® 24®®©®

5®®©® 10®@©@ 15®®©® 20®®©® 25®®©®

Chapter 18: Practice Exam 2 235

Subtest 1: General Science

Time: 11 minutes for 25 questions

Directions: This exam tests your knowledge of general science principles usually covered in high
school classes. Pick the best answer for each question and then mark the space on your answer
sheet that corresponds to the question number and the letter indicating your choice.

1. What is the change in body form that an
insect undergoes from birth to maturity?

(A) transformation

(B) metamorphosis

(D) transmutation

2. An earthquake that measures 4 on the
Richter scale would be how many times
stronger than an earthquake that
measured 2?

(A) 2 times stronger

(B) 4 times stronger

(D) 100 times stronger

3. Muscles attach to bone with

(A) nonconnective tissue.

(B) ligaments.

(D) rubber bands.

4. The male part of a flower is called

(A) the stamen.

(B) the pistil.

(D) stubborn.

5. Blood leaving the lungs is

(A) hydrogenated.

(B) coagulated.

(D) oxygenated.

6. Which river is the longest?

(A) Mississippi

(B) Nile

(D) Congo

7. The branch of science that studies matter
and energy is called

(A) chemistry.

(B) physics.

(D) trigonometry.

8. Which type of cloud's name comes from
the Latin word meaning "rain"?

(A) nimbus

(B) cirrus

(D) alto

9. Deoxyribonucleic acid is better known as

(A) antacid.

(B) carbohydrates.

(D) DNA.

10. The instrument used to measure wind
speed is

(A) barometer.

(B) anemometer.

(D) fanometer.

Go on to next page

236

Part V: Practice ASVAB Exams

11. Electric charges can be

(A) positive or negative.

(B) positive or neutral.

(D) neutral only.

12. Which planet in the solar system has the
most moons?

(A) Neptune

(B) Saturn

(D) Uranus

13. The law of gravitation was discovered by

(A) Albert Einstein.

(B) Isaac Newton.

(D) Rod Powers.

14. Which U.S. space program is responsible
for putting 12 men on the moon?

(A) Gemini

(B) Titan

(D) Apollo

15. Animals that eat both plants and animals
are called

(A) herbivores.

(B) carnivores.

(D) ambidextrous.

16. Unlike most other fish, sharks have no

(A) gills.

(B) bones.

(D) heart.

17. What human organ is responsible for
detoxification of red blood cells?

(A) liver

(B) kidneys

(D) stomach

18. Kinetic energy is the energy that

(A) is produced by sound waves.

(B) an object potentially has.

(D) results from the attraction of two
magnets.

19. The terrestrial planets consist of

(A) Jupiter, Saturn, Uranus, and Neptune.

(B) Pluto and Neptune.

(D) any planet.

20. A step-up transformer

(A) increases the voltage in a power line.

(B) decreases the voltage in a power line.

(D) measures the voltage in a power line.

21. Which animal has the heaviest brain?

(A) human

(B) elephant

(D) sperm whale

22. The sun is what type of star?
(A) type

(B)Gtype
(C)Ftype
(D) M type

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Chapter 18: Practice Exam 2 2? 7

23. Molecules are created when

(A) matter is created.

(B) matter is destroyed.

(D) atoms are separated.

24. An example of an embryonic plant would
be a

(A) tree.

(B) rose.

(D) cabbage.

25. The vernal equinox is

(A) the first day of winter.

(B) near the equator.

(D) a lunar eclipse.

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238

Part V: Practice ASVAB Exams

Subtest 2: Arithmetic Reasoning

Time: 36 minutes for 30 questions

Directions: The questions in the arithmetic test are each followed by four possible answers. Decide
which answer is correct and then mark the space on your answer sheet that has the same number
and letter as your choice. Use scratch paper for any figuring you need to do. Calculators are not
allowed.

If you roll two six-sided dice, what's
the probability of NOT rolling a five on
either die?

5. A half-pint of cream is what part of a
gallon?

(A)
(B)
(C)
(D)

25
36

Jack loaned Bob $1,500 at an annual inter-
est rate of 1%. After one year, how much
will Bob owe Jack?

(A) $105

(B) $1,500

(D) $1,507

A 2-ton truck is taxed at a rate of $0.12 per
pound. How much is the total tax bill?

(A) $480

(B) $240

(D) $600

If ab = 10 and a 2 + b 2 = 30, solve for y in the
equation y = (a + b) 2 .

(A) 40

(B)45

(D)55

(A)
(B)
(C)
(D)

The cost of a protein bar increased from
$2.50 to $2.80. The percent increase to the
$2.80 rate was how much?

(A) 16%

(B) 10%

(D) 12%

An aircraft flies over Boondock Air Force
Base at 10:20 a.m. At 10:32 a.m., the plane
passes over Sea Side Naval Air Station,
120 miles away. How fast is the aircraft
traveling?

(A) 400 mph

(B) 500 mph

(D) 700 mph

Last year, Margot grew 50 bushels of corn
in her backyard. This year, the yield has
increased 8%. How many bushels of corn
did Margot grow this year?

(A) 56

(B) 52

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Chapter 18: Practice Exam 2 23^

9. Junior has saved money in his piggy bank
over the winter. He wants to buy a $30
computer game. If he has 14 one-dollar
bills, 16 half dollars, 12 quarters, 8 dimes,
25 nickels, and 10 pennies, how much more
does he need to borrow from Dad to buy
the game?

(A) $27.15

(B) $2.85

(D) $1.85

10. Debbie receives a weekly salary of $80, plus
a 5% commission on any sales. During the
week, she has $800 in total sales. What's
the ratio of her commission to her salary?

(A) 2:1

(B) 1:2

(D) 1:3

11. How many quart cans can be filled from a
25-gallon bucket of paint?

(A) 50

(B)75

(D)80

12. If a crew of four people can paint the barn
in three days, how long will it take a crew
of two people?

(A) 4 days

(B) li days

(D) 6 days

13. Brian works for five hours and is paid $24.
Christina works for three hours and is paid
$10.95. How much more per hour does
Brian make than Christina?

(A) $1.15

(B) $1.25

(D) $1.37

14. Margaret is getting married and must be
ready by 11:15 a.m. If it's now 8:30 a.m.,
how much time does she have to get
ready?

(A) 1-^ hours

(B) 2-i hours

(D) 2^ hours

15. An accounting-firm employee is asked to
shred 900 documents. If he can shred docu-
ments at a rate of 7 per minute, the number
of documents remaining after 1-^ hours of
shredding is

(A) 630

(B) 90

(D) 810

16. A home stereo depreciates by 20% each
year. What's the value of a stereo, pur-
chased new for $1,200, after two years?

(A) $768

(B) $693

(D) $654

17. Janet's old pickup truck can only reach a
speed of 45 miles per hour. If she drives at
top speed, how long will it take her to
reach a city 135 miles away?

(A) 3 hours

(B) 2 hours

(D) 2^ hours

18. A blouse normally costs $18.50. How much
money is saved if the blouse is purchased
at a 20% discount?

(A) $1.85

(B) $14.80

(D) $3.70

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21*0

Part V: Practice ASVAB Exams

19. A clerk's weekly salary of $320 is increased
to $360. The percent increase is

(A) 10i%

(B) 11%

(D) 12%

20. Two go-carts are racing on a circular track
with a circumference of 360 feet. Camera
One is following Go-Cart One, and Camera
Two is following Go-Cart Two. If the angle
between the two cameras is 40 degrees,
how far apart are the two go-carts?

(A) 30 feet

(B) 40 feet

(D) 60 feet

21. Dinner at a nice restaurant cost $35.98. If
Joan gave the cashier $40.00, how much
change should she get back?

(A) $5.02

(B) $4.02

(D) $1.02

22. A balloonist circumnavigated the globe in
13 days, 12 hours, 16 minutes, and 13 sec-
onds. A plane circumnavigates the globe in
4 days, 10 hours, 15 minutes, and 7 sec-
onds. How much longer did it take for the
balloon to go around the world?

(A) 12 days, 7 hours, 11 minutes, and
35 seconds

(B) 9 days, 2 hours, 1 minute, and
6 seconds

(D) 9 days, 7 hours, 3 minutes, and
20 seconds

23. Darlene bought 12 boxes of cookies for
$48.00. What was the cost of each box of
cookies?

(A) $4.00

(B) $0.48

(D) $4.80

24.

25.

A tune-up increases a car's fuel efficiency
by 5%. If a car averaged 20 miles per gallon
before the tune-up, how many miles per
gallon will it average after the tune-up?

(A) 25

(B) 22

A lumberjack wishes to drive a spike
through the center of a tree with a circum-
ference of 43.96 feet. What's the minimum
length of the spike needed to go completely
through the tree, passing through the
center?

(A) 14 feet

(B) 15 feet

(D) 17 feet

26. A bin of hard candy holds 10-4 pounds. How

3
many ^-pound boxes of candy can be filled

from the bin?

(A) 30 boxes

(B) 15^- boxes

(D) 14 boxes

27. A patio measures 12 feet by 14 feet. How
many 8-inch-square paving stones are
needed to pave the patio?

(A) 21

(B) 252

(D) 168

28. A computer programmer is making $25,000
per year, and 28% of her salary is withheld
for federal and state deductions. How much
is the computer programmer's net pay?

(A) $20,000

(B) $7,000

(D) $18,000

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Chapter 18: Practice Exam 2 %(l /

29. Pam cuts a pie in half in a straight line. She
then cuts a line from the center to the edge,
creating a 55-degree angle. What's the sup-
plement of that angle?

(A) 55 degrees

(B) 125 degrees

(D) 130 degrees

30. A stack of lumber is 6 feet high. If each

piece of lumber is 4 inches thick, how many
pieces of lumber are in the stack?

(A) 72

(B)12

(D)10

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21*2

Part V: Practice ASVAB Exams

Subtest 3: Word Knowledge

Time: 11 minutes for 35 questions

Directions: This test's questions cover the meanings of words. Each question has an underlined
word. You may be asked to decide which one of the four words in the choices most nearly means
the same thing as the underlined word or which one of the four words means the opposite. If the
underlined word is used in a sentence, decide which of the four choices most nearly means the
same thing as the underlined word as used in the context of the sentence. Mark the corresponding
space on your answer sheet.

1. Abeyance most nearly means

(A) trustworthiness.

(B) passion.

(D) business.

2. It was a sturdy table.

(A) well-built

(B) ugly

(D) small

3. Bullock most nearly means

(A) ox.

(B) inattentive.

(D) panther.

4. Brevity is the soul of wit.

(A) beauty

(B) intelligence

(D) humor

5. Paradigm most nearly means

(A) twenty cents.

(B) model.

(D) basis.

6. He facilitated her promotion.

(A) hindered

(B) helped

(D) ignored

7. Quiescence most nearly means

(A) kill.

(B) preserve.

(D) quiet.

8. The spectator enjoyed the game.

(A) competitor

(B) observer

(D) organizer

9. Joy reclined against the far wall.

(A) sat

(B) leaned

(D) paraded

10. The teacher cited some examples.

(A) memorized

(B) finished

(D) examined

Go on to next page

Chapter 18: Practice Exam 2 2^3

11. Surround most nearly means

(A) line.

(B) benefit.

(D) speaker.

12. Illustrious most nearly means

(A) illustrated.

(B) famous.

(D) intelligent.

13. Habitant most nearly means

(A) invalid.

(B) nun.

(D) dweller.

14. Tim had a penchant for engaging in
subterfuge .

(A) religion

(B) evasion

(D) danger

15. Megan found the new shoes to be ghastly .

(A) hideous

(B) cute

(D) comfortable

16. Rigid most nearly means

(A) strong.

(B) weak.

(D) inflexible.

17. Billy yearned to join the fraternal
organization.

(A) brotherly

(B) large

(D) special

18. Deplore most nearly means

(A) accept.

(B) insult.

(D) salute.

19. Meager most nearly means

(A) space.

(B) sparse.

(D) thirsty.

20. Weal most nearly means

(A) happiness.

(B) blow.

(D) tire.

21. To be guileless , I think your hair looks ugly.

(A) helpful

(B) kind

(D) serious

22. The customs agent confiscated the goods.

(A) bought

(B) noticed

(D) stole

23. Dubious most nearly means

(A) long.

(B) beautiful.

(D) doubtful.

24. Illusion most nearly means

(A) mirage.

(B) distant.

(D) perspective.

Go on to next page

Part V: Practice ASVAB Exams

25.

26.

27.

28.

29.

30.

Beckv developed a sudden craving for ice
cream.

31.

Tom had to provide proof to the judge that
he was not indigent.

(A) disgust

(A) guilty

(B) passion

(B) rich

(D) desire

(D) ugly

Enmitv most nearlv means

32.

Impertinent most nearlv means

(A) enemy.

(A) fun.

(B) hatred.

(B) boring.

(D) childish.

(D) impatient.

Arbor most nearlv means

33.

Lustrous most nearlv means

(A) native.

(A) expensive.

(B) tree.

(B) lazy.

(D) delirious.

(D) bright.

Thev terminated his contract.

34.

Pardon most nearlv means

(A) bought

(A) courtesy.

(B) extended

(B) excuse.

(D) ended

(D) respect.

Tim always considered Chuck to be a big
buffoon.

(A) clown

(B) help

(D) pain

35.

Veracious most nearlv means

(A) fast.

(B) slow.

(D) truthful.

Null most nearly means

(A) zero.

(B) dull.

(D) rapid.

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Chapter 18: Practice Exam 2 2&S

Subtest %: Paragraph Comprehension

Time: 13 minutes for 15 questions

Directions: This test measures your ability to understand what you read. This section includes one
or more paragraphs of reading material followed by incomplete statements or questions. Read the
paragraph and select the choice that best completes the statement or answers the question.

Questions 1 and 2 are based on the following
passage.

There is not a single town of any size within
a distance of forty miles, yet already the rural
population of this county is quite large. The
whole country, within a wide circuit north,
south, east and west, partakes of the same gen-
eral character; mountain ridges, half tilled, half
wood, screening cultivated valleys, sprinkled
with farms and hamlets, among which some
pretty stream generally winds its way. The
waters in our immediate neighborhood all flow
to the southward, though only a few miles to the
north of our village, the brooks are found run-
ning in an opposite course, this valley lying just
within the borders of the dividing ridge. The
river itself, though farther south it becomes one
of the great streams of the country, cannot boast
of much breadth so near its source, and running
quietly among the meadows, half screened by
the groves and thickets, scarcely shows in the
general view.

1. According to this passage,

(A) the author lives in a large city.

(B) the author lives in the country.

(D) the author lives on Mars.

2. According to this passage, the brooks are
running in which direction within the
author's neighborhood?

(A) north

(B) south

(D) west

The Panama Canal is a ship canal that cuts
through the Isthmus of Panama, connecting the
Atlantic and Pacific oceans. Although several for-
eign companies tried to build the canal through-
out the 19th century, none were successful. After
the U.S. helped Panama revolt against Columbia,
the U.S. was given rights to the land the canal
occupied. The U.S. government finished the
canal in 1914.

3. According to this passage,

(A) Panama and Columbia fought a war
over the Panama Canal.

(B) the U.S. was given rights to the canal
land.

(D) Panama built the canal in 1914.

Extreme care must be exercised to ensure
proper handling and cleaning of soiled U.S. flags.
A torn flag may be professionally mended, but a
badly torn or tattered flag should be destroyed.
When the flag is in such a condition that it's no
longer a fitting emblem for display, destroy it in
a dignified manner, preferably by burning.

4. According to this passage, torn flags
should be

(A) mended.

(B) burned.

(D) all of the above

Go on to next page

246

Part V: Practice ASVAB Exams

Medieval guilds were similar to modern-day
labor unions. These groups of merchants or
craftspeople set rules regarding economic activ-
ity in order to protect themselves. Some guilds
held considerable economic power, but even
small guilds protected members. Guilds also
served a social purpose.

5. According to this passage, guilds

(A) had only one purpose.

(B) had little in common with modern
labor unions.

(D) held considerable economic power.

After a series of well-publicized failures by
various inventors, Orville and Wilbur Wright suc-
ceeded in flying and controlling a heavier-than-
air craft on December 17, 1903. The War
Department, stung by its investment in a failed
effort by Samuel Langley and compounded by
the Wright's own secretiveness, initially rejected
the brothers' overtures toward the government
to buy the aircraft. Prevailing sentiments held
that the immediate future still belonged to the
balloon. In August 1908, the two brothers deliv-
ered the first Army aircraft to the U.S.
Government. That the U.S. government managed
to purchase an airplane was a minor miracle. For
more than four years after the Wright brothers'
successful flight at Kitty Hawk, North Carolina,
the government refused to accept the fact that
man had flown in a heavier-than-air machine.

6. Which of the following statements is NOT
supported by the above passage?

(A) The U.S. Government felt that balloons
were more practical than airplanes.

(B) The Wright brothers' own secretive-
ness contributed to their problems in
getting the government interested in
their aircraft.

(D) It took more than six years for the
Wright brothers to interest the U.S.
Government in their airplane.

If anyone should be inclined to overrate the
state of our present knowledge of mental life, all
that would be needed to force him to assume a
modest attitude would be to remind him of the
function of memory. No psychologic theory has
yet been able to account for the connection
between the fundamental phenomena of remem-
bering and forgetting; indeed, even the complete
analysis of that which one can actually observe
has as yet scarcely been grasped. Today forget-
ting has perhaps grown more puzzling than
remembering, especially since we have learned
from the study of dreams and pathologic states
that even what for a long time we believed for-
gotten may suddenly return to consciousness.

7. The primary subject of this paragraph is

(A) bowling.

(B) puzzles.

(D) government service.

Troy weight is based on a pound of 12
ounces and an ounce of 480 grains. Common, or
avoirdupois, weight is based on a pound having
16 ounces and an ounce having 437.5 grains. A
common pound has 7,000 grains while a troy
pound has 5,760.

8. According to this passage,

(A) in common weight, an ounce is less
than 438 grains.

(B) a troy pound and a common pound are
the same weight.

(D) a troy ounce equals 437.5 grains.

Go on to next page

Chapter 18: Practice Exam 2 %(l 7

Good leaders get involved in their subordi-
nates' careers. People merely obey arbitrary
commands and orders, but they respond quickly
and usually give extra effort for leaders who gen-
uinely care for them. An often neglected leader-
ship principle in today's environment of
technology and specialization is knowing the
workers and showing sincere interest in their
problems, career development, and welfare.
Leadership is reflected in the degree of effi-
ciency, productivity, morale, and motivation
demonstrated by subordinates. Leadership
involvement is the key ingredient to maximizing
worker performance.

9. A key leadership principle that's often
ignored is

(A) leading by example.

(B) showing sincere interest in the prob-
lems of the workers.

(D) maximizing worker performance.

Leukemia is a blood disease in which white
blood cells in the blood or bone marrow repro-
duce rapidly, interfering with the body's ability
to produce red blood cells. Red blood cells are
needed to perform vital bodily functions.

10. According to this passage,

(A) white blood cells perform no vital func-
tion in the body.

(B) no treatment for leukemia exists.

(D) white blood cells are found only in the
blood.

Questions 11 and 12 are based on the following
passage.

Any discussion of distinctive military capa-
bilities would be incomplete without looking at
their relationship to the Joint Service vision of
the future. JV 2020 guides all the Services into
the next century with its vision of future war
fighting. JV 2020 sets forth four overarching
operational concepts: dominant maneuver,
precision engagement, focused logistics, and
full-dimensional protection. Each of these opera-
tional concepts reinforces the others. The aggre-
gate of these four concepts, along with their
interaction with information superiority and
innovation, allows joint forces to dominate the
full range of military operations from humanitar-
ian assistance through peace operations to the
highest intensity conflict.

11. According to the passage above, which
of the following is NOT an operational
concept?

(A) dominant maneuver

(B) focused logistics

(D) precision engagement

12. The document discussed in the above pas-
sage is primarily about

(A) military operations of the past.

(B) present military operations.

(D) training for future military operations.

Go on to next page

248

Part V: Practice ASVAB Exams

Questions 13 through 15 are based on the fol-
lowing passage.

Genetics is a branch of science dealing with
heredity. The field is concerned with how genes
operate and the way genes are transmitted to off-
spring. Subdivisions in the field include cytoge-
netics, which is the study of the cellular basis of
inheritance; microbial genetics, the study of
inheritance in microbes; molecular genetics, the
study of the biochemical foundation of inheri-
tance; and human genetics, the study of how
people inherit traits that are medically and
socially important. Genetic counselors are pri-
marily concerned with human genetics. They
advise couples and families on the chances of
their offspring having specific genetic defects.

13. In the passage above, cytogenetics is
defined as

(A) the study of the psychological impact
of genetics.

(B) the study of the cellular foundation of
inheritance.

(D) the study of human genetics.

14. According to the passage, genetics

(A) concerns how genes operate and how
they're passed along.

(B) is a field of study populated by quacks,
fakes, and frauds.

(D) is a new field of study.

15. According to the passage, it's reasonable to
assume that genetic counseling

(A) is restricted to the very rich.

(B) is used to diagnose diseases.

(D) can be used by parents to prevent their
offspring from inheriting a specific
genetic defect.

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Chapter 18: Practice Exam 2 2 Ix ty

Subtest 5: Mathematics Knowledge

Time: 24 minutes for 25 questions

Directions: This test is a test of your ability to solve general mathematical problems. Select the cor-
rect answer from the choices given and then mark the corresponding space on your answer sheet.
Use scratch paper to do any figuring.

x^x 4 ) =
(A)x 6

(B) x 8

(D) 2x 8

If a rectangle has a perimeter of 36 feet and
is 4 feet wide, what's its area?

(A) 56 square feet

(B) 128 square feet

(D) 16 square feet

The cube root of 64 is

(A) 3

(B)9

(D)4

Convert 314,000 to scientific notation.

(A) 3.14xl0 5

(B) 3.14xl0- 5

(D) 31.4x100

The reciprocal of j, is
b

(A)l
(B)3
(C)6

(D)

6. If 0.05 * x = 1, then* =

(A) 0.05

(B) 0.5

(D) 5.0

7. Factor x 2 - 6x + 9.

(A) (x + 6)(x + 6)

(B) (x-6)(x + 6)
(C)(x-3) 2

(D) (x + 3) 2

8. (3 x 2)(7 - 2)(6 + 2) = (6 x 4)x. What's the
value of x?

(A) -5

(B)5

(Q10

(D)l

9. Solve for x: 2x - 6 = x + 5.
(A) 3

0)ii

10. UI=Prt, and P= $1,000, r= 7%, and t = 1,
what does /equal?

(A) $35

(B) $1,000

(D) $70

Go on to next page

250

Part V: Practice ASVAB Exams

11.

12.

13.

14.

Solve for x in the equation (x - 7) 2 - 4 =
(x + l) 2 .

(A) 2\

(B)2|

(D)4|

A circle has a radius of 5 inches. What's its

approximate area?

(A) 78.5 inches

(B) 70.0 inches

(D) 25.0 inches

Solve the following inequality:
|(6x-9) + 4>5x + l.

(A) x > 6

(B) x < 6

(D) x < -3

A tube has a radius of 3 inches and a height
of 5 inches. What's its approximate
volume?

(A) 34 cubic inches

(B) 141 cubic inches

(D) 45 cubic inches

15. Triangle ABC (shown below) is a(n)

(A) right triangle.

(B) equilateral triangle.

(D) isosceles triangle.

16. The following figure what type of
quadrilateral?

18.

19.

-H-

D z

-H-

(A) square

(B) rhombus

(D) parallelogram

17. The angle shown below is a(n)

(A) complementary angle.

(B) supplementary angle.

(D) obtuse angle.

Solve for x: -x 2 - x + 30 = 0.

(A) 4, -8

(B) -6, 5

(D) 6, -3

A square box has a volume of 64 cubic
inches. What's the perimeter of one of its
faces?

(A) 8 inches

(B) 16 inches

(D) 32 inches

20. A cube has a volume of 64 cubic inches.
What's its surface area?

(A) 16 square inches

(B) 64 square inches

(D) 32 square inches

Go on to next page

Chapter 18: Practice Exam 2 25 1

21.

(x 3 )^

(A) 3x 3

(B)x 6

(Qx 9

(D) 2x 6

22.

4! =

(A) 16

(B) 40

(D)24

23.

If a 3 + b 3 =

(A) ft 3 - a 3

(B)x

(D)a

24. What's the sum of the integers from 1
to 300?

- x 3 , then b =

(A) 38,243

(B) 45,150

(D) 52,024

25. (y 2 ) 3 + y 2 =

(A)y 7

(B)y 6

(C)y 8 + y 2

(D) 3y 2

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252

Part V: Practice ASVAB Exams

Subtest 6: Electronics Information

Time: 9 minutes for 20 questions

Directions: This part tests your knowledge of electrical, radio, and electronics information. Select
the correct response from the choices given and then mark the corresponding space on your
answer sheet.

What is used to measure current that is
going through a circuit?

(A) multimeter

(B) amp gauge

(D) tri-gauge

Which of the following isn't a component of
a DC motor?

(A) rotor bars

(B) armature

(D) yoke

The television broadcast standards in the
United States is

(A) NTSC.

(B) RGB.

(D) RTSC.

In a closed electrical circuit,

(A) one terminal is always positive, and
one terminal is always negative.

(B) both terminals can be positive.

(D) terminals are neither positive nor
negative.

Electrical current is counted in what mea-
surement?

(A) hertz

(B) voltage

(D) ohms

6. The following symbol is a/an

(A) resistor.

(B) fuse.

(D) inductor.

7. In the United States, what is the specifica-
tion for an electrical outlet in a bathroom
near a sink?

(A) If within 6 feet of a sink, an outlet must
have a childproof cover.

(B) If within 2 feet of a sink, an outlet must
not be GFCI protected.

(D) If within 2 feet of a sink, an outlet must
also be within reach of the bathtub.

8. The following symbol is a/an

(A) lamp.

(B) fuse.

(D) bell.

Go on to next page

Chapter 18: Practice Exam 2 253

9. When a circuit breaker trips, in what posi-
tion will you find the operating handle?

(A) on position

(B) off position

(D) three-fourths of the way between the
on position and the off position

10. Which wire is smallest?

(A) 00 AWG

(B) 4 AWG

(D) 12 AWG

11. Which of the following is the best
conductor of electricity?

(A) plastic

(B) wood

12. How many paths of electrical flow can be
found in a series circuit?

(A) one

(B) two

(D) It can't be determined from the
information given.

13. A microwave is rated at 1,200 watts. At
120 volts, how much current does it draw?

(A) 1 amp

(B) 10 amps

(D) 1,440 amps

14. Electricians use the term low potential to
refer to

(A) electrical circuits with a low potential
for overload.

(B) building codes that reduce the risk
of fire.

(D) 600 watts or less.

15. Which of the following isn't a conductor of
electricity?

(A) water

(B) graphite

(D) glass

16. The ground wire is always

(A) green.

(B) black.

(D) blue.

17. What does AM mean?

(A) amp metrics

(B) alien mothers

(D) annoid matrix

18. Silver is a better conductor than copper.
But copper is more often used because of

(A) the cost of silver.

(B) the brittleness of copper.

(D) the tendency of silver to tarnish.

19. Electronic circuits that produce high
frequencies are called

(A) amplifiers.

(B) regulators.

(D) oscillators.

20. If you plug an appliance designed for AC
into a DC power source, the appliance

(A) will operate normally.

(B) will produce excessive heat.

(D) will explode into tiny pieces.

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251*

Part V: Practice ASVAB Exams

Subtest 7: Auto & Shop In formation

Time: 11 minutes for 25 questions

Directions: This test is about automobiles, shop practices, and the use of tools. Pick the best
answer for each question and then mark the corresponding space on your answer sheet.

1. If a car uses too much oil, which of the fol-
lowing parts may be worn?

(A) camshaft

(B) connecting rods

(D) piston rings

2. Clean air filters are important because

(A) dirty filters can cause a decrease in
fuel mileage.

(B) they remove pollutants, which can
decrease engine performance.

(D) both A and B

3. The alternator

(A) starts the engine.

(B) supplies power to the battery.

(D) can be used as an alternative to
motor oil.

4. In which automotive system would you find
a "wishbone"?

(A) transmission

(B) engine

(D) oil pan

5. If the electrolyte solution in a battery is too
low, you should add

(A) sulfuric acid.

(B) antifreeze.

(D) gasoline.

6. What area of your car should be
flushed periodically to maintain optimum
performance?

(A) exhaust system

(B) brake system

(D) ignition system

7. The primary purpose of a carburetor is to

(A) maintain engine timing.

(B) regulate oil pressure.

(D) monitor tire pressure.

8. Car restorers often seek NOS parts. What
does NOS stand for?

(A) Near Original Specifications

(B) NASCAR Operating Standards

(D) none of the above

9. To make spark plugs work effectively, the
coil and breaker

(A) provide a gap between the electrodes.

(B) ignite the spark.

(D) create a very high electrical voltage.

10. Schrader valves can be found in your car's

(A) tires.

(B) engine.

(D) electronic ignition.

Go on to next page

Chapter 18: Practice Exam 2 255

11. A bent frame causes

(A) improper tracking.

(B) auto accidents.

(D) excessive rust.

12. In the tire designation 205/55 R 15 92 H,
what does the "H" signify?

(A) tread type

(B) tire height

(D) turning radius

13. When the tightness of screws and/or bolts
is important, it's best to use

(A) a screwdriver.

(B) a torque wrench.

(D) a coping saw.

14. Hammer faces are commonly made of each
of the following materials EXCEPT

(A) steel.

(B) brass.

(D) lead.

15. Hammers, mallets, and sledges are all
striking tools, but mallets and sledges
don't have

(A) claws.

(B) metal parts.

(D) heads.

16. Round objects can be measured most
exactly using a

(A) rigid steel rule.

(B) folding rule.

(D) depth gauge.

17. The best chisel to use when making a
circular cut in metal is a

(A) cold chisel.

(B) socket chisel.

(D) round chisel.

18. A pipe wrench is also known as a

(A) strap wrench.

(B) hammer.

(D) Stillson wrench.

19. Painting on a surface with too much
moisture

(A) causes no problems.

(B) causes bubbling.

(D) takes longer.

20. A tool used to control the location and/or
motion of another tool is called a

(A) control tool.

(B) jig.

(D) static rectifier.

21. An 8-point saw

(A) has 7 teeth per inch.

(B) weighs 8 ounces.

(D) is 8 inches long.

22. Concrete is made by mixing

(A) cement and sand.

(B) cement, sand, and water.

(D) cement, sand, gravel, and water.

Go on to next page

250 Part V: Practice ASVAB Exams

23. Which of the following tools isn't used to
cut metal?

(A)

25. The following tool is a(n)

(B)

24. The following tool is used to

(A) Phillips screwdriver.

(B) Allen wrench.

(D) offset screwdriver.

(A) cut tile.

(B) cut wire.

(D) cut bolts.

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Chapter 18: Practice Exam 2 25 7

Subtest 8: Mechanical Comprehension

Time: 19 minutes for 25 questions

A simple pulley gives a mechanical advan-
tage of

(A) 2

(B)3

(C)l

(D) unknown

The baskets are balanced on the arm in the
figure below. If cherries are removed from
Basket B, then to rebalance the arm,

Basket A

Basket B

fulcrum

(A) the fulcrum will have to be moved to
the right.

(B) Basket B will have to be moved to
the right.

(D) Basket A will have to be moved to
the right.

3. If both Wheel A and Wheel B revolve at the
same rate in the figure below, Wheel A will
cover a linear distance of 12 feet

(A) faster than Wheel B.

(B) slower than Wheel B.

(D) half as quickly as Wheel B.

If a force of 200 pounds is exerted over an
area of 10 square inches, what's the psi?

(A) 10

(B)15

(D)200

Go on to next page

258

Part V: Practice ASVAB Exams

5. In the following figure, if you move Anvil A
toward the middle of the seesaw, Anvil B
will

Anvil A / \ Anvil B

(A) remain stationary.

(B) move toward the ground.

(D) lose weight.

6. If a ramp measures 6 feet in length and
3 feet in height, an object weighing
200 pounds requires how much effort
to move using the ramp?

(A) 200 pounds

(B) 100 pounds

(D) 300 pounds

7. A micrometer is used to measure

(A) small changes in temperature.

(B) changes in psi.

(D) objects invisible to the unaided eye.

8. If the weight is removed from Side B of the
seesaw, what happens to the weight on
Side A?

^g^^r ^^^

Side A

Side B

(A) The weight will never move from Side B.

(B) The weight on Side A will move up in
the air.

(D) Nothing will happen.

9. The force produced when two objects rub
against each other is called

(A) gravity.

(B) recoil.

(D) friction.

10. Normally, atmospheric pressure is
approximately

(A) 14.7 psi

(B) 23.2 psi

(D) 10.1 psi

11. For Gear A and Gear B to mesh properly in
the following figure,

12.

(A) they must be the same size.

(B) they must turn at different rates.

(D) their teeth must be of equal size.

Torsion springs

(A) produce a direct pull.

(B) exert no pull.

(D) coil but do not uncoil.

Go on to next page

Chapter 18: Practice Exam 2 250

13. To move a 400-pound crate from the floor
of a warehouse to the bed of a truck 4-feet
off the ground, the most efficient device to
use is a

(A) lever.

(B) inclined plane.

(D) jackscrew.

14. Water in an engine can cause damage in
winter weather because

(A) it can vaporize.

(B) water expands when it freezes.

(D) cold water creates more steam than
warm water.

15. The weight of the load is being carried on
the backs of the two anvils shown in the
figure. Which anvil is carrying the most
weight?

16.

Anvil A

Anvil B

(A) Anvil A

(B) Anvil B

(D) It can't be determined without more
information.

When the block-and-tackle arrangement
shown in the figure is used to lift a load,
all the following parts remain stationary
EXCEPT

Upper
Block

Lower
Block

LOAD

(A) the upper hook.

(B) the upper block.

(D) all the parts move.

17. In the following figure, what effort (E) must
be applied to lift the anvil?

(A) 7.0 pounds

(B) 9.0 pounds

(D) 10.5 pounds

Go on to next page

260

Part V: Practice ASVAB Exams

18. In the figure below, for each complete revo-
lution the cam makes, how many times will
the valve open?

cylinder

19.

-valve

cam -

r/o

(A)l
(B)6
(9 3
(D)2

In the following figure, assume the valves
are all open. Which valves need to be
closed for the tank to fill up completely?

Water
^Supply/

Valve 1

l Valve 3

Valve 2

-Drainage

Valve 4

Valve 5

(A) 3 and 4 only

(B) 3, 4, and 5

(D) 4 only

20. If Gear A turns left in the figure below,
Gear B

21.

(A) won't turn.

(B) turns left.

(D) It can't be determined.

If Gear 1 makes 10 complete clockwise
revolutions per minute in the figure below,
then

(A) Gear 2 makes 10 complete clockwise
revolutions per minute.

(B) Gear 2 makes 20 complete counter-
clockwise revolutions per minute.

(D) Gear 3 keeps Gear 2 from making any
revolutions.

Go on to next page

Chapter 18: Practice Exam 2 26 /

22. For the fuel to travel from Reservoir A to
Reservoir B, passing through Filters C and
D on the way, which valves must be open?

Filter C

Reservoir A

"e:

7ZL

:s_

24. If a water tank on a toilet keeps overflow-
ing, the problem is probably a

(A) defective float.

(B) clogged pipe.

(D) improper seal.

25. In the figure below, the board holds the
anvil. The board is placed on two identical
scales. Each scale reads

(A) 1, 2, 4, and 8

(B) 1, 2, and 3

(D) 4, 6, and 7

23. A yellow flame on a gas furnace indi-
cates that

(A) everything is fine.

(B) the fuel-air mixture is too rich.

(D) the gas pressure is too low.

scales are identica

(A) 24
(B)10
(C)12
(D)40

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262

Part V: Practice ASVAB Exams

Subtest 9: Assembling Objects

Time: 15 minutes for 25 questions

Directions: The Assembling Objects subtest consists of questions that measure your ability to men-
tally picture items in two dimensions. Each question is comprised of five separate drawings. The
problem is presented in the first drawing and the remaining four drawings are possible solutions.
Determine which of the choices best solves the problem shown in the first picture, then mark the
corresponding choice on your answer sheet.

4- f

A 1

B B

t-*-

<^>

A B

10.

11.

<$>

t) i

.r"?

-2-^t

12.

13.

A B

ll'W

< ^

14.

€^

ffo

€^

-f

|A A

& 1

15.

s- !

\rf

sH?

A B

16.

/TV Ka KJ K) Ra

Go on to netf jm#e

Chapter 18: Practice Exam 2 263

17.

18.

~A,a*

+ " B

iH-

j/r

19.

20.

J>A '

21.

^^x ^

± — ^

i^s^

>_^-

>^^

22.

0» b

4--0

o-^

23.

« o

OS)

G©

CED

OS)

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261} Part V: Practice ASVAB Exams

24.

Ma *

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DO NOT RETURN TO A PREVIOUS TEST.

Chapter 19

Practice Exam 2:
Answers and Explanations

Were are the answers and explanations for the practice exam in Chapter 18. Read over
each question from Chapter 18 as you check your answers. Doing so reminds you
what the question is about and serves as a helpful review. If you look at each question and
the possible answers, you can also identify some of the traps that you may run across on
theASVAB.

You don't have to be an algebra ace to determine whether you're making progress through
your review efforts. Simply compare the number of wrong answers you got on Practice
Exam 1 (Chapter 16) against the number of wrong answers you got on this test. If you put
the work in, you'll probably find that you made fewer errors on Practice Exam 2.

By the time you've scored Practice Exam 2, you should have a good idea of your strengths
and weaknesses. If some subjects or subtests still give you problems, keep studying — just
follow the cross-references for some tips and additional practice questions. If you find you
need in-depth study, check out Chapter 17, where I name some books on various subjects
covered in the subtests.

The ASVAB is technically scored by comparing your raw score to the scores of other people,
which produces a scaled score. Turn to Chapter 2 to find out how the ASVAB is scored.

Subtest 1: General Science Answers

The answers to the questions on the General Science subtest are fairly straightforward —
you either know the answer or you don't. This can be a hard subject to study for because
General Science includes the entire scope of scientific disciplines. The good news is you
may not even have to score well on this subtest — it depends on the job you're interested
in. See Appendix A for military jobs that require a good General Science score. You can find
additional science practice questions in Chapter 15.

l.B 6. B 11. A 16. B 21. D

7. B

12. C

17. A

22. B

3. C

8. A

13. B

18. C

23. C

4. A

9. D

14. D

19. C

24. C

5. D

10. B

15. C

20. A

25. C

266

Part V: Practice ASVAB Exams

Subtest 2: Arithmetic Reasoning Answers

This subtest is one of the most important because it makes up a portion of your AFQT
score, the score that determines your overall mental qualifications to enlist in the military.

If you think you need more in-depth study, review Chapters 7 and 8 or see whether you can
find some high school-level math textbooks at your local library. Chapter 9 has some addi-
tional practice questions.

1. D. For each die, the probability of rolling a 5 is 1 out of 6 that is,^ , so the probability of
not rolling a 5 is 1 - -~, or -~. With two dice, the probability of not rolling a 5 is -~ x ^, or -^ .

2. C. Multiply $1,500 by 7%, or 0.07, and get $105. Then add $105 to $1,500 to find the answer,
$1,605.

Sometimes you can actually save time by not working the problem. In this problem, simply
recognizing that the answer has to be more than $1,500 makes it obvious that Choices (A)
and (B) are wrong. It also should be obvious that 1% of $1,500 has to be more than $7, so
Choice (D) is also wrong. That only leaves the correct answer, Choice (C).

3. A. Two tons = 4,000 pounds; 4,000 x $0.12 = $480.

4. C. y = (a + ft) 2 . Expanding the equation results in y = a 2 + b 2 + lab. You know that a 2 + b 2 = 30
and ab = 10. When you substitute these known values into the equation, you get y = 30 + 2(10).
Solving for y results in y = 50.

5. C. There are 2 pints in a quart, and 4 quarts make up a gallon; therefore, a gallon contains
2x4 = 8 pints, or 16 half-pints. One half-pint equals tf of a gallon.

6. D. First subtract the old cost from the new cost: $2.80 - $2.50 = $0.30. Then divide the dif-
ference by the old cost to find the percent difference: $0.30 + $2.50 = 0.12 = 12%.

1 5

7. C. The aircraft travels 120 miles in 12 minutes, which is 4 of an hour. Therefore, in # (or

1 hour), it would travel 5 x 120, or 600 miles. The aircraft is traveling 600 miles per hour.

8. D. Multiply 50 bushels by 8% to find the yield increase in bushels: 50 x 0.08 = 4. Add 4 bush-
els (the amount of the increase) to 50 bushels (the original yield) to determine that an 8%
increase equals 54 bushels.

9. B. Convert the change to dollars or fractions of dollars and add:

14 dollars = $14.00

16 half dollars =$8.00

12 quarters = $3.00

8 dimes = $0.80

25 nickels =$1.25

10 pennies =$0.10
= $27.15

Subtract the total from $30.00 to determine how much money Junior has to borrow:

$30.00 -$27.15 = $2.85.

10. B. Her commission for the week was $40 (because 0.05 x 800 = 40). The ratio of her com-
mission to her salary is 40:80, which can be reduced to 1:2.

11. C. A gallon consists of 4 quarts, and 4x 25 = 100.

Chapter 19: Practice Exam 2: Answers and Explanations 2 O 7

12. D. Four members is twice as many as two members. Multiply the number of days it would
take four people to paint by 2 (that is, 3 x 2 = 6) to determine how long it would take two
people to do the same task.

13. A. Brian's hourly wage is 24 * 5 = $4.80. Christina's hourly wage is 10.95 * 3 = $3.65.
$4.80 -$3.65 = $1.15.

14. C. The amount of time from 8:30 a.m. to 11:15 a.m. is 2 hours, 45 minutes. From 8:30 a.m.

until 10:30 a.m. is 2 hours. From 10:30 until 11:15 is 45 minutes, or 4 of an hour, for a total of
o 4

2 j hours.

15. C. At a rate of 7 documents per minute, the employee can shred 630 documents in 90 min-
utes. How do you come up with that number? Multiply 7 by 90 (the number of minutes in
li hours). Subtract 630 from 900 total documents to determine that after li hours of
shredding, 270 documents remain.

16. A. If the stereo depreciates 20%, the value of the stereo then becomes 80% of its original
value. After depreciation, the value of the stereo the first year is $960 (0.8 x 1,200). The
value of the stereo after the second year is $768 (0.8 x 960). $768 is Choice (A)

17. A. Divide the distance (135 miles) by the speed (45 miles per hour) to determine that Janet
will take 3 hours to reach the city.

18. D. Multiply the price of the blouse by the amount of the discount: $18.50 x 0.20 = $3.70.

19. C. Subtract the original salary from the new salary to get the difference in salary: $360 -
$320 = $40. Then divide the difference in salary ($40) by the original salary ($320) to deter-
mine the percent increase: 40 + 320 = 0.125 = 12.5%.

20. B. A circle is 360 degrees, so 40 degrees is i of a circle (360° ± 40° = 9). To get the answer,

multiply the circumference of the track by -^ : 360 ft. x ^ = 40 ft. .

21. B. Subtract $35.98 from $40.00 to get $4.02.

22. B. Subtract the time of the plane from the time of the balloon to determine how much
longer it took the balloonist:

13 days 12 hours 16 minutes 13 seconds

- 4 days 10 hours 15 minutes 7 seconds

9 days 2 hours 1 minute 6 seconds

23. A. Divide the total cost by the number of boxes purchased to determine the cost per box:

$48 ^ 12 = $4.

24. D. Multiply 20 x 0.05 to determine how many more miles per gallon the car will get. The
answer is 1. Then add the number of additional miles per gallon the car will get to the orig-
inal number of miles per gallon the car gets to reach the new average: 1 + 20 = 21.

25. A. The minimum length of spike is equal to the diameter of the tree. To find the diameter
of the tree, use the formula, C = nd, where C = 43.96 and n = 3.14: 43.96 = 3.14 xd;d = 43.96 +
3.14; d= 14.

1 3 1

26. D. Divide 104 by 4. You can perform this operation by multiplying 104 by the reciprocal

of -|: 10^ x 4 = ^ x 4 = "^- Divide 84 by 6 - and the answer is 14.

27. C. First figure out how many stones will be needed along the 12-foot side of the patio and
then how many stones will be needed along the 14-foot side of the patio. Then multiply
those two numbers together to get the total number of stones required. Here's the math:
Convert 12 feet to inches: 12 ft. x 12 in./ft. = 144 inches. The paving stones are 8 inches
square, so divide 144 inches by 8 inches (144 + 8), which gives you 18 stones.

268

Part V: Practice ASVAB Exams

Do the same math for the 14-foot length: 14 ft. x 12 in./ft. = 168 in., and 168 * 8 = 21.
Therefore, 21 stones are needed on the 14-foot side.

Now multiply the stones: 18 stones x 21 stones = 378 stones, which is Choice (C).

28. D. Calculate the amount of the deduction by multiplying her salary by the percent deducted:
$25,000 x 28% = $25,000 x 0.28 = $7,000. Subtract that product from the salary to determine
the net pay: $25,000 - $7,000 = $18,000.

29. B. When the sum of two angles is 180 degrees, the angles are said to be supplementary to
each other. To find the supplement, subtract 55 from 180: 180 - 55 = 125.

30. C. Multiply the height of the stack in feet by 12 to determine the height of the stack in
inches: 6 x 12 = 72 inches. Divide that number by 4 inches, the thickness of each board,
to determine the number of pieces of lumber in the stack: 72 * 4 = 18.

Subtest 3: Word Knowledge Answers

Your score on the Word Knowledge subtest is important — it counts toward your AFQT
score (see Chapter 1).

If your score on the Word Knowledge subtest has improved since you took the first test,
congratulations! If not, don't be too surprised. Improving your score on this subtest in a
short period of time is difficult, but it can be done. Review the information from Chapter 4
and set aside time each day (maybe several times a day, depending on how soon you plan
on taking the ASVAB) to memorize words, roots, prefixes, and suffixes. Chapter 6 has some
additional practice questions for you to sink your dictionaries into.

l.C 8. B 15. A 22. C 29. A

2. A

9.B

16. D

23. D

30. A

3. A

10. C

17. A

24. A

31. C

4. C

11. C

18. C

25. D

32. C

5.B

12. B

19. B

26. B

33. D

6. B

13. D

20. A

27. B

34. B

7. D

14. B

21. C

28. D

35. D

Subtest 4: Paragraph Comprehension Answers

Doing well on the Paragraph Comprehension subtest is really important if you want to enlist
in the military — this score counts toward your AFQT score. If you're missing more answers
than you should, review the info in Chapter 5 and concentrate on improving your analytical
reading skills. For example, when you're reading the evening newspaper, ask yourself what
the main point of an article is. Or when you finish a news story, set the paper down and try
to remember what the President said about the budget deficit. Think of this technique as a
workout for your mind. You can find more practice questions in Chapter 6.

Chapter 19: Practice Exam 2: Answers and Explanations £Oy

1. B. The author is describing a quaint country setting.

2. B. The passage states that the brooks in the village run south, so the answer is Choice (B).
A few miles north, the brooks run in an opposite direction (north).

3. B. The passage states that Panama revolted against Columbia, not that they fought over the
canal, so Choice (A) is incorrect. The passage states that the foreign companies were unsuc-
cessful in building the canal, so Choice (C) is incorrect. The United States, not Panama, built
the canal, so Choice (D) is wrong. In the next to last sentence, the passage states that the
U.S. was given rights to the land the canal occupied, making Choice (B) the correct answer.

4. D. According to the passage, a torn U.S. flag can be professionally mended, but a severely
torn flag should be destroyed. The preferred method of destruction is by burning.

5. D. The passage states that guilds had economic and social purposes, so Choice (A) is
incorrect. The passage states that guilds were similar to labor unions, so Choice (B) is
incorrect. The passage states that guilds protected merchants and craftspeople; it says
nothing about exploiting workers, so Choice (C) is incorrect. The third sentence states
that some guilds held considerable economic power, but even small guilds protected mem-
bers, making Choice (D) the correct answer.

6. D. According to the passage, it took more than four years for the government to believe
that anyone had flown a heavier-than-air craft. The historic flight was in December 1903,
and the Wright brothers delivered the first aircraft to the government in August 1908,
4.5 years later. The passage supports all the other statements.

7. C. Freud comments on the characteristics of memory throughout the entire passage.

8. A. The passage describes how troy and common weights are different, so Choice (B) is incor-
rect. Common and avoirdupois are the same system, so Choice (C) is incorrect. A troy ounce
is 480 grains, so Choice (D) is incorrect. Choice (A) is the correct answer because the second
sentence states that a common ounce is 437.5 grains, which is just shy of than 438 grains.

9. B. The passage doesn't address leading by example or use of technology by workers, so
Choices (A) and (C) are incorrect. Maximizing worker performance is a result of leadership
involvement, not a principle of leadership, making Choice (D) incorrect. The correct
answer, showing interest in workers' problems, is in the third sentence of the passage.

10. C. The passage doesn't support Choices (A) or (B). The passage states that white blood
cells are found in blood and bone marrow, so Choice (D) is wrong. The correct answer,
Choice (C), can be found in the first sentence. The passage states that leukemia interferes
with "the body's ability to produce red blood cells."

11. C. High intensity conflict is listed as a type of military operation (in the last sentence), not
one of the four operational concepts.

12. C. The JV 2020 guides all the military services with its vision of future war fighting.
Although Choice (D) is close, the passage doesn't specifically reference military training.

13. B. Cytogenetics is the study of the cellular basis of inheritance; the text doesn't support
Choices (A), (C), or (D).

14. A. Nothing in the passage supports Choices (B) or (D). Although human genetics is an
important subfield of genetics, nothing in the passage suggests that it's the only concern of
geneticists. Microbial genetics, as the passage mentions, is a subfield in genetics that has
nothing to do with humans, so Choice (C) is incorrect. Choice (A) is the correct answer —
the second sentence mentions genes and their transmission to offspring.

15. C. Nothing in the passage supports Choices (A), (B), or (D). Choice (C) is the correct
answer because the last sentence in the passage states, "[Genetic counselors] advise cou-
ples and families on the chances of their offspring having specific genetic defects." Note it
does not state that genetic counselors use genetics to prevent offspring from inheriting
defects, which is what Choice (D) states, making Choice (D) an incorrect answer.

270

Part V: Practice ASVAB Exams

Subtest 5: Mathematics Knowledge Answers

Although the military doesn't expect you to be the next Einstein, a solid grasp of mathemat-
ics is important because math skills make up half of your AFQT score. If you're still strug-
gling on this subtest, it's time to hit the books. (Actually, as much as you may feel like it,
I don't recommend that you actually hit the books — just study them.) See Chapter 9 for
some more fun practice questions.

1. A. If two exponents have the same base, you can multiply them by keeping the base and
adding the exponents together: x^x 4 ) = x 2+4 = x 6 ,

2. A. To find area, multiply length times width (A = Iw). You have the width, so you need to
find the length. For a rectangle, P = 2/ + 2w, so plug in the values you know and solve for /.
To determine the length, subtract two times the width from the perimeter: 36 - 2(4) = 36 -
8 = 28. Divide the answer by 2 to determine the length of one side: 28 * 2 = 14. Then multi-
ply length times width to determine the area: A - 14 x 4 = 56.

3. D. The cube of 4 is 4 x 4 x 4 = 64, so 4 is the cube root of 64.

4. A. To convert this number to scientific notation, move the decimal point to the left until
it's to the immediate right of the first number, while counting the number of moves. In this
case, you move it five places. The result is then multiplied by 10 raised to the power of the
number of places the decimal point was moved. The exponent is positive here because the
original number, 314,000, is larger than 3.14. Choice (B), 3.14 x 10" 5 , is equal to 0.0000314,
so it's incorrect.

5. C. A reciprocal is the number by which a number can be multiplied to produce 1. The
reciprocal -~ is 6, because ^ x 6 = 1.

6. A. You start with 0.05 * x - 1. Multiply both sides of the equation by x: 0.05 = korx= 0.05.
Check by substituting 0.05 for x in the original equation.

7. C. x 2 - 6x + 9 = (x - 3)(x -3) = (x - 3) 2

8. C. You start with (3 x 2)(7 - 2)(6 + 2) = (6 x 4)x Solve the left side of the equation first.
(6)(5)(8) = (30)(8) = 240. Therefore, 240 = (6 x 4)x, which equals 240 = 24x. Now isolate x by
dividing both sides of the equation by 24: 240 + 24 = 24x * 24, or 10 = x Check your answer
by substituting 10 for x in the original equation.

9. B. Isolate x on one side of the equation. Subtract x from both sides of the equation and
then add 6 to both sides:

2x - 6 = x + 5

x-6 = 5

x= 11

Check by substituting 11 for x in the original equation.

10. D. Solve for/. /= (1,000)(7%)(1), or/= (1,000)(0.07)(1) = 70.

11. B. Multiply out what's in parentheses. Then simplify and solve for x:

(x-7) 2 -4 = (x + l) 2

(x-7)(x-7)-4 = (x + l)(x + l)

x 2 -7x-7x + 49-4 = x 2 +x + x + l

x 2 -14x + 45 = x 2 +2x + l

-14x + 45 = 2x + l

-16x = -44

x 4 z 4

Chapter 19: Practice Exam 2: Answers and Explanations 271

12. A. The area of a circle is A = nr 2 . A = 7t5 2 . The number n is approximately 3.14, so 3.14 x 25
means A is approximately 78.5 square inches.

13. D. Distribute the %, simplify, and solve for x. Note that when you divide by a negative

number, you have to switch the direction of the inequality sign.
|(6x-9) + 4>5x + l

Ax - 6 + 4 > 5x + 1
Ax - 2 > 5x + 1
Ax > 5x + 3
-x> 3
x<-3

14. B. For cylinders, Volume = nr^h. In this problem, V - 7i(3 2 )(5). Assume n is approximately
3.14. Vis approximately equal to (3.14)(9)(5), or 141 cubic inches.

15. A. A right triangle has one right angle (one 90° angle).

16. D. Parallelograms have opposite sides of equal length.

17. D. Angles measuring more than 90 degrees are obtuse angles.

18. B. This is a quadratic equation, which you solve by factoring. First factor out the -1; then
factor the quadratic expression and solve for x:

-x 2 -x + 30 =

l(x 2 +x-30) =

x 2 + x - 30 =

(x+6)(x-5) =

x+6 =

x-5 =

x = -6

x = 5

19. B. Volume equals length times width times height (V - Iwti). In this case, V - 64, so one
edge of the box is 4 inches long (because 4 is the cube root of 64: 64 = 4 x 4 x 4). Find the
perimeter by adding the four sides together: 4 + 4 + 4 + 4= 16.

20. C. You calculate volume by multiplying length times width times height (V - Iwti). Because
the edges are equal on a cube, each edge is 4 inches (because 4x4x4 = 64). The area of
one face of the cube is 4 x 4 = 16 square inches, and because a cube has 6 sides, you multi-
ply 16 x 6 to find the surface area of the cube, 96 square inches.

21. C. (x 3 ) 3 is the same as 0c 3 )(x J )(Jc 3 ). Multiply exponents with the same base by keeping the
base and adding the exponents: (* 3 )0c 3 )(jc s ) = x 3+3+3 = x 9 .

22. D. 4! (4 factorial) = 4x3x2x1 = 24.

23. B. You start with a 3 + b 3 = a 3 + x 3 . To solve, subtract a 3 from both sides of the equation and
then take the cube root:

a 3 + b 3 - a 3

6 3 =x 3

b - x

272

Part V: Practice ASVAB Exams

24. B. The formula to find the sum of a finite arithmetic sequence is 5 = y(a + b), where n is the

number of terms, a is the first term in the sequence, and b is the last term in the sequence.
In this case there are 300 terms (n), and the first term is 1 and the final term is 300.

5 = | (a + b)
5=300(1 + 300)

5 = 150(301)
5 = 45,150

25. B. (y 2 ) 3 is the same as (y 2 )(y 2 )(y 2 ). Multiply exponents with the same base by keeping the
base and adding the exponents: (y 2 ~)(y 2 ~)(y 2 ~) = y 2 * 2 * 2 = y 6 . The second y 2 in the equation
cannot be added into the first term because now they are not like terms, so the answer is
Choice (B), y 6 + y 2 . Tricky, eh?

Subtest 6: Electronics Information Answers

If you're having difficulty defining the difference between AC and DC, you may want to
spend some additional time studying basic electronic information. Reviewing Chapter 13
can help. You can also wrap your wires around the practice questions in Chapter 15.

On the other hand, you may not be interested in a military job that requires a decent score
on this subtest (see Appendix A), in which case, don't bother.

1. A. A multimeter includes several pieces of test equipment, including an ammeter, which
measures inline current.

2. A. Rotor bars are only on AC induction motors, not DC motors.

3. A. NTSC stands for National Television Analog Committee and, although gradually being
replaced by ATSC (Advanced Television Systems Committee), NTSC is currently the broad-
cast standard in the U.S. Choice (B) is incorrect because RGB stands for red, green, and
blue — the colors of light used to create an image. Although most televisions use this stan-
dard, it is not a broadcast standard. Choice (C) is incorrect because SECAM (Sequentiel
couleur avec memoire, or sequential color with memory) is a standard used in other coun-
tries. Choice (D) is RTSC, which stands for Raytheon Technical Services Company and is
obviously not the correct answer.

4. A. In a closed circuit, one terminal is always positive, and the other is always negative.

5. C. Amperes (or amps) are the unit of measure of electric current. Hertz is the unit of mea-
surement of frequency, not current. Current equals voltage divided by resistance.
Resistance is measured in ohms. Therefore, neither voltage nor ohms can be the unit of
measure for current.

6. B. The symbol is a fuse. Fuses are designed to blow (melt) if the current flowing through it
exceeds a specified value.

7. C. This is code prescribed by the NEC (National Electric Code). Outlets within 6 feet of a
sink need to be GFCI protected for safety reasons.

8. A. The symbol is a lamp. A lamp is a transducer that converts electrical energy to light.

9. C. Conventional circuit breaker handles have four positions: on, off, trip, and reset. When
tripped, the handle moves to the middle position.

10. D. The smaller the wire, the larger the number.

Chapter 19: Practice Exam 2: Answers and Explanations 2 /3

11. D. Plastic does not conduct, and wood is a poor conductor. Aluminum is a good conductor
but not better than copper.

12. A. A series circuit has only one path, so if you break the circuit's path at any point, elec-
tricity stops flowing. An example of a series circuit is a string of Christmas lights that no
longer works if a single bulb burns out.

13. B. /(current) = Power (watts) + Effort (volts). In this case, / = 1,200 + 120 = 10 amperes.

14. D. Potential equals voltage; low potential is anything less than 600 watts.

15. D. Glass is an insulator. Other insulators include plastics, paper, and rubber.

16. A. Ground wires are always green.

17. C. Amplitude modulation (AM) was the first type of audio modulation to be used in radio.
It works well with high frequency (HF) and Morse code.

18. A. Silver is a better conductor, but it's more brittle than copper and more expensive.

19. D. Oscillators produce high frequencies. An amplifier changes the amplitude of a signal.
A regulator is a circuit that maintains a constant voltage. A transformer is a device that
changes (transforms) the voltage at its input side to a different voltage on its output side.

20. B. When DC is applied to an AC appliance, the amount of resistance is less, so more cur-
rent flows through the wire and heat builds up.

Subtest 7: Auto & Shop In formation Answers

You need to do well on this subtest to qualify for certain military jobs (see Appendix A). If
you care about those jobs and you're missing more than a few questions on this subtest, it's
time for more extreme measures — like taking your mother's car apart and putting it back
together (or going back over Chapter 11).

Drive back to Chapter 15 for more practice questions.

l.D 6.C 11. A

2. D 7. C 12. C

3. B 8. C 13. B

4. A 9. D 14. C

5. C 10. A 15. A

Subtest 8: Mechanical Comprehension Answers

If you need to do well on the Mechanical Comprehension subtest (as in you're hoping for a
military career that requires a score for this subtest) but you're still missing more answers
than you should be, ask yourself whether your math skills need work. Go back to Chapters 7
and 8 if they do. Many of the formulas you need to know for this subtest require an under-
standing of arithmetic and basic algebra.

16. C

21. A

17. D

22. D

18. D

23. B

19. B

24. D

20. B

25. B

27b

Part V: Practice ASVAB Exams

Usually, improving your arithmetic and basic-algebra skills will improve your score on the
Mechanical Comprehension subtest. Improving your knowledge of physics is also beneficial.
Take a gander at Chapter 12 and the practice questions in Chapter 15.

1. C. A simple pulley gives no mechanical advantage, although it does make work easier by
spreading out the work needed over several tries. The mechanical advantage is 1.

2. D. Moving Basket A to the right counterbalances the loss of cherries from Basket B.

3. A. Wheel B has to make more revolutions to cover the same ground as Wheel A, so it
covers the distance more slowly.

4. C. You can calculate psi as Pressure = Force * Area. So in this problem, P = 200 * 10 = 20.

5. B. If you move Anvil A toward the center, Anvil B will move toward the ground.

6. B. The formula to determine mechanical advantage of an inclined plane is Length of Ramp *
Height of Ramp = Weight of Object * Effort. Plugging in the numbers gives you

6_200
3" E

6£ = 600

£ = 100

7. C. Micrometers measure very small but not microscopic objects.

8. C. Reducing the weight on Side B will cause Side A to move toward the ground.

9. D. Objects rubbing together produce friction.

10. A. Normal atmospheric pressure (the average atmospheric pressure at sea level) is 14.7 psi.

11. D. Gears of unequal size can mesh properly as long as their teeth are of equal size.

12. C. Torsion springs coil or uncoil and produce a twisting action, not a direct pull; in other
words, torsion springs apply torque.

13. B. To move a heavy object a few feet in height, the inclined plane is the most efficient
device (of those listed) to use. Note: The mechanical advantage of an inclined plane is
equal to the slope of the plane divided by the height. The longer the slope is (compared to
the height), the greater the mechanical advantage will be.

14. B. Water expands when it freezes, possibly damaging engine components.

15. A. The load is closer to Anvil A, so it's carrying the greater portion of the weight.

16. C. All the listed parts remain stationary except the lower block.

17. A. Apply the leverage formula: Length of Effort Arm * Length of Resistance Arm =

Resistance Force * Effort Force:

9 _ 21
3" £

o_21

a ~ E

3£ = 21

£ = 7

Chapter 19: Practice Exam 2: Answers and Explanations 2 75

18. C. The valve will open each time a high point of the cam hits it. The cam has three high
points, so the valve will open three times per revolution.

19. A. Closing only Valves 3 and 4 keeps the water from leaving the tank.

20. C. Gears in mesh always turn in opposite directions.

21. B. If Gear 1 turns at 10 rpm, then Gear 2, which is half the size, turns twice as fast, at a rate
of 20 rpm.

22. A. Opening Valves 1, 2, 4, and 8 allows the fuel to travel through the filters. Opening Valves
1, 2, and 3 doesn't allow the fuel to travel through Filter D. Opening Valves 6, 7, and 8
doesn't allow the fuel to travel through the filters. Opening Valves 4, 6, and 7 doesn't allow
fuel to travel to Reservoir B.

23. B. A yellow flame indicates too much fuel or not enough air. More air should be allowed to
enter and mix with the gas. Thus, the fuel-air mixture is too rich.

24. A. The float measures the water level in the tank. If the tank overflows, the float is proba-
bly defective.

25. C. The 20-pound anvil and the 4-pound board weigh 24 pounds total or, divided by 2,
12 pounds per scale.

Subtest 9: Assembling Objects Answers

So far, only the Navy has elected to use scores from the Assembling Objects subtest and
only for a few jobs. If you're planning on joining the Navy and you're interested in a Navy
career that requires a score on this subtest (see Appendix A), review Chapter 14 for help on
improving your score. For additional practice questions, see Chapter 15.

l.B 6.A 11. C 16.D 21. A

2. A

7. B

12. B

17. C

22. D

3. C

8. C

13. A

18. B

23. C

4.D

9. D

14. B

19. C

24. B

5. C

10. D

15. D

20. C

25. D

276

Part V: Practice ASVAB Exams

Chapter 20

Practice Exam 3

■ suggest you take the third practice exam a week or so before you're scheduled to take
«S the real ASVAB. Use it to refresh your memory of the material or to cram for any of the
subtests that you have to do better on than you've been doing.

$JABE*

Don't forget to use the test-taking strategies and the guessing tips in each of the subtest
chapters earlier in this book. Chapter 3 provides additional information on how to improve
your score just by using smart test-taking strategies.

This sample test features nine subtests and follows the same format as the actual ASVAB.
To get the most out of this sample test, take it under the same conditions as the real ASVAB:

v* Allow yourself about three hours to take the entire exam, and take the whole thing at
one time.

i*" Find a quiet place where you won't be interrupted.

i*" Bring a timer that you can set for various lengths of time, some scratch paper, and a
pencil.

J-" Use the answer sheet that's provided.

j-" Don't take a break during any subtest. You can take a short one- or two-minute break
between subtests if you need it.

After you complete the entire test, check your answers against the answer keys and expla-
nations in Chapter 21. Then compare the results to your results on Practice Exams 1 and 2.
You should see some improvement.

21 S

Part V: Practice ASVAB Exams

Answer Sheet for Practice Emm 3

Subtest 1: General Science

Subtest 2: Arithmetic Reasoning

Subtest 3: Word Knowledge

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Subtest 4: Paragraph Comprehension

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Subtest 5: Mathematics Knowledge

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4 ®®@® 9 ®@©@

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Subtest 6: Electronics Information

1 ®®©® 5 ®@©®

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2 ®@©@ 6 ®®©®

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3 ®@©® 7 ®®©®

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4 ®®©® 8 ®@©®

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Subtest 7: Auto & Shop Information

1 ®®©@ 6 ®@©®

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2 ®@©@ 7 ®®©®

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Subtest 8: Mechanical Comprehension

Subtest 9: Assembling Objects

Chapter 20: Practice Exam 3 2 70

Subtest 1: General Science

Time: 11 minutes for 25 questions

Directions: This test challenges your knowledge of general science principles usually covered in
high school classes. Pick the best answer for each question and then mark the space on your
answer sheet that corresponds to the question number and the letter indicating your choice.

The moon completes a revolution around
the Earth approximately every

(A) 28 days.

(B) 365 days.

(D) 7 days.

Carcinogens are chemicals that cause

(A) high blood pressure.

(B) genome mutations.

(D) diabetes.

A Paramecium is

(A) a one-celled organism.

(B) algae.

(D) a many-celled organism.

What substance is essential for the func-
tion of the thyroid gland?

(A) potassium chloride (salt)

(B) hemoglobin

(D) iodine

The brainstem controls

(A) vision.

(B) voluntary muscle movements.

(D) some involuntary activities.

10.

Which element is the most abundant one in
the atmosphere?

(A) oxygen

(B) nitrogen

(D) hydrogen

Minerals are necessary for

(A) respiration.

(B) eliminating waste.

(D) metabolic function.

What's the only metallic element found as a
liquid at room temperature?

(A) bromine

(B) tellurium

(D) silver

Which of the following isn't a type of
telescope?

(A) reflecting

(B) convexing

(D) catadioptric

A dekagram

(A) is larger than a kilogram.

(B) is smaller than a kilogram.

(D) doesn't exist.

Go on to next page

280

Part V: Practice ASVAB Exams

11. The aurora borealis can be seen only in the

(A) winter.

(B) summer.

(D) Northern Hemisphere.

12. The three important properties of sound
waves are

(A) wavelength, speed, and crest.

(B) speed, frequency, and reflection.

(D) wavelength, frequency, and speed.

13. Between which two planets can most of the
asteroids in the solar system be found?

(A) Mars and Jupiter

(B) Saturn and Jupiter

(D) Mercury and Venus

14. At room temperature, an element is a

(A) gas.

(B) liquid or gas.

(D) liquid, gas, or solid.

15. The elements hydrogen and helium com-
prise what percentage of almost all matter
in the universe?

(A) 75%

(B) 82%

(D) 98%

16. Compounds are created when

(A) atoms of two or more like elements are
combined.

(B) atoms of two or more different ele-
ments are combined.

(D) a molecule decomposes.

17. What theory suggests the universe will
come to an end when its ever-increasing
rate of expansion causes all matter to fly
apart?

(A) The Big Rip

(B) The Big Bang

(D) The Big Easy

18. A watt-hour measures

(A) how much electricity is converted.

(B) the number of electrons moving past a
specific point.

(D) voltage.

19. Which of the following planets, known as
gas giants, have no rings?

(A) Neptune

(B) Jupiter

(D) They all have rings.

20. Gas particles move

(A) more slowly than liquid particles.

(B) more slowly than solid particles.

(D) at the same rate as all other particles.

21. Absolute zero is

(A) degrees Fahrenheit.

(B) degrees Celsius.

(D) -32 degrees Fahrenheit.

22. Radiology is employed when doing which
of the following?

(A) using a Magnetic Resonance Imaging
machine

(B) using a blood pressure cuff

(D) breathing

Go on to next page

Chapter 20: Practice Exam 3 28 1

23. Which of the following statements is NOT
true?

(A) The human female chin is usually more
rounded or pointed than the human
male chin.

(B) The human female pelvis is usually nar-
rower than the human male pelvis.

(D) The human male skull has a larger
brow ridge than the human female
skull.

24. A lunar eclipse occurs when

(A) the Earth moves into the moon's
shadow.

(B) the sun blocks the moon from view.

(D) the moon moves into the Earth's
shadow.

25. What chemical can be used to detect
blood, even if it's been wiped from a
surface?

(A) luminol

(B) cyanide

(D) alcohol

STOPI

DO NOTTURNTHE PAGE UNTILTOLDTO DO SO.
DO NOT RETURN TO A PREVIOUS TEST.

282

Part V: Practice ASVAB Exams

Subtest 2: Arithmetic Reasoning

Time: 36 minutes for 30 questions

Directions: This test is about arithmetic. Each question is followed by four possible answers.
Decide which answer is correct and then mark the space on your answer sheet that has the same
number and letter as your choice. Calculators are not permitted. Use scratch paper for any figuring
you need to do.

A baker sells a dozen donuts for $3.99. The
cost to make three donuts is $0.45. How
much is the total profit on 5 dozen donuts?

(A) $17.70

(B) $13.20

(D) $10.95

Your piggy bank contains $19.75 in dimes
and quarters. There are 100 coins in all.
How many dimes are there?

(A) 25

(B) 30

A bricklayer charges $8 per square foot to
lay a patio. How much would it cost for the
bricklayer to lay a 12-foot by 16-foot patio?

(A) $960

(B) $192

(D) $1,536

Terry earns three times more per hour
than Tim. Tim earns $2 more per hour than
Angie. As a group, they earn $43 per hour.
What's Angie's hourly wage?

(A) $7.00

(B) $8.00

(D) $10.00

If four people can run eight machines, how
many machines can two people run?

(A) 2

(B)4

(C)l

(D)3

The price of daily admission at an amuse-
ment park is $36. The park sells an unlim-
ited season pass for $240. How many trips
would you need to make with the season
pass in order for it to cost less than paying
the daily admission rate?

(A) 6

(B)7

(D)9

A plumber needs four lengths of pipe, each
3 feet, 6 inches long. Pipes are sold by the
foot. How many feet does he need to buy?

(A) 15

(B)16

(D)12

The product of two consecutive odd num-
bers is 399. What are the numbers?

(A) 17 and 19

(B) 19 and 21

(D) 25 and 27

Go on to next page

Chapter 20: Practice Exam 3 283

9. A personal trainer earns a 65% commission
on her training sales. If she sells $530 worth
of training, how much commission does
she make?

(A) $874.50

(B) $34.45

(D) $185.50

10. A rectangle is 1 inch longer than it is wide.
Its diagonal is 5 inches. What's the width of
the rectangle?

(A) 2 inches

(B) 3 inches

(D) 5 inches

11. A treasure map is drawn to a scale of

2 inches equals 3 miles. On the map, the
distance between Point A and X-marks-the-
spot is 9-k inches. How many actual miles
does this represent?

(A) 20 i miles

(B) 14-| miles

(D) 19 miles

12. A painter has painted a picture on a piece
of canvas that measures 10 by 14 inches.
To accommodate a frame, he has left an
unpainted margin of 1 inch all the way
around. What part of the canvas has been
painted?

(A) 96%

(B) 91%

(D) 69%

13. A dog trainer is building a rectangular dog
run that measures 9 by 16 feet. If she wants
to fence the perimeter of the run, how
many feet of chain link fence will she need?

(A) 144 feet

(B) 25 feet

(D) 50 feet

14.

15.

16.

17.

A rectangle is li times as long as it is wide.

The perimeter of the rectangle is 100 inches.
What's the length of the rectangle?

(A) 20 inches

(B) 30 inches

(D) 45 inches

Miguel passed seven of his history quizzes
and failed three. The fraction of quizzes he
passed is correctly expressed as

(A) J

0)4

(D)

A 3-yard-long ribbon was used to trim four
dresses. Each dress used the same amount
of ribbon. How much ribbon was used for
each dress?

(A) 1 yard

(B) | yard

(C)iyard
(D) | yard

Kelly bought a painting at an antiques sale
for $500 and the following day she was able
to sell it for an additional $30. What per-
centage of the sale price was her profit?

(A) 5%

(B) 6%

18. A bin of bolts at the hardware store con-
tains 7 dozen bolts when full. The stock
clerk is supposed to reorder bolts when

the bin is 4 full. How many bolts are in the

bin when it's time to reorder?

(A) 14 bolts

(B) 1 bolt

(D) 12 bolts

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28b

Part V: Practice ASVAB Exams

19. Two bicyclists head toward each other
from the opposite ends of Main Street,
which is 6 miles long. The first biker
started at 2:05 going 12 mph. The second
biker began peddling 4 minutes later at a
rate of 14 mph. What time will they meet?

(A) 2:13

(B) 2:24

(D) 2:34

20. A recipe calls for 8 ounces of black beans
or red beans. The cheapest option to buy
and use would be

(A) two 4-ounce cans of black beans at
$0.79 each.

(B) one 8-ounce can of red beans at $1.49.

(D) three 3-ounce cans of red beans at
$0.65 each.

21. A street vendor sells $25.70 worth of pret-
zels on Friday, $32.30 on Saturday, and
$31.80 on Sunday. He spends a fourth of the
money over the weekend. How much
money does he have left?

(A) $89.80

(B) $22.45

(D) $67.35

22. A recruit has $30.00. He saw some camou-
flage socks for $3.95 a pair. How many pairs
of socks can he buy?

(A) 9

(B)7

(D)4

23. A crate containing a puppy weighs

60 pounds, 5 ounces. The puppy weighs
43 pounds, 7 ounces. How much does
the crate alone weigh?

(A) 16 pounds, 8 ounces

(B) 16 pounds, 2 ounces

(D) 16 pounds, 14 ounces

24.

25.

26.

27.

28.

In a manufacturing plant that produces new
computers, a 0.15 probability exists that a
computer will be defective. If five comput-
ers are manufactured, what's the probabil-
ity that all of them will be defective?

(A) 7.6

(B) 0.60

(D) 0.000076

A house contains one 12-foot x 14-foot bed-
room, one 12-foot x 10-foot bedroom, and
one 8-foot x 12-foot bedroom. What's the
total amount of carpeting needed to carpet
all three bedrooms?

(A) 383 square yards

(B) 128 square yards

(D) 43 square yards

Rafael can type 9 pages an hour. How long
will it take him to type 126 pages?

(A) 14 hours

(B) 9 hours

(D) 16 hours

In a 60-minute gym class, 48 girls want to
play volleyball, but only 12 can play at a
time. For each player to get the same
amount of playing time, how many minutes
should each person play?

(A) 1^ minutes

(B) 6 minutes

(D) 15 minutes

The movie-rental store charges $2.00 for
the first day a rented DVD is overdue and
$1.25 for each day after that. If a person
paid $8.25 in late fees, how many days was
the DVD overdue?

(A) 7 days

(B) 6 days

(D) 5 days

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Chapter 20: Practice Exam 3 285

29. Janet is trying to watch her weight. A half-
cup of pudding has 150 calories. The same
amount of broccoli has 60 calories. How
much broccoli can Janet eat to equal the

same number of calories in the i cup of
pudding?

(A) 2 cups

(B) 2^ cups

(Ql^cups
(0)1-1 cups

30. The neighbor's dog barks at a raccoon
every 15 minutes at night. If he first barks
at 10 p.m., when you're trying to fall asleep,
how many times will he have barked by
2 a.m., when you give up trying to sleep
and decide to read a book instead?

(A) 16 times

(B) 132 times

(D) 15 times

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286

Part V: Practice ASVAB Exams

Subtest 3: Word Knortiedqe

Time: 11 minutes for 35 questions

Directions: This test is about the meanings of words. Each question has an underlined word. You
may be asked to decide which one of the four words in the choices most nearly means the same
thing as the underlined word or which one of the four words means the opposite. If the underlined
word is used in a sentence, decide which of the four choices most nearly means the same thing as
the underlined word as used in the context of the sentence. Mark the corresponding space on your
answer sheet.

1. Lackadaisical most nearly means 6.

(A) flowerless.

(B) listless.

(D) suitable.

2. The fruit was edible . 7.

(A) waxy

(B) expensive

(D) digestible

3. Universities and colleges should be

designed to cater to the philomaths . 8.

(A) athletes

(B) scholars

(D) faculty

4. Pretense most nearly means 9.

(A) politeness.

(B) dishonesty.

(D) appearance.

5. At an early age Jane showed a proclivity for 10.
music and dancing.

(A) predisposition

(B) interest

(D) fever

Her conversation was incoherent .

(A) eloquent

(B) succinct

(D) amusing

The week following Joe DiMaggio's death
was filled with often mawkish eulogies.

(A) long

(B) sentimental

(D) detailed

She established proof.

(A) offered

(B) invented

(D) demonstrated

Ephemeral most nearly means

(A) short-lived.

(B) mythical.

(D) exceptional.

Avocation most nearly means

(A) hobby.

(B) occupation.

(D) education.

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Chapter 20: Practice Exam 3 28 7

11. Kvetch most nearly means

(A) assert.

(B) yell.

(D) argue.

12. Her eyesight was acute .

(A) sharp

(B) poor

(D) tested

13. Inamorata most nearly means

(A) boyfriend.

(B) mistress.

(D) acquaintance.

14. Her thoughts on the matter were
inconsequential .

(A) profound

(B) disturbing

(D) confused

15. Debouch most nearly means

(A) emerge.

(B) fight.

(D) capture.

16. He was an amateur astronomer.

(A) veteran

(B) novice

(D) pleased

17. She had no idea how to react to her ludic
boyfriend.

(A) playful

(B) cheating

(D) lazy

18. The rose was crimson .

(A) blooming

(B) colorful

(D) red

19. The word most opposite in meaning to
benison is

(A) theft.

(B) replaceable.

(D) heavy.

20. She was exempt from gym class.

(A) banned

(B) excused

(D) refreshed

21. The eldritch light of the desert can play
tricks on your eyes.

(A) bright

(B) wavering

(D) yellow

22. Defective most nearly means

(A) flawed.

(B) noticeable.

(D) durable.

23. Allot most nearly means

(A) plow.

(B) assign.

(D) test.

24. The doctor gave the patient a cursory
examination.

(A) in-depth

(B) painful

(D) superficial

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288

Part V: Practice ASVAB Exams

25. Arcanum most nearly means

(A) rare.

(B) secret.

(D) false.

26. Her answer was terse .

(A) defensive

(B) angry

(D) brief

27. The dulcet songs of the band got the atten-
tion of the audience.

(A) harmonious

(B) love

28. He was arrested on a misdemeanor charge.

(A) theft

(B) serious

(D) bogus

29. Embonpoint most nearly means

(A) plumpness.

(B) height.

(D) cold.

30. He concocted a story about me.

(A) told

(B) rehearsed

(D) remembered

31. He spent his days searching fruitlessly for
that chimera , his true self.

(A) personality

(B) enigma

(D) monster

32. Her former home was in Colorado.

(A) previous

(B) current
(C) second
(D) abandoned

33. Mulct most nearly means

(A) complain.

(B) play.

(D) defraud.

34. My voice is strident .

(A) soft

(B) melodious

(D) baritone

35. Raffish most nearly means

(A) clean.

(B) serene.

(D) expensive.

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Chapter 20: Practice Exam 3 280

Subtest %: Paragraph Comprehension

Time: 13 minutes for 15 questions

Directions: This test measures your ability to understand what you read. This section includes
paragraphs of reading material followed by incomplete statements or questions. Read each para-
graph and select the choice that best completes the statement or answers the question. Mark your
choice on your answer sheet by using the correct letter with each question number.

Because leadership is charged with bringing
new ideas, methods, or solutions into use, inno-
vation is inextricably connected with the pro-
cess of being an effective leader. Innovation
means change, and change requires leadership.
Leaders must be the chief transformation offi-
cers in their organizations and learn everything
there is to know about the change before it even
takes place. Furthermore, they must learn how
to deal with the emotions that result from the
chaos and fear associated with change.

1. According to the passage,

(A) leaders should resist making changes
that subordinates are likely to resist.

(B) innovation and change are distinctly
different processes.

(D) change is often associated with panic
and disorder.

Cougars are the most wide-ranging big cats
in North America, inhabiting a wide variety of
environments. A cougar, also called a puma or a
mountain lion, lives about 18 years in the wild,
can jump 20 feet (in distance) at a time, and can
range 50 miles when on the prowl for food.

2. According to this passage,

(A) a cougar isn't the same thing as a
mountain lion.

(B) cougars are an endangered species.

(D) cougars live only a few years in the
wild.

A helping relationship refers to interactions
in which the counselor makes a determined effort
to contribute in a positive way to the counselee's
improvement. In counseling, the counselor estab-
lishes a helping relationship by drawing on
practices that help the counselee live more in
harmony with himself or herself and others and
with a greater self-understanding. The relation-
ship develops because the counselee needs assis-
tance, instruction, or understanding.

3. Which of the following statements is NOT
supported by the passage?

(A) Successful counseling requires devel-
oping a relationship.

(B) Most counselees initially reject advice
given by the counselor.

(D) Counseling relationships are developed
by relying on helpful practices.

Many small cities and towns rely on volunteer
fire departments to put out fires. A professional
fire department, however, has more training,
more expertise, and more experience in fighting
fires and investigating their causes. In many
cases, it's worthwhile for even very small towns
to hire professional firefighters.

4. According to this passage, it's reasonable
to assume that

(A) volunteer firefighters have less train-
ing, expertise, and experience than
professional firefighters.

(B) volunteer firefighters have the skills
and resources to investigate the causes
of fires.

(D) a professional fire department is cost-
prohibitive for small towns.

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290

Part V: Practice ASVAB Exams

The idea being an alarming one, he scrambled
out of bed and groped his way to the window. He
was obliged to rub the frost off with the sleeve of
his dressing-gown before he could see anything
and could see very little then. All he could make
out was that it was still very foggy and extremely
cold and that there was no noise of people run-
ning to and fro and making a great stir, as there
unquestionably would've been if night had beaten
off bright day, and taken possession of the world.

5. This story takes place

(A) in Ireland.

(B) on a calm summer evening.

(D) both A and C.

Epidemiology is the study of what causes
diseases, injuries, and other physiological
damage to humans and why such problems
occur. Epidemiologists examine where and when
disease outbreaks occur. By using statistics and
other scientific methods, epidemiologists deter-
mine what factors affect the frequency and
severity of disease patterns. The primary goal of
epidemiology is to control or prevent outbreaks
of disease — other goals are subordinate.

6. What would be the best title for this passage?

(A) "Epidemiology: The Study of Disease
Patterns"

(B) "Goals for the Future of Epidemiology"

(D) "Employment Outlook for
Epidemiologists"

Buddhism is a religion that must be viewed
from many angles. Its original form, as preached
by Gautama in India and developed in the early
years succeeding and as embodied in the sacred
literature of early Buddhism, isn't representative
of the actual Buddhism of any land today.

7. According to this passage,

(A) most Buddhists live in India.

(B) Buddhist teachings have changed over
the years.

(D) Buddhist temples can be found in any
land of the world.

Questions 8 and 9 are based on the following
passage.

Many criminal-law statutes permit more
severe punishment of a person convicted of a
crime if he or she intended to harm another
person. For example, voluntary manslaughter
carries a heavier penalty than involuntary man-
slaughter in most states. Planned crimes are also
punished more severely than spur-of-the-
moment crimes.

The problem is that juries find it difficult to
know what the intent of a person was at the time
he or she committed a crime. Many defendants
will deny that they intended to harm the other
person and claim that any harm that occurred
was "accidental." The law asks too much of
juries when it expects them to determine what a
person was thinking. Juries should only be asked
to weigh objective evidence.

8. The author of this passage would agree that

(A) laws should not punish people based
on intention.

(B) juries aren't intelligent enough to weigh
evidence.

(D) lawyers will lie about anything.

9. According to this passage,

(A) most states don't distinguish between
voluntary and involuntary manslaughter.

(B) punishing people more severely for vol-
untary manslaughter is unconstitutional.

(D) prosecutors can, through careful ques-
tioning, show a defendant's intention at
the time a crime was committed.

Questions 10 through 12 are based on the fol-
lowing passage.

Ergonomics is the science of designing and
arranging workspaces so that people and objects
interact efficiently and safely. Lack of attention
to ergonomics causes thousands of workers to

Go on to next page

Chapter 20: Practice Exam 3 2 ^ /

suffer repetitive stress injury, eye fatigue, muscle
soreness, and many other medical problems
each year.

Adequate lighting, well-designed chairs, and
clutter-free work areas contribute to effective
ergonomic design. The opportunity to take short
breaks every hour or two, especially for desk-
bound workers, is also helpful. It's also impor-
tant for workers to avoid performing the same
movements over and over for hours at a time.
Variety in the type of work being done can
decrease the chance of injury.

10. According to this passage,

(A) ergonomics can cause injuries.

(B) ergonomics is about designing and
arranging workspaces efficiently and
safely.

(D) few people experience problems due to
poor ergonomics.

11. According to this passage,

(A) adequate lighting and well-designed
chairs, although important, have noth-
ing to do with ergonomics.

(B) repetition in the type of work people
do helps them accomplish their tasks
safely and efficiently.

(D) ergonomic design also includes keeping
work areas well-lit and clutter-free.

12. According to this passage, it's reasonable
to assume that

(A) employers should invest in ergonomic
design to protect workers.

(B) lack of ergonomic design isn't

dangerous.

(D) poor design is responsible for most
employee accidents.

Questions 13 through 15 are based on the fol-
lowing passage.

Electricity is the most inefficient and costly
way to heat a home. One kilowatt-hour of elec-
tricity creates about 3,400 British thermal units
(BTUs). (BTUs are a standard heat measure-
ment.) The price of electricity per kilowatt-hour
is between $0.10 and $0.25 or between $29.35
and $73.13 per million BTUs.

In contrast, fuel oil, which produces 140,000
BTUs per gallon, costs about $8.33 to $13.89 per
million BTUs. Natural gas, which produces
100,000 BTUs per therm, can be purchased for
$5.00 to $22.50 per million BTUs. Oak firewood,
which produces 26,000,000 BTUs per cord, costs
$5.77 to $13.46 per million BTUs.

Choosing the right heating method for your
home, based on the cost of fuel, may be more
expensive at installation but will be cheaper in
the long run.

13. According to the passage, a BTU

(A) is an unusual method of measuring
heat.

(B) stands for "British thermal unit."

(D) can heat a 9 x 12 room.

14. According to the passage,

(A) heating with fuel oil is always cheaper
than other methods.

(B) oak firewood produces fewer BTUs per
dollar than the other types of fuel.

(D) electricity is always the most expensive
way to heat a house.

15. The title of this passage should be

(A) "Choosing the Right Heating Method"

(B) "Heating Methods for Houses"

(D) "Price List for Fuel"

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292

Part V: Practice ASVAB Exams

Subtest 5: Mathematics Knowledge

Time: 24 minutes for 25 questions

Directions: This section tests your ability to solve general mathematical problems. Select the cor-
rect answer from the choices given and then mark the corresponding space on your answer sheet.
Use scratch paper to do any figuring you want.

If y = 6, then 2y x y

x(x 2 ) =

(A) 12

(A)x 2

(B) 72

(B) 2x

(D) 242

squals

(D)x 3

If 0.05x = 1, then .re

J(5 + x) 2 =

< A >A

(A) 5-x

(B) 20
(Q10
(D)5

(B) 5 + x
(C)V5-^x"

(D)^ + >/x

^25x 2 =

(3 x 3)(5 - 3)(6 + 2) = x 2 . What's the value
of X?

(A)x

(A) 6

(B)x 2

(B)12

(D) -5x 2

(D)64

Factor: 9X 3 + 18x 2 -

x-2

If -5x = 25, x equals

(A) (9x 2 - l)(x + 2)

(A) -5

(B) (9x 2 + l)(x-2)

(B)5

(D) (9x 2 - 2)(x + 1)

(D)0

Solve for x: 5x + 7 =

6(x-2)-4(2x-3)

10.

A circle measures 12 feet in diameter.

(A)l

What's its area to the nearest foot?

(B)-l

(A) 452

(B) 24

(D)-2

Go on to next page

Chapter 20: Practice Exam 3 2 ^?

12.

13.

14.

15.

A square box has 6-inch sides. What's its
volume?

(A) 18 cubic inches

(B) 216 cubic inches

16. In the following figure, the sum of Angles 1
and 2 equals

(D) 36 cubic inches

A circle has a diameter of 10 inches

What's

(A) 180 degrees

(B) 90 degrees

(D) 360 degrees

its approximate area?

(A) 7t(10 2 )

(B) tc(25)

17.

Solve for x: 3(2x - 5) - 2(4* + 1) = -5(x + 3) -

(D) ti(10 2 )(10)

(A)0

A cylinder has a diameter of 12 inches and

0)1

a height of 10 inches. What's its approxi-

mate volume?

(D)3

(A) 4,521 cubic inches

(B) 120 cubic inches

18.

A cube has a volume of 64 cubic inches.
What's the length of one side of the cube?

(A) 4 inches.

(D) 1,440 cubic inches

(B) 16 inches.

Triangle ABC is a(n)

(D) 32 inches.

19.

(x 3 )^

c / \ a

(A)* 5
(B)x 6

A 1 2 )

(C)x 9

A b

(D) 2x 3

(A) equilateral triangle.

(B) right triangle.

(D) isosceles triangle.

20.

If i inches of rain fall in one minute, how
many inches fall in h hours?

(A) ih * 60

(B) 60/ - h

The angles of the following quadrilateral

(D) 60/ft

21.

If x = y, then 6 + 4(x - y) =

(A) 6xy + 4

(B) 6 + 4xy

(A) are all right angles.

(B) each equal 45 degrees.

(D) total 180 degrees.

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Part V: Practice ASVAB Exams

22. ^820 is a number between

(A) 20 and 30.

(B) 10 and 20.

(D) 40 and 50.

23. (x + 2)(x + 2) =

(A) x 2 + 2x + 4

(B) x 2 + 4x + 4

(D) x 2 + 2x +

24.

25.

Evaluate the expression 6a - 3x - 2y if

a = -3, x = -7, and y = 4.

(A) -5

(B) -40

(CD 31

(D)40

(x + 4)(3.

r + 5)

(A) 3x 2 +

9x +

(B) 3x 2 +

17x-

H 15

17x-

f20

(D)3x2 +

9x +

STOP!

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Chapter 20: Practice Exam 3 2 ty5

Subtest 6: Electronics Information

Time: 9 minutes for 20 questions

Directions: This section tests your knowledge of electrical, radio, and electronics information.
Select the correct response from the choices given and then mark the corresponding space on your
answer sheet.

1. What effect does a speaker wire's gauge
have on speaker sound quality?

(A) higher gauge wires are thicker with
better sound quality

(B) lower gauge wires are thicker with
better sound quality

(D) higher gauge wires are thicker with
lesser sound quality

2. What's the primary advantage of a quad-
band cell phone over a dual-band cell
phone?

(A) transmission strength

(B) coverage area

(D) smaller phone size

3. When working with electricity, you should
assume that all electrical equipment is
alive unless you know for certain other-
wise. This prevents

(A) damage to circuits.

(B) personal injury.

(D) overheating the equipment.

4. The heat effect of current occurs

(A) when the pressure of the current in the
wire breaks up impurities in the wire,
creating heat.

(B) when the current in the wire decays
electrons, causing them to move more
quickly, creating heat.

(D) The heat effect of current is only theo-
retical; it has never been proven

to exist.

5. What special type of diode is commonly
used to regulate voltage?

(A) capacitor

(B) transistor

(D) LED

6. This symbol means

(A) ohm.

(B) ampere.

(D) wattage.

7. Electromotive force is another way of
saying

(A) frequency.

(B) watts.

(D) voltage.

8. A primary advantage of using a Li-Ion bat-
tery instead of a NiMH battery in your cell
phone is

(A) Li-Ion batteries are lighter.

(B) Li-Ion batteries last longer.

(D) none of the above.

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296

Part V: Practice ASVAB Exams

9. Transistors contain at least three terminals
called the

(A) base, emitter, and collector.

(B) base, positive terminal, and negative
terminal.

(D) base and two gates.

10. To control a light fixture from two different
wall switches, you should use

(A) a single-pole switch and a four-way
switch.

(B) two three-way switches.

(D) two single-pole switches.

11. A transistor is also called a(n)

(A) rectifier.

(B) cathode.

(D) semiconductor.

12. This symbol means

(A) ground.

(B) resistor.

(D) battery.

13. To decrease capacitance, capacitors

(A) should have less voltage applied to them.

(B) should be connected in parallel.

(D) should be eliminated.

14. A resistor marked 2.5K ohms has the
value of

(A) 2.5 ohms.

(B) 250 watts.

(D) 25,000 ohms.

15. A 9-volt transistor contains

(A) 1 cell.

(B) 6 cells.

(D) 3 cells.

16. The hot wire is always

(A) purple.

(B) green.

(D) black.

17. How wide is the full AT motherboard?

(A) 11 inches

(B) 11.5 inches

(D) 12.5 inches

18. The following symbol represents a(n)

(A) relay.

(B) on-off switch.

(D) connected wire.

19. If a 120-volt current is protected by a 25-amp
circuit breaker, what's the largest number of
watts an appliance can safely use?

(A) 1,200 watts

(B) 1,800 watts

(D) 3,600 watts

20. The following symbol represents a

(A) rheostat.

(B) capacitor.

(D) potentiometer.

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Chapter 20: Practice Exam 3 2 i) 7

Subtest 7: Auto & Shop In formation

Time: 11 minutes for 25 questions

Directions: This test contains questions about automobiles, shop practices, and the use of tools. Pick
the best answer for each question and then mark the corresponding space on your answer sheet.

1. A symptom of worn piston rings is

(A) a knocking and pinging sound when
driving.

(B) soft and spongy acceleration.

(D) an engine using excessive amounts
of oil.

2. What term refers to the rebuilding of an
engine to precise factory specifications?

(A) blueprinting

(B) speccing

(D) silver rebuild

3. The number of cranks a crankshaft has on
a V-8 engine is

(A) 6.

(B)4.

(0)3.

(D)8.

4. When an engine runs on after the ignition
key is turned off, it's called

(A) dieseling.

(B) sputtering.

(D) ignition malfunction.

5. If a radiator fails, the engine

(A) will idle roughly.

(B) may burn fuel less efficiently.

(D) can quickly overheat.

6. On modern automobile engines, what's the
purpose of the intake manifold?

(A) It regulates airflow to the cooling
system.

(B) It provide airflow to the air-conditioner
and heater.

(D) It regulates fuel pump pressure.

7. Brake systems work by

(A) applying friction to the wheels to stop
their rotation.

(B) reversing power to the wheels.

(D) interrupting power to the transmission.

8. Which of the following isn't a component of
the cooling system?

(A) heater core

(B) radiator

(D) hydrator

9. A catalytic converter

(A) combines the fuel-air mixture.

(B) reduces dangerous exhaust emissions.

(D) charges the battery when the engine is
in operation.

10. If the steering wheel vibrates at high
speeds, the most likely problem is

(A) front end alignment.

(B) front tire balance.

(D) overinflated tires.

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298

Part V: Practice ASVAB Exams

11. During the compression stroke on a four-
cycle engine,

(A) the intake valve opens to fill the cylin-
der with fuel.

(B) the burning fuel mixture forces the
piston to the bottom of the cylinder.

(D) the exhaust valve releases the
burned gas.

12. On older cars, the air filter can be found

(A) on top of the engine.

(B) under the engine.

(D) on the left or right side of the engine.

13. Glazing is the process of

(A) cutting glass to size.

(B) using putty to hold glass to a window
frame.

(D) removing glass from a window.

14. A wrench with fixed, open jaws is called a(n)

(A) adjustable wrench.

(B) Allen wrench.

(D) open-end wrench.

15. All hammers have a

(A) head, face, and handle.

(B) head, toe, and handle.

(D) head and claw.

16. To determine the number of threads per
inch on a fastener, use a

(A) depth gauge.

(B) thread gauge.

(D) wire gauge.

17. To chip or cut wood in close, the best tool
is a

(A) screwdriver.

(B) butt chisel.

(D) mortising chisel.

18. Machine screws

(A) are made by machines.

(B) can be used interchangeably with wood
screws.

(D) are machined to fine tolerances.

19. Double-headed nails are used

(A) to reinforce a joint.

(B) on temporary construction.

(D) when a larger striking surface is
needed.

20. To thin oil-based paint, use

(A) turpentine.

(B) baby oil.

(D) varnish.

21. When finishing a piece of wood, it's best to
sand

(A) diagonal to the grain.

(B) against the grain.

(D) in small circles.

22. To transfer an angle, the best tool to use is a

(A) square.

(B) caliper.

(D) sliding T-bevel.

Go on to next page

Chapter 20: Practice Exam 3 2>^

23. The following tool is a(n)

25. The following tool is used to

(A) pipe wrench.

(B) socket wrench.

(D) box-end wrench.

24. Which of the following screw heads
requires a Phillips screwdriver?

(A) punch holes.

(B) drive nails.

(D) set nails.

(A)

(C)

(B)

(D)

STOPI

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300

Part V: Practice ASVAB Exams

Subtest 8: Mechanical Comprehension

Time: 19 minutes for 25 questions

Helical gears have

(A) straight teeth.

(B) slanted teeth.

(D) no advantage over spur gears.

In the following figure, which pillar sup-
ports the greater load of the anvil?

1»

\ i \

1 -^ 1

(A) Pillar A

(B) Pillar B

(D) It's impossible to determine from the
information given.

Wheel A has a diameter of 10 feet. Wheel B
has a diameter of 8 feet. If both wheels
revolve at the same rate, Wheel B will
cover a linear distance of 16 feet

(A) at the same time as Wheel A.

(B) more slowly than Wheel A.

(D) faster than Wheel A.

What effort must be used to lift a 30-pound
anvil (see the following figure) using a first-
class lever? (Don't include the weight of
the lever in your calculations.)

30 pound
anvil

(A) 10 pounds

(B) 15 pounds

(D) 5 pounds

Go on to next paqe

Chapter 20: Practice Exam 3 *%01

5. What mechanical advantage does the block-
and-tackle arrangement in the following
figure give?

(A)l
(B)3
(C)2
(D)4

6. If a ramp is 8 feet long and 4 feet high, how
much effort is required to move a
400-pound object up the ramp?

(A) 35 pounds

(B) 150 pounds

(D) 200 pounds

7. 33,000 foot-pounds of work done in one
minute is called

(A) a job for an enlisted soldier.

(B) 1 horsepower.

(D) meaningful force.

8. A 130-pound woman is wearing shoes with
high heels that measure 1-inch square. If
the woman is standing on one heel, what
psi does the heel exert as it rests on the
ground? (Disregard atmospheric pressure
from your calculations.)

(A) 130

(B) 65

9. Clothes from the dryer stick together
because of

(A) gravity.

(B) magnetism.

(D) static electricity.

10. An aneroid barometer measures

(A) atmospheric pressure.

(B) water pressure.

(D) the ambient temperature.

11. If Gear A is revolving in a clockwise
manner, as in the following figure, Gear B

12.

(A) remains stationary.

(B) revolves in a clockwise manner.

(D) turns more slowly than Gear A.

Springs are used for the following purposes
EXCEPT

(A) to store energy for part of a mechanical
cycle.

(B) to force a mechanical component
to maintain contact with another
component.

(D) to increase the weight of a mechanism.

Go on to next page

302

Part V: Practice ASVAB Exams

13. The floats in Tubes A and B measure spe-
cific gravity. Which tube contains the liquid
with the higher specific gravity?

14.

15.

A B

(A) Tube A

(B) Tube B

(D) Both Tube A and Tube B have the same
specific gravity.

Universal joints are used to

(A) connect ball bearings.

(B) fix two shafts so they don't pivot or
rotate.

(D) couple two shafts set at different
angles.

The try-cock in the following schematic
measures

16. The steel plate below is held in place by
different machine screws, each indicated
by different symbols. How many different
types of machine screws have been used?

©@(D

@0@@«o

□

(A) 6
(B)15
(C)5
(D)9

17. The amount of force (F) needed to balance
the lever in the following figure is most
nearly

10 pound 5 pound
anvil anvil

(A) 15 pounds.

(B) 13 pounds.

(D) 20 pounds.

Water line

try-cock

(A) temperature of water.

(B) pressure of water.

(D) level of water.

Chapter 20: Practice Exam 3 3 Q 2

18. With one complete revolution of the cable
winch shown below, the load will move

Drum circumference 24 inches

20.

(A) 12 inches.

(B) 6 inches.

(D) 36 inches.

19. In the following figure, assume the valves
are all closed. Which valves need to be
open to fill the tank entirely?

Water
Supply

Valve 1

Valve 3

Valve 2

Drainage

Valve 4

Valve 5

(A) 1 and 2 only

(B) 1 only

(D) 2 only

21.

22.

23.

If Gear 1 in the following figure makes
10 complete clockwise revolutions per
minute, then

(A) Gear 2 makes 2 clockwise revolutions
per minute.

(B) Gear 3 makes 8 clockwise revolutions
per minute.

(D) Gear 3 makes 9 counterclockwise revo-
lutions per minute.

A gear and pinion have a ratio of 1 to 4. If
the gear makes 200 revolutions per minute,
the speed of the pinion is

(A) 50 rpm.

(B) 800 rpm.

(D) 200 rpm.

The gas gauge in an automobile relies on
what mechanical device to measure the
amount of gas in the tank?

(A) ball and cock

(B) automatic valve

(D) mechanical switch

Using a runner gives you a mechanical
advantage of

(A) 4.

(B)2.

(D)l.

Go on to next page

30U

Part V: Practice ASVAB Exams

24. For the valve shown in the figure below to
open once each second, the cam must
revolve at a rate of

25. The following figure represents a water
tank. Which of the following statements is
NOT true?

valve

Water
Supply

carn-

Valve 1

(A) 6 rpm.

(B) 10 rpm.

(D) 3 rpm.

Valve 3

Water level

Drainage

Valve 2

Valve 4 Valve 5

(A) If Valves 1 and 2 are open and Valves 3,
4, and 5 are closed, the tank will even-
tually overflow.

(B) If all valves are open, the water will
remain at a constant level as long as
the rate of intake is equal to the rate of
discharge.

(D) The tank will empty entirely if Valves 1
and 2 are closed and Valves 4 and 5 are
open.

STOPI

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DO NOT RETURN TO A PREVIOUS TEST.

Chapter 20: Practice Exam 3 3 Q£y

Subtest 9: Assembling Objects

Time: 15 minutes for 25 questions

Directions: The Assembling Objects subtest consists of questions that measure your ability to men-
tally picture items in two dimensions. Each question is comprised of five separate drawings. The
problem is presented in the first drawing and the remaining four drawings are possible solutions.
Determine which of the choices best solves the problem shown in the first picture, and then mark
the corresponding choice on your answer sheet.

>=^|

r^>

p^ o o e>

10.

*A A

grQ

<^J

11.

12.

A B C D

/ B B

&-^

13.

A B C D

14.

A B C D

■ — | A A

r b b

<^^t?

A B C D

15.

Q* j

d- 1

□^

A B C D

16.

Q?s x (ID £>

A B C D

Go on to next page

3 06 Part V: Practice ASVAB Exams

17.

18. CV A A

f> B

19.

20.

21.

23.

Go on to netf jm#e

Chapter 20: Practice Exam 3 $07

24.

^ 1

0= B

r°

25.

STOPI

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DO NOT RETURN TO A PREVIOUS TEST.

308

Part V: Practice ASVAB Exams

Chapter 21

Practice Exam 3:
Answers and Explanations

M^ ead over each question from Chapter 20 as you check the answer key. I hope you did
w ▼well on this practice exam. If you find you need to study more for any subtest, follow
the cross-references. (And for in-depth study, check out some of the book recommenda-
tions in Chapter 17.)

Subtest 1: General Science Answers

If you're still having problems figuring out the difference between an isotope and an ion,
remember you may not have to do well on this subtest. It depends on the military career
you're interested in. (See Appendix A for a list of military jobs that require a competent
General Science score.) If this subtest is important to your military career aspirations, con-
sider putting in some extra study. You can find additional information in Chapter 10, and
Chapter 15 has a few more practice questions.

l.A 6. B 11. D 16. B 21. C

2. B

7. D

12. D

17. A

22. A

3. A

8. C

13. A

18. A

23. B

4.D

9. B

14. D

19. D

24. D

5. D

10. B

15. D

20. C

25. A

Subtest 2: Arithmetic Reasoning Answers

You have to do well on this subtest to qualify for military enlistment — your score from the
Arithmetic Reasoning subtest counts toward your AFQT score. If you're still doing poorly on
this test, you may want to postpone taking the ASVAB until you have more study time under
your belt (and perhaps take a math class or two). You may also want to review Chapters 7
and 8 and the practice questions in Chapter 9.

1. D. Multiply $0.45 (the cost of making three donuts) by 4 to find the cost of making a dozen
donuts: $0.45 x 4 = $1.80. Then subtract the cost of making one dozen donuts from the sell-
ing price of one dozen donuts to get the profit on one dozen donuts: $3.99 - $1.80 = $2.19.

Because the baker sold five dozen donuts, multiply the profit on one dozen donuts times 5
to determine the profit on five dozen donuts: $2.19 x 5 = $10.95.

310

Part V: Practice ASVAB Exams

2. C. Let x equal the number of dimes. Then 100 - x represents the number of quarters. You
have $0.10x in dimes and $0.25(100 - x~) in quarters, so set up your equation and solve for x:

0.10x + 0.25(100 -x) = 19.75

0.10x+25-0.25x = 19.75

-0.15* = -5.25

x = 35

3. D. First determine the square footage of the patio: 12 feet x 16 feet = 192 square feet. Then
multiply this number by the cost per square foot to determine what the bricklayer
charges: 192 x $8 = $1,536.

4. A. Let x equal Angie's hourly wage; x + 2 would then represent Tim's hourly wage, and
3(x + 2) would represent Terry's hourly wage. Set up your equation and solve for x:

x + (x +

2) +

3(x +2) =

= 43

x + x + 2

+ 3x

+ 6 =

= 43

+ 8 =
5x -

x --

= 43
= 35

= 7

5. B. Two people is half as many as four people. Multiply the number of machines four people
can run by i to determine how many machines two people can run: 8x^ = 4.

6. B. Let x equal the number of daily tickets you would purchase; 36x equals the daily ticket
cost:

240 < 36x
~36~ <x

o
You would need to use the ticket more than 6-=j times (or 7 times) for it to be cheaper to

use the season ticket.

7. C. You can convert the lengths of the pipes from feet and inches to inches and then divide
the total inches needed by 12 to get the total number of feet of pipe needed. However, the
easiest and fastest way to do this problem is to realize that 3 feet, 6 inches is 3.5 feet.
Multiply the number of pipes needed by 3.5 feet to get the number of feet of pipe needed.

4x3.5= 14

8. B. The fastest way to solve this is to simply multiply the possible choices together (19x21 =
399). However, you can also solve this with algebra. Let x equal the first number and x + 2
equal the second number:

x(x + 2) = 399

x 2 + 2x = 399

This is a quadratic equation that you can solve by setting it equal to zero and factoring.

x 2 + 2x - 399 =

(x-19)(x + 21) =

x-19 = or

x+21 =0

x= 19

x = -21

x + 2 = 21

x+2 = -19

Two solutions are possible: 19 and 21, and -21 and -19. Because the latter pair isn't one of
the answer choices, the first pair is the correct answer.

Chapter 21: Practice Exam 3: Answers and Explanations 37 7

9. C. Multiply her total sales by her percent commission to find her commission: $530 x 0.65 =
$344.50.

10. B. The formula for the length of the diagonal of a rectangle is d 2 = I 2 + w 2 (this is the
Pythagorean theorem, where / and w are the sides of a right triangle and d is the hypote-
nuse). In this case, d - 5 and / = w + 1. Substituting the known values into the formula
results in 5 2 = (w + l) 2 + w 2 .

5 2 = (w + Y)(w + 1) + w 2

25 = w 2 + 2w + 1 + w 2

25 = 2u; 2 + 2w + 1

This equation is a quadratic equation, which you can solve by setting it equal to zero and
factoring.

= 2u; 2 + 2w - 24

±(0)=±(2w 2 + 2w-24~)

= w 2 + w-l2

= (w- 3)(u; + 4)

(£>-3 = or u; + 4 =

w = 3 w = -4 (not a possible solution)

11. B. If 2 inches = 3 miles, then 1 inch equals 1.5 miles: 3 + 2 = 1.5. Multiply 1.5 miles x 9.5 inches
to determine the actual distance: 1.5 x 9.5 = 14.25, or 144- miles.

12. D. The area of the entire piece of canvas = 10 inches x 14 inches = 140 square inches. The
portion painted on equals 8 inches x 12 inches = 96 square inches. (This is determined by
subtracting 2 inches — 1 inch on each side — from the length of each side to account for
the margins.) Divide 96 by 140 to determine that about 68.596 of the canvas is covered with
paint. You can round up to 6996.

13. D. Calculate perimeter by adding the lengths of all four sides of a quadrilateral: 9 + 9 + 16 +
16 = 50 feet.

14. B. The formula for the perimeter of a rectangle is P = 2/ + 2w. In this case, P = 100 and
/ = \.5w. Set up your equation and solve for w:

100 = 2(1.5«;) + 2w

100 = 3w + 2w

100 = 5w

w = 20

The width of the rectangle is 20 inches. Because the length is l-k times the width, 1.5 x 20 = 30.

15. C. The total number of quizzes is 10. If he passed seven of them, the fraction would be

expressed as y^r.

16. D. Divide the amount of ribbon (in yards) used by the number of dresses to determine how
much ribbon (in yards) was used in each dress: 3 + 4 = 4. Three-quarters of a yard of
ribbon was used to make each dress.

17. B. Divide $30 by $530 ($500 + $30) to determine the percentage of the sale price that the
profit comprised: 30 * 530 = 0.056 = 696.

18. A. First find how many bolts a full bin contains: 7 x 12 = 84 bolts. Then multiply the total

number of bolts in a full bin by 4 to find how many bolts are in the bin when it's -4 full:

i 84 6 6

84x4- = -^-= 14 bolts.
6 6

312

Part V: Practice ASVAB Exams

Tip: A shortcut is to find -~ of a dozen first and then multiply by 7, the number of dozens. That
is, 12 x ^ = 2 bolts, and 2 x 7 = 14 bolts. You can this because multiplication is commutative —
you can multiply the numbers in any order.

19. C. The first bike got a =-mile head start (12 mph x ^yhr. = ^ = = mi.). Therefore, by the
time the second bike leaves, there are 5-=^ miles between them (6--^). Their combined rate
of travel is 12 + 14 = 26 mph. Let t = the number of hours the second bike travels.

26f =

•4

26f =

' 5

t =

26 .
" 5 '

26
1

t =

. 26 x
" 5 X

1
26

t =

1
5

One-fifth of an hour

meet at 2:21.

60 4- 5 =12 minutes. The second bike left at 2:09, so both bikes will

20. B. Choice (B) is the cheapest option that gives you enough beans. Calculate each answer
option and compare:

V Choice (A): 2 x $0.79 = $1.58

^ Choice (B): $1.49

j-" Choice (C): Two 3-ounce cans give you less than 8 ounces, so this answer can't be
correct.

V Choice (D): 3 x $0.65 = $1.95

21. D. Add the sales amounts together: $25.70 + $32.30 + $31.80 = $89.80. Then multiply the
total sales by -j to determine how much money he has left: $89.80 x 0.75 = $67.35.

22. B. Divide $30.00 by $3.95. The whole number is the number of pairs of socks the recruit
could buy: $30.00 * $3.95 = 7.59, or 7 pairs of socks.

23. D. Subtract 43 pounds, 7 ounces (the weight of the puppy) from 60 pounds, 5 ounces (the
weight of the crate). Converting an additional pound of the crate to ounces makes the sub-
traction possible. Sixteen ounces make a pound, so 60 pounds, 5 ounces is the same as

59 pounds, 21 ounces. Do the subtraction:

59 pounds 21 ounces
- 43 pounds 7 ounces

16 pounds 14 ounces

24. D. The probability that all five computers will be defective is 0. 15x0. 15x0. 15x0. 15x0. 15 =
0.0000759 (round up to 0.000076).

25. D. Find the area of each bedroom and add them together: 12x14= 168; 12x10 = 120; 8x12 =
96; and 168 + 120 + 96 = 384 square feet. Then, because 9 square feet make up a square yard,
divide the total area in square feet by 9 to determine the number of square yards needed:
384 + 9 = 42.6 square yards. You can round up to 43 square yards.

26. A. Divide the total number of pages to be typed by the number of pages Rafael can type
per hour to find the number of hours it will take him to type the pages: 126 pages * 9 pages
per hour = 14 hours.

Chapter 21 : Practice Exam 3: Answers and Explanations A J A

27. D. Divide the group of 48 girls by the number of girls who can play at the same time:

48 + 12 = 4. This means four groups of girls have to share the 60 minutes: 60 minutes + 4 =
15 minutes. Thus, each girl plays for 15 minutes.

28. B. Subtract the first day's late charge from the total: $8.25 - $2.00 = $6.25. Then divide that
amount by $1.25 to determine the number of additional days the movie was overdue: $6.25 +
$1.25 = 5. Add those 5 days to the first day the movie was late to find that the movie was

6 days overdue.

29. D. Divide the number of calories in the pudding by the number of calories in the broccoli:
150 + 60 = 2.5. Janet can eat 2.5 times the amount of broccoli as she can eat pudding for
the same number of calories. Multiply 2.5 by 0.5 cup (the amount of pudding that con-
tains 150 calories) to find how many cups of broccoli she can eat for 150 calories:

2.5 x 0.5 = 1.25 = licups.

30. C. The dog is barking every 15 minutes, or 4 times per hour. The time between 10 p.m. and
2 a.m. is 4 hours. Multiply the total number of hours in the time period by 4 barks per
hour. Then add 1 because the dog barked at the beginning of the period also: (4 x 4) + 1 =
16+1 = 17.

Subtest 3: Word Knowledge Answers

The Word Knowledge subtest is another one of the "big four" that counts toward your AFQT
score. If you're not seeing the improvement in your scores that you need to see, work with a
partner who can quiz you on vocabulary. Review your vocabulary words intensely, even
several times a day, to ensure your success on this subtest. See Chapter 4 for more help on
improving your word knowledge. Additional practice questions are available in Chapter 6,
and you also have a chance to practice this subtest in the practice AFQT in Chapter 22.

l.B 8. D 15. A 22. A 29. A

9. A

16. B

23. B

30. C

3.B

10. A

17. A

24. D

31. D

4. B

11. C

18. D

25. B

32. A

5. A

12. A

19. C

26. D

33. D

6. C

13. B

20. B

27. A

34. C

7. B

14. C

21. C

28. C

35. C

Subtest %: Paragraph Comprehension Answers

Because the military bigwigs use the Paragraph Comprehension subtest to determine
whether you even qualify for enlistment (it counts toward your AFQT score), you need to
do well here. If you're still struggling, remember to take your time when you read the pas-
sages. And after you read each question, you can quickly reread the passage just to make
sure you're on the money. The information is in the paragraph; you just have to concentrate
to pull it out. Turn to Chapter 5 and the practice questions in Chapter 6 if you still need
additional help to pull off a good score on this subtest. An additional opportunity to prac-
tice taking this subtest is in the next chapter.

Part V: Practice ASVAB Exams

1. D. The last sentence in the passage states that chaos and fear are associated with change,
making Choice (D) the correct choice. The passage states that leaders must learn to deal
with negative emotions connected with change, making Choice (A) incorrect. The second
sentence makes it clear that innovation means change, so Choice (B) is incorrect. The
third sentence clearly states that leaders must learn everything there is to know about the
change, making Choice (C) the wrong choice.

2. C. The first sentence says cougars are wide-ranging big cats in North America, making
Choice (C) correct. The passage states that pumas, mountain lions, and cougars are the
same thing, so Choice (A) is incorrect. Nothing in the passage supports Choice (B), which
says cougars are endangered. The passage states that cougars live about 18 years in the
wild, so Choice (D) is incorrect.

3. B. The counseling process works because the counselee feels the need for assistance,
instruction, or understanding. Therefore, Choice (B) — counselees initially reject the
advice of their counselors — isn't supported by the passage. The other three choices are
all supported by the content of the paragraph.

4. A. The second sentence says that professional fire departments have more training, exper-
tise, and experience. Therefore, the reader can infer that volunteer departments have less
training, expertise, and experience than professionals. The passage says that profession-
als, not volunteers, have the skills needed to investigate fires, so Choice (B) is incorrect.
The passage states that professional firefighters have more experience investigating the
causes of fires, so Choice (C) is incorrect. The passage states that hiring professional fire-
fighters is worthwhile, so Choice (D) is incorrect.

5. C. The passage doesn't state the locale of the story, so Choices (A) and (D) are incorrect.
The references to extreme cold and lack of light makes Choice (B) an incorrect answer. In
sentence three, the author says it was still very foggy and extremely cold, so Choice (C) is
the answer.

6. A. The main point of the passage is to define epidemiology, as evidenced by the opening
sentence. Epidemiology is the study of what causes diseases. Choices (B), (C), and (D)
aren't the main points of the passage.

7. B. The only statement that's supported by the passage is Choice (B), which says Buddhist
teachings have changed. In fact, this sentence is the primary theme of the passage. The
other choices aren't supported by information contained in the paragraph.

8. A. Choice (B), which questions jurors' intelligence, isn't supported by the passage.
Choice (C), which asks for more laws that take intent into consideration, is the opposite
of what the author argues. The text doesn't support Choice (D), which calls lawyers liars.
The first line of the passage states that statutes permit more severe punishment of a
person convicted of a crime if he or she intended to harm another person. The last sen-
tence says juries should only be asked to weigh objective evidence, so the author would
no doubt agree that laws should not punish people based on intention, Choice (A).

9. C. The passage says that most states punish voluntary manslaughter more severely than
involuntary manslaughter, so Choice (A) is incorrect. The argument that punishing people
more severely for voluntary manslaughter is unconstitutional isn't made in the passage, so
Choice (B) is incorrect. The passage doesn't support Choice (D), which says prosecutors
can establish intent. The first sentence of the second paragraph states that juries find it
difficult to know what the intent of a person was at the time he or she committed a crime,
so Choice (C) is correct.

10. B. Lack of attention to ergonomics, not ergonomics itself, can cause injury, so Choice (A)
is incorrect. The passage doesn't support Choice (C), which discusses cost and time. The
passage states that many people suffer injuries when sufficient attention isn't paid to ergo-
nomics, so Choice (D) is incorrect. The first says, "Ergonomics is the science of designing
and arranging workspaces so that people and objects interact efficiently and safely," so
Choice (B) is correct.

Chapter 21 : Practice Exam 3: Answers and Explanations j 1 5

11. D. The passage states that adequate lighting and well-designed chairs are part of ergo-
nomic design, so Choice (A) is incorrect. The passage states that repetitious work can
cause injury, so Choice (B) is incorrect. The passage states that desk-bound workers
should take breaks, so Choice (C) is incorrect. The first sentence in the second paragraph
states that adequate lighting, well-designed chairs, and clutter-free work areas contribute
to effective ergonomic design, so Choice (D) is correct.

12. A. The passage makes it clear that lack of ergonomic design is dangerous, so Choice (B)
is incorrect. Nothing in the passage supports Choice (C), which brings up labor unions.
Although the passage claims that lack of ergonomic design causes injury, nothing in the pas-
sage supports Choice (D). The passage's second sentence says that lack of attention to ergo-
nomics causes thousands of workers to suffer repetitive stress injury, eye fatigue, muscle
soreness, and many other medical problems, so it's reasonable to assume that employers
should invest in ergonomic design to protect workers, which makes Choice (A) correct.

13. B. The passage says that BTUs are the standard measure of heat, so Choice (A) is incor-
rect. BTU stands for British thermal unit, so Choice (C) is incorrect. Nothing in the passage
supports Choice (D), which names room dimensions.

14. D. The passage shows that fuel oil can be more expensive than other heating methods,
so Choice (A) is incorrect. Oak firewood is sometimes less expensive than other types of
fuel, so Choice (B) is incorrect. Natural gas can sometimes cost less than firewood, so
Choice (C) is incorrect. The first sentence states that electricity is always the most ineffi-
cient and costly way to heat a home, which makes Choice (D) correct.

15. A. The main point of this passage deals with choosing the right fuel based on price; only
Choice (A) summarizes this point. Choices (B), (C), and (D) are less important points.
Because after discussing costs by BTU of the various fuels, the final sentence makes
Choice (A) correct.

Subtest 5: Mathematics Knotfiedqe Answers

The Mathematics Knowledge subtest is used to determine whether you qualify for enlist-
ment, so you need to do well. If you're still missing too many questions, you may need to
take more drastic measures, such as enrolling in a basic-algebra class at a local community
college. If your scores are improving, keep hitting the books and testing yourself up until the
day of the ASVAB. Turn to Chapter 7 and the practice questions in Chapter 9 for more infor-
mation. The practice AFQT in Chapter 22 also gives you a chance to gauge your progress.

1. B. Substitute 6 for y in the equation: 2(6) x6=12x6 = 72.

2. B. Divide both sides of the equation by 0.05 to isolate x: 0.05* 4- 0.05 = 1 * 0.05, or x = 20. To
check your answer, substitute 20 for x in the original equation.

3. C.V25x 2 =V( 5x ) 2 = 5x

4. A. 9X 3 + 18x 2 - x - 2 = 9x 2 (x + 2) - l(x + 2) = (9x 2 - l)(x + 2).

The fully factored answer is (3x - l)(3x + l)(x + 2), but that's not what the question asks.
Make sure you look for the answer to the question.

5. B. Solve for x:

5x + 7 = 6(x - 2) - 4(2* - 3)
5x+ 7 = 6x-12-8x+ 12
5x + 7 = -2x
Ix + 7 =
7x = -7
x = -\

316

Part V: Practice ASVAB Exams

6. D. If two powers have the same base, they can be multiplied by keeping the base and
adding the exponents together. In this case, x is the same as x 1 : x + x 2 = x 1+2 - x 3 ,

7. B. This is so easy that it may tempt you to think that the correct answer is too obvious.
The square root of (5 + x) 2 is simply 5 + x.

8. B. You start with (3 x 3)(5 - 3)(6 + 2) = x 2 . First solve the left side of the equation: (9)(2)(8) =
144. So x 2 = 144. Find the square root of each side: x = 12.

9. A. You start with -5x = 25. Isolate x by dividing each side of the equation by -5: x = -5.

10. C. The area of a circle equals n times the radius squared. The radius is half the diameter,
which is 12 in this problem. Plug in the known values: A = jxr 2 ; A = jt6 2 = 36ti. If n is approxi-
mately 3.14, the area of the circle is approximately 3.14 x 36, or 113 square feet.

11. B. Volume equals length x width x height (V '= Iwli): 6x6x6 = 36 x6 = 216 cubic inches.

12. B. The area of a circle is A = nr 2 . Radius is half the diameter, so the radius is 5. In this
problem, A = ji5 2 = 25jt.

13. C. For cylinders, Volume = ni^Qti). Because the radius is half the diameter, you can calculate
the problem this way: V= 7t(6 2 )10 = 7t(36)10. If % is approximately 3.14, then 3.14 x 36 x 10 =
1,130 cubic inches.

14. D. In an isosceles triangle, sides a and c are equal, and angles 1 and 2 are equal.

15. A. Rectangles have four equal angles, and all angles are right angles.

16. A. Supplementary angles always equal 180 degrees.

17. A. Solve for x:

3(2x - 5) - 2(4x + 1) = -5(x + 3) - 2
6x-15-8x-2 = -5x-15-2
-2x-17 = -5x-17
3x-17 = -17
3x=0
x=0

18. A. Volume equals length x width x height (V = Iwli). Finding the cube root of 64 shows that
each edge measures 4 inches (4x4x4 = 64).

19. B. (x 3 ) 2 is the same as (x 3 )(x 3 ). To multiply exponents with the same base, keep the base
and add the exponents: (x 3 )(x 3 ) = x 3 * 3 = x 6 .

20. D. To find out how much rain falls in an hour, multiply the amount that falls in one minute
by 60, because 60 minutes make up an hour. In h hours, the amount of rain is 60//?.

21. D. Because x = y, you can plug inx for eachy in the problem. Therefore, 6 + 4(x-x) =
6 + 4(0) = 6 + = 6.

22. A. The problem asks for the square root of 810. You know that 20 2 = 400 and 30 2 = 900, so
the range of 20 to 30 is correct.

23. B. The problem asks you to find (x + 2)(x + 2). Using the FOIL method (First, Outside, Inside,
Last), systematically multiply each term in the first set of parentheses by each term in the
second set of parentheses:

Iv* Multiply the First terms: x(x) = x 2 .
j-" Multiply the Outside terms: x(2) = 2x.

Chapter 21: Practice Exam 3: Answers and Explanations 377

Iv* Multiply the Inside terms: 2(x) = 2x.
u* Multiply the Last terms: 2x2 = 4.

Now add all the products together, and you get x 2 + 2x + 2x + 4. Add like terms to get the
final answer of x 2 + Ax + 4.

24. A. Replace the unknowns with the numbers given: 6(-3) - 3(-7) - 2(4) = -18 + 21 - 8 = -5.

25. C. The problem asks you to find (x + 4)(3x + 5). Use the FOIL method:
v* Multiply the First terms: x(3x) = Zx 2 .
v* Multiply the Outside terms: x(5) = 5x.
v* Multiply the Inside terms: 4(3x) = 12x.
W Multiply the Last terms: 4(5) = 20.

Now add all the products together, and you get 3x 2 + 5x + 12x + 20. Add like terms to get
the final answer, 3x 2 + 17x + 20.

Subtest 6: Electronics In formation Answers

If you need to do well on the Electronics Information subtest to qualify for a certain military
career (see Appendix A) and you're still missing questions, review Chapter 13 and spend
some time memorizing key electronics concepts, including the mathematical formulas (like
Power = Voltage x Current) that help you solve all kinds of electronics problems.

You can find additional practice questions can be found in Chapter 15.

1. B. Unless a specific gauge is specified by the speaker manufacturer, you should always
choose lower gauges for better sound quality.

2. B. There are four frequency bands used throughout the world. A quad-band cell phone
would be able to access any of these frequency bands.

3. B. The greatest concern when dealing with electricity is personal injury.

4. C. Heat effect occurs when electrical current must overcome the resistance of the wire.
Heat effect can be quite obvious or very subtle.

5. C. Like other diodes, Zener diodes allow current in only direction, except if the voltage
across it is greater than a threshold voltage (called breakdown voltage). Current also flows
through the Zener diode in the opposite direction. This action allows the Zener diode to
regulate voltage.

6. A. The symbol stands for ohm.

7. D. Electromotive force is the difference of potential, so the term is another way of saying
voltage.

8. A. Lithium-ion (Li-Ion) batteries are much lighter than nickel metal hydride (NiMH) batteries.

9. A. The three terminals a transistor must have are the base, emitter, and collector.

10. B. To control a light fixture from two different positions, use two three-way switches.

1 1. C. Amplifier is another name for transistor.

318

Part V: Practice ASVAB Exams

12. A. The symbol means ground.

13. C. Capacitance is the ability to hold an electrical charge. Connecting capacitors in series
reduces the capacitance.

14. C. 2.5K ohms is 2,500 ohms. K = 1 kilo, or 1,000.

15. B. A cell is equal to about 1.5 volts, so 9 * 1.5 = 6.

16. D. Primary live wires are black.

17. C. A motherboard is the physical arrangement in a computer that contains the computer's
basic circuitry and components. Motherboards come in various sizes and component
arrangements referred to as form factors to fit standard case sizes, components required,
and so on. AT is a standard form factor that has a width of 12 inches and a length of

13.8 inches.

18. B. An on-off switch allows current to flow only when it's in the closed (on) position.

19. C. Determine the wattage that could cause the circuit breaker to trip with this formula:
Watts = Volts x Amps, or 120 x 25 = 3,000 watts.

20. A. A rheostat is a type of variable resister that's usually used to control voltage.

Subtest 7: Auto & Shop Information Answers

If you have your heart set on fixing Jeeps and tanks or doing other related military jobs (see
Appendix A) and you're still struggling on this test, review Chapter 11 and do the practice
questions in Chapter 15.

6. C

11. C

16. B

21. C

2. A

7. A

12. A

17. B

22. D

8. D

13. B

18. C

23. C

4. A

9. B

14. D

19. B

24. B

5. D

10. B

15. A

20. A

25. A

Subtest 8: Mechanical Comprehension Answers

If you need to do well on the Mechanical Comprehension subtest, don't forget to apply your
math skills to the concepts. (A little extra physics study wouldn't hurt, either.) But simply
using your common sense can help you quite a bit, too. For example, you may not know
exactly why a metal spoon feels colder than a wooden spoon when they're at the same tem-
perature, but at least you know that it feels colder. And knowing that may help you answer
a question correctly. See Chapter 12 and the additional practice questions in Chapter 15 for
more information.

1. B. The teeth of helical gears are slanted.

2. B. The anvil is closer to Pillar B, so Pillar B bears more weight.

3. B. Wheel B is smaller. It has to make more revolutions than Wheel A to cover the same
amount of distance, so it will take longer.

Chapter 21: Practice Exam 3: Answers and Explanations A f Q

4. A. E stands for effort needed. Here's how to set up the equation: 30 (weight of the anvil) x 2
(length of resistance arm) = x(6) (length of effort arm). Do a little multiplication, and you get
60 = 6x. To isolate x, divide each side by 6: 10 = x.

5. A. A fixed, simple pulley gives no mechanical advantage, so its mechanical advantage
number is 1.

6. D. The formula to determine the mechanical advantage of an inclined plane is Length of
Ramp * Height of Ramp = Weight of Object * Effort:

8 400

4 E
8E = 400(4)
8£ = 1,600

£• = 200

7. B. One horsepower equals 33,000 foot-pounds per minute.

8. A. Pressure = Force * Area. Psi stands for pounds per square inch, so you don't have to
change the units of measurement. Just plug in your numbers: P = 130 lbs. * 1 in. 2 = 130 psi.

9. D. Static electricity is the buildup of electrical charge on surfaces, which causes materials
to "stick" together this way.

10. A. An aneroid barometer measures atmospheric pressure.

11. C. Meshed gears always turn in opposite directions.

12. D. Springs are used for all the listed purposes except to add weight.

13. B. Specific gravity is a comparison between the density of a liquid and the density of water.
The liquid with the higher specific gravity will have a float that rises higher.

14. D. Universal joints are used to connect shafts that aren't in the same plane.

15. D. Try-cocks are valves that measure water level. Water seeks a level throughout a system,
so in the schematic, the try-cock correctly indicates the water level.

16. A. There are six different symbols, so six different types of machine screws were used.

17. B. To determine the amount of force the anvils exert, first multiply the length of the resis-
tance arm (as it applies to the anvil) by the weight of each anvil and add the products
together. The 10-pound anvil is supported by the entire weight of the resistance arm, so 5 x
10 = 50. The 5-pound anvil is being supported by 3 feet of the resistance arm, so 3 x 5 = 15.
Add 'em up: 50 + 15 = 65. This number is equal to the length of the resistance arm times
effort (force), or 65 = 5F. To isolate F, divide both sides by 5: 13 = F.

18. C. One revolution of the winch will move the weight 24 inches, the circumference of the
winch drum.

19. A. Valves 1 and 2 need to be open to fill the tank.

20. B. The number of revolutions a gear makes is inversely proportional to its difference in
size from the gear that's turning it. Gear 1 makes 10 clockwise revolutions per minute.
Gear 2 is half the size of Gear 1, so to determine the number of revolutions it makes, multiply
the number of revolutions Gear 1 makes by the inverse (reciprocal) of -k, which is y (or
just 2): 10x2 = 20. Therefore, Gear 2 makes 20 counterclockwise revolutions per minute.

Gear 3 is 2.5 times (or ^ times) the size of Gear 2. To determine the number of revolutions

5
Gear 3 makes, multiply the inverse of 4f by the number of revolutions Gear 2 makes:

2 40

■w x 20 = -¥- = 8 revolutions per minute.

21. B. The pinion turns four times as often as the gear: 4 x 200 = 800 rpm.

320

Part V: Practice ASVAB Exams

22. C. A float indicates the level of liquid in a container.

23. B. Using a runner (a single, moveable pulley) gives a mechanical advantage of 2.

24. A. Because 60 seconds comprise a minute, the valve must open 60 times per minute. The
cam will open the valve 10 times per revolution, and 60 + 10 = 6. The cam must make 6 rev-
olutions per minute to raise the valve 60 times per minute.

25. D. Because Valve 4 is above the bottom of the tank, some water will remain in the tank
below the level of the valve, so the tank will never be completely empty.

Subtest 9: Assembling Objects Answers

At present, only the Navy uses the scores from this subtest. If you plan to sail the Seven
Seas and you want one of the few Navy jobs that requires you to put parts A and B together,
you may want to go over the practice subtests again. For additional practice questions, see
Chapter 15.

l.C

6. D

11. D

16. C

21. B

2. A

7. C

12. A

17. A

22. D

3. A

8. C

13. C

18. B

23. D

4. B

9. B

14. B

19. A

24. A

5.C

10. A

15. D

20. C

25. C

Chapter 22

Practice AFQT Exam

■ f you're wondering what in the world this exam is doing in a book on the ASVAB,
«S don't be confused. The Armed Forces Qualification Test, or AFQT, is part of the ASVAB —
in a way, it's a test within a test. Your scaled AFQT score is derived from four subtests of
the ASVAB, and it determines your overall mental qualification to join the service branch of
your choice. Each of the five branches of military service has set its own minimum AFQT
score in order to qualify for enlistment. The four subtests that can make or break your
chances of joining the military are Arithmetic Reasoning (AR), Word Knowledge (WK),
Paragraph Comprehension (PC), and Mathematics Knowledge (MK).

Because I like you (and because you were kind enough to buy this book), I've included an
extra chance for you to evaluate your communication and math skills before you head over
to the MEPS (military entrance processing station) or your school or the local National
Guard Armory for the real deal.

After you complete the entire practice test, check your answers in Chapter 23.

.VABE/f

Your goal here is to determine where you may still need to spend some more study time. If
you miss only one question on the Word Knowledge subtest but you miss 15 on Arithmetic
Reasoning, you may want to dedicate some extra study time to further develop your math
skills before you take the actual ASVAB.

322

Part V: Practice ASVAB Exams

Answer Sheet for Practice AFQT Exam

Subtest 1: Arithmetic Reasoning

1 ®@©®

7 ®®©®

13 ®®©®

19 ®®©®

25 ®@©@

2 ®(D©®

8 ®®©®

14 ®®©®

20 ®®©@

26 ®@©@

3 ®®©®

9 ®®©®

15 ®®©®

21 ®®©@

27 ®@©®

4 ®®©®

10 ®@©@

16 ®®©®

22 ® ® © ®

28 ® ® © ®

5 ®@©®

11 ®@©@

17 ®@©®

23 ® ® © ®

29 ® ® © ®

6 ®®©®

12 ®@©@

18 ®®©@

24 ® ® © ®

30 ® ® © ®

Subtest 2: Word Knowledge

1 ®®©@

8 ®®©®

15 ®®©®

22 ® ® © ®

29 ® ® © ®

2 ®®©®

9 ®®©®

16 ®®©®

23 ®®©®

30 ®®©@

3 ®®©@

10 ®®@®

17 ®®©®

24 ®®©®

31 ®@©®

4 ®®©®

11 ®@©®

18 ®®©®

25 ®®©®

32 ® ® © ®

5 ®®©@

12 ®@©@

19 ®@©®

26 ® ® © ®

33 ® ® © ®

6 ®®@®

13 ®@©@

20 ®@©®

27 ®®@®

34 ® ® © ®

7 ®@©®

14 ®®©@

21 ®@©@

28 ®®©®

35 ® ® © ®

Subtest 3: Paragraph Comprehension

1 ®®©@

4 ®®©®

7 ®@©®

10 ®®©®

13 ®®©®

2 ®®©®

5 ®®©@

8 ®®@®

11 ®®©@

14 ®@©@

3 ®®©®

6 ®®©@

9 ®®©®

12 ®@©@

15 ®@©@

Subtest 4: Mathematics Knowledge

1 ®®©@

6 ®®©®

11 ®®©®

16 ®®©®

21 ®®©@

2 ®®©®

7 ®®©®

12 ®®©®

17 ®®©®

22 ®@©@

3 ®®©®

8 ®@©@

13 ®®©@

18 ®®©@

23 ®@©@

4 ®®©®

9 ®@©@

14 ®®©®

19 ®®©®

24 ® ® © ®

5 ®@©®

10 ®@©@

15 ®®©@

20 ®®©®

25 ® ® © ®

Chapter 22: Practice AFQT Exam 2 2?

Subtest 1: Arithmetic Reasoning

Time: 36 minutes for 30 questions

1. If a barber is capable of cutting the hair of
35 people per day and he works 7 days per
week, how many haircuts could he give
during the months of April, May, and June?

(A) 3,185

(B) 3,150

(D) 2,555

2. If you type 45 words per minute, how many
words can you type in 12 minutes?

(A) 490

(B) 540

(D) 615

3. Tom is flying a kite at the end of a 500-foot
string. His friend Kathy is standing directly
under the kite 300 feet away from Tom.
How high is the kite flying?

(A) 300 feet

(B) 350 feet

(D) 450 feet

4. Amy wants to fence in a yard using 400 feet
of fencing. If she wants the yard to be

30 feet wide, how long will it be?

(A) 170 feet

(B) 175 feet

(D) 185 feet

5. A three-digit code must be used to access a
computer file. The first digit must be an A
or a B. The second digit must be a number
between and 9. The final digit is a single
letter from the alphabet from A to Z. How
many possible access codes can there be?

(A) 38

(B) 468

6. The sun is 93 million miles from Earth, and
light travels at a rate of 186,000 miles per
second. How long does it take for light from
the sun to reach the Earth?

(A) 5 minutes

(B) 6-4 minutes

(D) 8-^ minutes

7. A tanning-bed pass for unlimited tanning
costs $53 per month this year, but it was
only $50 per month last year. What was the
percentage of increase?

(A) 5%

(B) 5.5%

(D) 6.5%

8. Eleven plus forty-one is divided by a number.
If the result is thirteen, what's the number?

(A) 2

0)4

(D)8

Go on to next page

321,

Part V: Practice ASVAB Exams

9. Mark received an hourly wage of $9.25. His
boss gave him a 496 raise. How much does
Mark make per hour now?

(A) $9.29

(B) $9.62

(D) $9.99

10. How many pounds of nails costing $7 per
pound must be mixed with 6 pounds of
nails costing $3 per pound to yield a mix-
ture costing $4 per pound?

(A) 2 pounds

(B) 2.5 pounds

(D) 3.5 pounds

11. Theodore has 24 baseball cards. He sells 4-
of his cards to Tom and ^ of his cards to
Larry, and his Mom accidently throws away
^ of his cards. How many baseball cards
does Theodore have left?

(A) 2
(B)18

(9 12

(D)6

12. Theresa bought five karaoke CDs on sale.
A karaoke CD normally costs $24, but she
was able to purchase the CDs for $22.50
each. How much money did Theresa save
on her entire purchase?

(A) $7.50

(B) $1.50

(D) $22.50

13. On a trip to the beach, you travel 200 miles
in 300 minutes. How fast did you travel?

(A) 30 mph

(B) 40 mph

(D) 60 mph

14. Twenty-one students, or 6096 of the class,
passed the final exam. How many students
are in the class?

(A) 45

(B)40

(D)30

15. Joan invests $4,000 in an account that
earns 3/6 simple interest. How much will
Joan have in the account in 10 years?

(A) $4,500

(B) $4,800

(D) $5,400

16. A rectangle has a perimeter of 36 inches.
Its length is 3 inches greater than twice the
width. What's the rectangle's length?

(A) 5 inches

(B) 13 inches

(D) 20 inches

17. A backyard is 50 feet by 100 feet. What's its
area?

(A) 150 square feet

(B) 500 square feet

(D) 5,000 square feet

18. Eric is driving a car in which the speedome-
ter is calibrated in kilometers per hour (kph).
He notes that his car is traveling at a rate of
75 kph, when he passes a speed limit sign
stating the limit is 40 miles per hour (mph).

He knows that a kilometer is about -^ of a

mile. If a police officer stops him at this point,
how many miles per hour over the limit will
the ticket read?

(A) 5

(B)7

(D)ll

Go on to next page

Chapter 22: Practice AFQT Exam 2 25

19. Three apples and twice as many pears add
up to one-half the number of grapes in a
fruit basket. How many grapes are in the
basket?

(A) 8

(B)18

(D)38

20. Apples are on sale for "Buy 2 pounds get

1 free." How many pounds must Janet pur-
chase to get 2 pounds free?

(A) 2 pounds

(B) 4 pounds

(D) 3 pounds

21. If four pipes of equal length measure 44 feet
when they're connected together, how long
is each pipe?

(A) 11 feet

(B) 4 feet

(D) 9 feet

22. A German Shepherd and an Alaskan
Malamute are both headed toward the
same fire hydrant. The German Shepherd
is 120 feet away from the hydrant, and the
Alaskan Malamute is 75 feet away from the
hydrant. How much closer to the hydrant
is the Alaskan Malamute?

(A) 45 feet

(B) 25 feet

(D) 195 feet

23. A recruit reporting to boot camp took a bus
from her home to the military processing
center in another city. The trip took

14 hours. If she left at 6 a.m., what time
did she arrive at the processing center?

(A) 7 p.m.

(B) 12 a.m.

(D) 9 p.m.

24. A farmer sold 3 pints of strawberries for
$1.98 each, 5 pints of raspberries for $2.49
each, and a bushel of peaches for $5.50 at
his roadside stand. How much money did
the farmer make?

(A) $9.97

(B) $23.89

(D) $18.91

25. A librarian wants to shelve 532 books. If
four books fit on a 1-foot length of shelving,
how many feet of shelving does she need to
shelve all the books?

(A) 13

(B)45

(D) 133

26. A student buys a science textbook for
$18.00, a math textbook for $14.50, and a
dictionary for $9.95. What's the total cost
of the books?

(A) $27.95

(B) $42.45

(D) $38.50

27. Debra works an 8-hour shift on Friday. How
many minutes does she work on Friday?

(A) 480 minutes

(B) 800 minutes

(D) 400 minutes

28. Six people can run three machines in the
factory. How many machines can 18 people
run?

(A) 7

(B)9

(D)8

Go on to next page

326

Part V: Practice ASVAB Exams

29.

On a map drawn to scale, i inch equals
1 mile. What length on the map equals
5 miles?

(A) 2.5 inches

(B) 5.0 inches

(D) 1.5 inches

30. A man bought a pair of jeans for $23.00, a
shirt for $14.95, and two ties for $7.98 each.
What was the total cost of his clothing?

(A) $53.91

(B) $45.93

(D) $54.50

STOPI

DO NOTTURNTHE PAGE UNTILTOLDTO DO SO.
DO NOT RETURN TO A PREVIOUS TEST.

Chapter 22: Practice AFQT Exam $27

Subtest 2: Word Knortiedqe

Time: 11 minutes for 35 questions

Directions: This test has questions about the meanings of words. Each question has an underlined
word. You need to decide which one of the four words in the choices most nearly means the same
thing as the underlined word and then mark the corresponding space on your answer sheet.

1. The abhorrent smell from the lake over-
powered the picnickers gathered on the
shore.

(A) strong

(B) pleasant

(D) tantalizing

2. Belie most nearly means

(A) pleasure.

(B) rule.

(D) misrepresent.

3. The water was calm that day with detritus
slowly moving in the small eddies.

(A) fish

(B) lily pads

(D) debris

4. The prime minister was always cautious
about leaving his redoubt in Belgrade.

(A) city

(B) stronghold

(D) country

5. Mike was afraid he might be ostracized for
stepping out of line.

(A) banished

(B) scolded

(D) arrested

10.

The hotel was specifically designed for the
wayworn traveler.

(A) lost

(B) weary

(D) happy

The park has no showers and no potable
water.

(A) usable

(B) clear

(D) tasty

Decamp most nearly means

(A) to backpack.

(B) to leave.

(D) to act with abandon.

Glorious most nearly means

(A) splendid.

(B) particular.

(D) contentious.

Hypocrisy most nearly means

(A) hyperactivity.

(B) god-like.

(D) criticalness.

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328

Part V: Practice ASVAB Exams

11. Mallet most nearly means

(A) sermon.

(B) participate.

(D) fish.

12. Hosiery most nearly means

(A) dangerous.

(B) illegal.

(D) automatic.

13. Hale most nearly means

(A) old.

(B) healthy.

(D) uninformed.

14. Magnitude most nearly means

(A) importance.

(B) peculiar.

(D) tantamount.

15. His vapid presentation earned him a C in
the class.

(A) mediocre

(B) plagiarized

(D) polished

16. Percival was unpopular at the meeting
because he imparted so much extraneous
data.

(A) extensive

(B) unwelcome

(D) radical

17. She was often solicitous of her father's
feelings.

(A) careful

(B) ignorant

(D) abusive

18. I could never get over her liquid blue,
limpid eyes.

(A) bright

(B) clear

(D) dull

19. The goal of the treaty is to develop interna-
tional amity and reciprocal trade.

(A) agreement

(B) friendship

(D) understanding

20. He often bragged about the bravery of his
favorite cohort .

(A) person

(B) teacher

(D) employee

21. Speechlessness most nearly means

(A) well spoken.

(B) silence.

(D) talkative.

22. Indigenous most nearly means

(A) poor.

(B) rich.

(D) native.

23. Illusive most nearly means

(A) insignificant.

(B) deceptive.

(D) hidden.

24. Hesitate most nearly means

(A) slam.

(B) slow to act.

(D) end.

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Chapter 22: Practice AFQT Exam ?2^

25. Gravity most nearly means

(A) planet.

(B) relationship.

(D) seriousness.

26. Fondle most nearly means

(A) stir.

(B) handle.

(D) radiate.

27. Fete most nearly means

(A) festival.

(B) criticize.

(D) eat.

28. Encore most nearly means

(A) play.

(B) applause.

(D) excite.

29. Diverse most nearly means

(A) various.

(B) hidden.

(D) pastime.

30. Detest most nearly means

(A) anger.

(B) hate.

(D) excite.

31. Tim was known as a smart aleck, able to
deliver acerbic one-liners with no effort.

(A) funny

(B) cheap

(D) poetic

32. It took a great degree of inexorable force to
break into the cavern.

(A) strong

(B) unyielding

(D) powerful

33. Attendents were stationed at intervals,
with the obvious intent to hector those
who moved too slowly.

(A) hurry

(B) harass

(D) note

34. Reggy was as gauche in this group of polite
company as he always had been.

(A) funny

(B) entertaining

(D) embarrassed

35. Confident most nearly means

(A) assured.

(B) positive.

(D) educated.

STOPI

DO NOTTURNTHE PAGE UNTILTOLDTO DO SO.
DO NOT RETURN TO A PREVIOUS TEST.

330

Part V: Practice ASVAB Exams

Subtest 3: Paragraph Comprehension

Time: 13 minutes for 15 questions

Directions: This test contains items that measure your ability to understand what you read. This
section includes one or more paragraphs of reading material followed by incomplete statements or
questions. Read the paragraph and select the choice that best completes the statement or answers
the question. Mark your choice on your answer sheet by using the correct letter with each question
number.

On June 22, 1944, President Franklin Delano
Roosevelt signed into law one of the most signifi-
cant pieces of legislation ever produced by the
United States government: The Servicemembers'
Readjustment Act of 1944, commonly known as
the GI Bill of Rights. By the time the original GI
Bill ended in July 1956, 7.8 million World War II
veterans had participated in an education or
training program, and 2.4 million veterans had
home loans backed by the Veterans
Administration (VA).

1. The G.I. Bill provided

(A) free housing, training, and education.

(B) medical coverage, education, and assis-
tance to veterans.

(D) a means to exempt veterans from
Social Security taxes.

You can put up to $3,000 a year into an
individual retirement account (IRA) on a tax-
deductible basis if your spouse isn't covered
by a retirement plan at work or as long as your
combined income isn't too high. You also can put
the same amount tax-deferred into an IRA for a
nonworking spouse if you file your income tax
return jointly.

2. The maximum amount that a married
couple could possibly save in a tax-deferred
IRA during a year is

(A) $3,000.

(B) $6,000.

(D) The question can't be answered based
on the information contained in the
passage.

Presidential appointments are an ongoing
effort. Some of a president's appointments
require Senate confirmation. These appoint-
ments are for positions throughout the federal
government, for the Cabinet and subcabinet, for
members of regulatory commissions, for ambas-
sadorships, for judgeships, and for members of
numerous advisory boards.

3. Which of the following statements is NOT
true?

(A) All presidential appointments require
Senate confirmation.

(B) A position on a regulatory commission
is an example of a presidential
appointment.

(D) All of the above statements are true.

Go on to next page

Chapter 22: Practice AFQT Exam 22 f

A link between advertising and alcohol 6.

consumption is intuitively compelling but hasn't
been consistently supported by research. Because
alcohol advertising is pervasive, econometric
studies may not be sensitive to change or assess
in a range where change actually makes a differ-
ence. In dealing with advertising, partial bans
aren't likely to be effective, and total bans aren't
practical. Advertising bans in one medium also are
weakened by substitution of increased advertising
in alternative media and/or other promotions.

4. The author of this passage believes that

(A) advertisement of alcoholic beverages
should be illegal.

(B) partial bans on alcohol advertising
could be effective in some cases.

(D) clear links have been established
between alcohol consumption and
advertising.

Which of the following statements is NOT
supported by the passage?

(A) Bankruptcy must be filed in a federal
court.

(B) Bankruptcy is designed to help individ-
uals and protect businesses.

(D) Bankruptcy must be filed in the
bankruptcy court.

Questions 7 and 8 are based on the following
passage.

The etymology of the word or name Alabama
has evoked much discussion among philological
researchers. It was the name of a noted southern
Indian tribe whose habitat when first known to
Europeans was in what is now central Alabama.
One of the major waterways in the state was
named for this group and from this river, in turn, 7.

the name of the state was derived. According to
some investigations, the tribal name Alabama
must be sought in the Choctaw tongue, because
it isn't uncommon for tribes to accept a name
given them by a neighboring tribe.

5. The state of Alabama was named after

(A) a Choctaw Indian tribe. 8.

(B) European settlers.

(D) an Indian chief.

Each of the 94 federal judicial districts
handles bankruptcy matters, and in almost all
districts, bankruptcy cases are filed in the bank-
ruptcy court. Bankruptcy cases can't be filed in
state court. Bankruptcy laws help people who
can no longer pay their creditors get a fresh start
by liquidating their assets to pay their debts or
by creating a repayment plan. Bankruptcy laws
also protect troubled businesses and provide for
orderly distributions to business creditors
through reorganization or liquidation.

The U.S. Department of Justice has prepared
a report about hate crimes in the United States
between 1997 and 1999. In 6096 of hate crime inci-
dents, the most serious offense was a violent
crime, most commonly intimidation or simple
assault. The majority of incidents motivated by
race, ethnicity, sexual orientation, or disability
involved a violent offense, while two-thirds of
incidents motivated by religion involved a prop-
erty offense, most commonly vandalism. Younger
offenders were responsible for most hate crimes.
Thirty-one percent of violent offenders and 4696
of property offenders were under age 18.

Most property offense hate crimes were
motivated by

(A) religion.

(B) race.

(D) abortion.

The majority of hate crimes during this
period can be classified as

(A) property offenses.

(B) violent crimes.

(D) intimidation.

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332

Part V: Practice ASVAB Exams

Linewatch operations are conducted near
international boundaries and coastlines in areas
of Border Patrol jurisdiction to prevent the ille-
gal entry and smuggling of aliens into the United
States and to intercept those who do enter ille-
gally before they can escape from border areas.
Signcutting is the detection and the interpreta-
tion of any disturbances in natural terrain condi-
tions that indicate the presence or passage of
people, animals, or vehicles.

9. The activity that's designed to detect
changes in the natural environment, which
may indicate passage of illegal aliens, is
called

(A) linewatching.

(B) signcutting.

(D) Terrain Observation.

Wales was in ancient times divided into three
parts nearly equal, consideration having been
paid, in this division, more to the value than to
the just quantity or proportion of territory.
They were Venedotia, now called North Wales;
Demetia, or South Wales, which in British is
called Deheubarth, that is, the southern part; and
Powys, the middle or eastern district. Roderic
the Great, or Rhodri Mawr, who was king over all
Wales, was the cause of this division. He had
three sons, Mervin, Anarawt, and Cadell, amongst
whom he partitioned the whole principality.

10. Wales was divided into divisions because

(A) natural boundaries such as rivers and
mountains made the division necessary.

(B) Wales was too large for the King to
oversee personally.

(D) all of the above

Questions 11 and 12 are based on the following
passage.

The fierce and warlike tribe, called the Huns,
who'd driven the Goths to seek new homes,
came from Asia into Southeastern Europe and
took possession of a large territory lying north of
the River Danube. During the first half of the fifth
century, the Huns had a famous king named
Attila. He was only 21 years old when he became
their king. But although he was young, he was
very brave and ambitious, and he wanted to be a
great and powerful king. As soon as his army was
ready, he marched with it into countries, which
belonged to Rome. He defeated the Romans in
several great battles and captured many of their
cities. The Roman Emperor Theodosius had to
ask for terms of peace. Attila agreed that there
should be peace, but soon afterwards he found
out that Theodosius had formed a plot to
murder him. He was so enraged at this that he
again began war. He plundered and burned cities
wherever he went, and at last the emperor had
to give him a large sum of money and a portion
of the country south of the Danube.

11. A good title for the above paragraph
would be

(A) "The Burning of Rome"

(B) "Emperor Theodosius"

(D) "Rome for Dummies"

12. After terms of peace were offered, Attila
resumed the war against Rome because

(A) he discovered the emperor wanted to
assassinate him.

(B) he wanted to further expand his
kingdom.

(D) Danube, his second-in-charge, advised
him not to accept the peace terms.

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Chapter 22: Practice AFQT Exam 33%

Questions 13 through 15 are based on the fol-
lowing passage.

In the military, as in all professions, the issue
of competence is directly relevant to profes-
sional integrity. Because human life, national
security, and expenditures from the national
treasury are so frequently at issue when the mili-
tary acts, the obligation to be competent isn't
merely prudential. That obligation is a moral
one, and culpable incompetence here is clearly a
violation of professional integrity. Part of the
social aspect of professional integrity involves
the joint responsibility for conduct and compe-
tence shared by all members of the profession.
Only fellow professionals are capable of evaluat-
ing competence in some instances; hence, fellow
professionals must accept the responsibility of
upholding the standards of the profession.
Fellow military members can spot derelictions of
duty, failures of leadership, failures of compe-
tence, and the venalities of conduct that inter-
fere with the goals of the military mission. Often,
the obligations of professional integrity may be
pitted against personal loyalties or friendships;
and, where the stakes for society are so high,
professional integrity should win out.

14. Professional competence is

(A) a moral obligation.

(B) directly relevant to professional
integrity.

(D) all of the above

15. The author of the passage would agree that

(A) friendship must often take a back seat
to professional integrity.

(B) only fellow professionals should evalu-
ate competence.

(D) all of the above

13. One word that best describes the primary
theme of this passage would be

(A) proficiency.

(B) equality.

(D) relationships.

STOPI

DO NOT TURN THE PAGE UNTILTOLDTO DO SO.
DO NOT RETURN TO A PREVIOUS TEST.

33d

Part V: Practice ASVAB Exams

Subtest ft: Mathematics Knowledge

Time: 24 minutes for 25 questions

Directions: This section is a test of your ability to solve general mathematical problems. Select the
correct answer from the choices given and then mark the corresponding space on your answer
sheet. Use scratch paper to do any figuring. Calculators are not allowed.

Solve for x: 5x - 2x = Ix + 2x - 24

(12 yards + 14 feet) * 2 =

(A) 2

(A) 25 feet

(B)-2

(B) 12 feet

(D)-4

(D) 8 feet

The cube of 6 is

x 3 (x 3 ) =

(A) 125

(A)* 9

(B) 225

(B) 2x 9

(D) 238

(D)x 6

In the equation 3x + ly = 21, at what point is
the x-axis intersected?

4 +1 f + 4=

(A) (7, 0)

(A)6l

(B) (0, 7)

(D) (4, 0)

x + y = 6 and x - y = 4. Solve for x.

(D)7l

1.5 x 10 2 =

(A) 45

(B) 150

(D) 15

(A) 3
(B)5
(C)7
(D)8

Solve for y: 4(y + 3) + 7 = 3

(A) 2
(B)-2
(C)4
(D)-4

10.

The average of 54, 61, 70, and 75 is

(A) 50

(B) 52

Go on to next page

Chapter 22: Practice AFQT Exam ?35

11.

12.

13.

14.

2 feet, 4 inches + 4 feet, 8 inches

(A) 6 feet, 8 inches

(B) 7 feet

(D) 8 feet

If x - 4, then x 4 * x =

(A) 12

(B) 36
(C)64
(D) 72

3x> 14 + 6x

Solve for x: 5 ■

(A) x > -1

(B) x < -1

(D) x < -1

(900 x 3) * 6 =

(A) 45

(B) 450

(D) 550

15. If x = 2, then x^x*) =

(A) 16

(B) 2x*
(C)8
(D)24

16. Solve for x.x 2 - 2x- 15 =

(A) 4, -2

(B) 3, -3

17.

49 W64:

(A)
(B)
(C)
(D)

18. If5y 2 = 80, then y is

(A) a positive number.

(B) a negative number.

(D) an imaginary number.

19. If 2 + x > 15, what's the value of x?

(A) x < 13

(B) x > 13
(C)x>13
(D)x<13

20. If a circle has a radius of 15 feet, what is its
circumference most nearly?

(A) 24 feet

(B) 72 feet

(D) 36 feet

21. What's the volume of a box measuring
12 inches long by 8 inches deep by

10 inches high?

(A) 960 cubic inches

(B) 128 cubic inches

(D) 288 cubic inches

22. The following figure is a(n)

_EL

(A) parallelogram.

(B) obtuse triangle.

(D) rectangle.

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336

Part V: Practice ASVAB Exams

23. The sum of the measures of the angles of a
parallelogram is

(A) 360 degrees.

(B) 540 degrees.

(D) 720 degrees.

24. What is the prime factorization of 100?

(A) 2 x 50

(B) 2 2 x 5 2

(D) 25 2

25. -jm is an example of a(n)

(A) real number.

(B) imaginary number.

(D) sloping number.

STOPI

DO NOTTURNTHE PAGE UNTILTOLDTO DO SO.
DO NOT RETURN TO A PREVIOUS TEST.

Chapter 23

Practice AFQT Exam:
Answers and Explanations

M M se this answer key to score the Practice AFQT Exam in Chapter 22. Note that the
%rw actual AFQT is scored by comparing your raw score to the scores of other people,
which produces a scaled score. Turn to Chapter 1 to find out how the AFQT score is
derived from the Arithmetic Reasoning, Word Knowledge, Paragraph Comprehension, and
Mathematics Knowledge subtests. Keep in mind that these four subtests determine whether
you can even get into the military. If you find you're still struggling in any of these subtest
areas, you may want to concentrate some additional study effort before knocking on the
recruiter's door to say, "I'm ready!"

Subtest 1: Arithmetic Reasoning Answers

Mathematical word problems can be tough for some people. You have to develop a skill for
determining which factors are relevant to the problem and then be able to convert those
factors into a mathematical formula to arrive at a correct solution. Yikes! No wonder there
are so many math books on the market! If you still need work on this subtest, I recommend
a few good math books in Chapter 17. Reviewing Chapters 7 and 8 and the additional prac-
tice questions in Chapter 9 may also help.

1. A. There are 30 days in April, 31 days in May, and 30 days in June for a total of 91 days.
Multiply the number of days by the number of haircuts per day: 91 x 35 = 3,185.

2. B. Multiply the number of words you can type per minute (45) by the number of minutes
you'll be typing (12): 45 x 12 = 540.

3. C. Visualize a right triangle, where the kite string represents the hypotenuse and the line
between Tom and Kathy represents one of the legs. The Pythagorean theorem states that if
you know the length of two sides of a right triangle, you can determine the length of the
third side using the formula a 2 + b 2 = c 2 . In this case, 300 2 + b 2 = 500 2 . Solve for b:

90, 000 + b 2 =250,000

b 2 =250,000-90,000
b 2 = 160,000

6 = ^160,000

b = 400

4. A. The formula used to determine the perimeter of a rectangle is P = 2(1 + w). The width is 30,
and the perimeter is 400. Plug in the numbers and solve for I:

400 = 2(1 + 30)

400 = 2/ + 60

340 = 2/

/= 170

338

Part V: Practice ASVAB Exams

5. C. There are two possibilities for the first digit (A or B), 10 possibilities for the second digit
(0 to 9), and 26 possibilities for the third digit. Using the multiplication principle, 2 x 10 x
26 = 520 possible access codes.

6. D. The distance formula is distance equals rate times time, or d - rt. Substitute the known
values: 93,000,000 = 186,000?. Therefore, t = 500 seconds. Divide 500 by 60 to convert to
minutes: 500 seconds * 60 seconds/minute = 8=, minutes.

7. C. The difference in the price is $3, so divide the difference by the original price: $3 + $50 =
0.06, or 6%.

8. B. Let x - the unknown number. Set up the formula as = 13. Then solve for x:

11 + 41 _ io

52-

= 13

52 =

= 13*

X-

= 4

9. B. Mark received a 4% raise, so to calculate the new wage, start off by taking $9.25 x 0.04 =
$0.37. Then add that number (the amount of Mark's raise) to his original hourly wage.
Mark's new hourly wage is $9.25 + $0.37 = $9.62.

10. A. Let x = the number of nails costing $7 per pound. The total cost of the mixture (M)
equals the sum of the cost for each type of nail, or M = A + B, where A = Ix, B - 3(6), and
M = 4(6 + x). Substitute the known values into the equation and solve for x:

4(6 + x) = Ix + 18

24 + Ax = Ix + 18

24-18 = Ix-Ax

6 = 3x

x = 2

11. D. You need to add the fractions, so convert the different denominators to a common
denominator — 4, 3, and 6 all divide evenly into 12, so use 12 as the common denominator.

To convert 4-, divide 12 (the new common denominator) by 4 (the original common

13 3

denominator) to get 3. Then multiply 4- by # (another way of saying 1). The product is j^

13 4o 1412

(that is, -r = yt). Do the same calculation for the other fractions: ^t = to and -~ = ===y

To add the fractions, first add the new numerators together: 3 + 4 + 2 = 9. Place the added

numerator over the new denominator, 12, and you can see that ^ of the cards have been
sold or lost. You can reduce ^ to |, which equals 75%. Now find 75% of 24: 24 x 0.75 = 18.

Eighteen of 24 cards have been sold or lost, so subtract to find the remaining cards: 24 - 18 =
6 cards remaining.

12. A. Subtract the sale price from the regular price: $24.00 - $22.50 = $1.50. Multiply the differ-
ence by the number of CDs to find out how much Theresa saved altogether: $1.50 x 5 = $7.50.

13. B. First convert the 300 minutes to hours by dividing by 60 (300 minutes + 60 minutes/
hour = 5 hours). Use the distance formula (d = rf) and substitute the known values: 200 = 5r;
r = 40 mph.

14. C. Let x = the number of people in the class; 60% of x = 21, so 0.60x = 21, andx = 35.

15. C. Use the interest formula (I - Prt) to determine the amount of interest earned, where the
principal (P) is 4,000, the rate (r) is 0.03 (3%), and the time (t) is 10. / = 4,000(0.03)(10), or
/= $1,200. Add the interest earned to the original amount invested: $4,000 + $1,200 = $5,200.

Chapter 23: Practice AFQT Exam: Answers and Explanations $3 9

16. B. A rectangle's perimeter is determined by the formula P =2(1 + w). The length of this rect-
angle is 3 + 2w. Substituting the known values into the formula results in

36 = 2(w + 3 + 2w)

36 = 2(3w + 3)

18 = 3w + 3

I5 = 3w

w = 5

The length is 3 + 2w, so / = 3 + 2(5) = 13.

17. D. The area of a rectangle is the length x the width of the rectangle, or A = Iw: 50 x 100 =
5,000 square feet.

5 5 375

18. B. A kilometer is % of a mile, so multiply 75 x % = ^-^-. Divide 375 by 8 to determine that

Eric was traveling at about 47 miles per hour, 7 mph over the 40 mph posted limit.

19. B. Let x = the number of grapes; 3 apples and 6 pears (twice the number of apples) equals
i of x, or

3 + 6 = -ix

9=2*
2(9) = x
x = 18

20. B. If Janet must purchase 2 pounds of apples to get 1 free pound, then to get 2 free pounds,
she would need to purchase twice as many apples, or 4 pounds of apples.

21. A. All pipes are equal in length, so divide the total length, 44 feet, by the total number of
pipes, 4. The answer, 11, is the length of each individual pipe. You can check this answer
by multiplying: 4 x 11 = 44.

22. A. Subtract the Malamute's distance from the German Shepherd's distance (120 - 75 = 45)
to determine how much closer the Malamute is to the hydrant.

23. C. Simply add 14 hours to 6 a.m. to reach 8 p.m. Twelve hours from 6 a.m. is 6 p.m., and
two hours after that brings you to 8 p.m.

24. B. Multiply 3 pints of strawberries at $1.98 (3 x $1.98 = $5.94), 5 pints of raspberries at
$2.49 (5 x $2.49 = $12.45), and 1 bushel of peaches at $5.50 (1 x $5.50 = $5.50). Add the
products together to determine the amount of cash the farmer earned: $5.94 + $12.45 +
$5.50 = $23.89.

25. D. Divide 532 by 4 to determine how many feet of shelving will be needed: 532 books * 4
books/foot =133 feet.

26. B. Simply add the cost of all the books: $18.00 + $14.50 + $9.95 = $42.45.

27. A. 8 hours x 60 minutes/hour = 480 minutes.

28. B. Eighteen people can run three times the number of machines six people can run, because
18 = 3x6 (divide 18 by 6). Six people can run three machines, so multiply 3x3 machines =

9 machines. Therefore, 18 people can run nine machines.

1 115 5

29. A. Multiply the scale measurement for 1 mile Qk inch per mile) by 5 miles: ix5 = yXy = ^.

Divide 5 by 2, and you get 2.5 inches.

30. A. Simply add the cost of all the items: $23.00 + $14.95 + $7.98 + $7.98 = $53.91.

360 Part V: Practice ASVAB Exams

Subtest 2: Word Knowledge Answers

I hope you did well on this subtest. (I was crossing my fingers the whole time!) If not, you
may want to take another gander at Chapter 4 and the practice questions in Chapter 6.

l.C

8. B

15. C

22. D

29. A

9. A

16. C

23. B

30. B

10. C

17. A

24. B

31. C

4. B

11. C

18. B

25. D

32. B

5. A

12. C

19. B

26. B

33. B

6. B

13. B

20. C

27. A

34. C

7.C

14. A

21. B

28. C

35. A

Subtest 3: Paragraph Comprehension Answers

If you still need to boost your score, engage in some more reading practice. Improving your
vocabulary can also help improve your reading comprehension skills. See Chapter 5 for
some tips. You may also want to try a few of the practice questions in Chapter 6.

1. C. According to the passage, millions of veterans received home loan guarantees, education,
and training, making Choice (C) the correct answer. Be careful here, because Choice (A) is
tempting, but nothing in the passage indicates that the housing, education, and training were
totally free.

2. B. The paragraph states that the maximum amount one can place into a tax-deferred IRA is
$3,000, plus an additional $3,000 if the spouse isn't employed. The question asks about a
couple, so add $3,000 + $3,000 to get $6,000.

3. A. Although many presidential appointments require Senate confirmation, not all do. The
passage mentions only some appointments, so Choice (A) is an incorrect statement.

4. C. The author specifically states that partial bans on alcohol advertising isn't likely to be
effective and that total bans wouldn't be practical.

5. C. According to the passage, a river was named after the Alabama Indian Tribe, and the
state derived its name from this river.

6. D. The first sentence states that bankruptcy is usually (not always) filed in bankruptcy
court, making Choice (D) an incorrect statement.

7. A. The second sentence states that most violent crimes were motivated by such factors as
race and sexual orientation, and most property crimes were motivated by religion. The
question refers to property crimes, so Choice (A) is the right answer.

8. B. Sixty percent of all hate crimes during the period were violent crimes. Assault and intim-
idation are examples of violent crimes.

9. B. The last sentence in the passage describes the signcutting operation.

10. C. The rationale for the division is explained in the final sentence, which mentions the
king's sons. The passage makes no reference to the size of Wales or the natural boundaries.

11. C. The primary subject of this paragraph is Attila, who was king of the Huns.

Chapter 23: Practice AFQT Exam: Answers and Explanations ju, J

12. A. Attila agreed to peace but soon after discovered that the Roman emperor had launched
a plot to kill him.

13. A. The primary theme of the passage is stated in the first sentence. Proficiency is closest in
meaning to the word competence, which is the primary theme of the passage.

14. D. The passage directly supports all the statements.

15. A. The author specifically states that when pitted against friendship, professional integrity
should win out. The author explains that only fellow professionals can evaluate other pro-
fessionals in some (not all) cases, making Choice (B) incorrect. Choice (C) isn't supported
by information in the passage.

Subtest ft: Mathematics Knotfiedqe Answers

It's too bad the ASVAB folks don't allow calculators! That would make this subtest a breeze.
Don't be discouraged. The problems are purposely designed so that they can be solved using
only a scratch paper, the ol' No. 2 pencil, and a little brain sweat. If you're still having diffi-
culty, give Chapter 7 another gander. There are additional practice questions in Chapter 9.

1. C. 5x - 2x = Ix + 2x - 24; 3x = 9x - 24; -6x = -24; 6x = 24; x = 4

2. C. The cube of 6 is 6 3 = 6 x 6 x 6 = 216.

3. A. The equation 3x + ly = 21 is the equation for a line, and a line intersects the x-axis at the
point where the y-coordinate is (y = 0). Substitute for the y variable in the equation and
solve for x: 3x + ly = 21; 3x + 7(0) = 21;3x=21;x=7. The point's coordinates are (7, 0).

4. B. This problem gives you is a system of equations — two equations with two variables.
You can find x by solving one of the equations for y and plugging that value into the other
equation. First, x + y = 6, so y = 6 - x. Substitute this known value for y in the second equa-
tion and solve for x:

x-y = 4

x-(6-x) = 4

x- 6 + x = 4

2x-6 = 4

2x= 10

x = 5

5. D.

4(y + 3) + 7 = 3
4y + 12 + 7 = 3
4y+ 19 = 3
4y = -16
v = -4

6. A. Convert 12 yards, 14 feet to feet: (12 yards x 3 feet/yard) + 14 feet = 36 feet + 14 feet =
50 feet. Divide by 2 as instructed: 50 feet * 2 = 25 feet.

7. D. If two powers have the same base, the numbers can be multiplied by keeping the base
the same and adding the powers (exponents) together: x 3 (x 3 ) = x 3 * 3 = x 6 .

8. B. Convert to the lowest common denominator (which is 10), and then add:

aJ_j_ i 2. i q_3_ _ a _2__i_i _4_i "i_3_ _ q 9
4 5 + 1 5 +-5 10" 4 10 +i 10 +,3 10" 5 10-

342

Part V: Practice ASVAB Exams

9. B. Following the order of operations, you have to find the power (10 2 ) before multiplying:

1.5 x 10 2 = 1.5 x (10 x 10) = 1.5 x 100 = 150.

10. D. Add the numbers and then divide by the number of terms to find the mean. The sum is
54 + 61 + 70 + 75 = 260. You have four numbers, and 260 * 4 = 65.

11. B. 2 feet + 4 feet = 6 feet, and 4 inches plus 8 inches = 12 inches (the equivalent to 1 foot).
Therefore, you have a total of 7 feet.

12. C. Your first reaction may be to substitute 4 for each x and then do the math. But you can
save yourself some work (and time) by first dividing x 4 by x, which is x 3 . Then substitute
4 for each x, and you find that the equation is now 4x4x4. Then multiply: 4 x 4 is 16, and
16 x 4 is 64, which is your final answer.

13. B. As you solve this inequality, remember that when you multiply or divide an inequality
by a negative number, you need to reverse the direction of the inequality sign:

5-3x> 14 + 6x

5-3x-6x>14

-9x>14-5

-9x>9

x<-l

14. B. (900 x 3) * 6 = 2,700 * 6 = 450.

15. A. Substitute 2 for all the x's: x x (x x ) = 2 2 x 2 2 = 4 x 4 = 16.

16. C. This is a quadratic equation that you can solve by factoring and setting each factor
equal to zero:

x 2 -2x-15 =

(x-5)(x + 3) =

x-5 = or x+3 =

x = 5 x = -3

17. D. Find the square roots before dividing. The square root of 49 is 7, and the square root of
64 is 8. Now divide: 7 ■*■ 8 = X.

18. C. The square root of a positive number can be either positive or negative. For instance,
the square root of 16 is ±4, because 4 2 and (-4) 2 both give you the positive number 16.

19. C. Solving this equation doesn't require multiplying or dividing by a negative number, so
the inequality sign remains the same: 2 + x > 15; x > 13.

20. C. Circumference equals n times diameter, and diameter is equal to two times the radius.
In other words, C = nd, and d = 2r. Thus, C = 7i(2)(15) = 7i30. If you round n to 3.14, the
answer is 94.2, or about 94 feet.

21. A. Volume equals length times width times height (V= Iwh). Plug in the numbers and solve:
V= 12 x 8 x 10 = 960 cubic inches.

22. C. In a trapezoid, two of four sides are parallel to each other.

23. A. All quadrilaterals have angles that total 360 degrees.

24. B. Here's how you may have found the prime factors of 100: 100 = 4 x 25 = 2x2x5x5 =
2 2 x 5 2 .

25. B. The square root of a negative number doesn't exist as far as real numbers are concerned.
In mathematics, this is called an imaginary number, and it's represented by the letter ;'.

Part VI

The Part of Tens

The 5 th Wave

By Rich Tennant

" Okay— novr tha-t the paramedic is here viith

the defibrillator and swelling salts, prepare

■bo open your test booklets...*

In this part . . .

■# ou can put your pencil down now — no more quizzes
^r- or sample tests like the ones in Part V. This part is
the Part of Tens, which features my personal ASVAB top-
ten lists. I couldn't write a For Dummies book and not
include this part.

I give you important information for doing well on the
ASVAB, offer some pointers for memorizing crucial con-
cepts, and point you in the right direction for finding
more information if you need it. This part presents mate-
rial in quick tidbits so you can get into the chapters and
then get out.

Good luck taking your ASVAB. I hope you get stationed in
Hawaii!

Chapter 24

Ten Surefire Ways to Fail the ASVAB

In This Chapter

Avoiding common ASVAB-preparation mistakes
Steering clear of other people's mistakes

Technically, you can't fail the ASVAB — it's not a pass/fail test but instead a tool the mili-
tary uses to measure your potential for learning military duties and military occupa-
tions. But realistically, each of the branches has established minimum AFQT scores to
qualify for enlistment and minimum line scores to qualify for certain military jobs. If you
don't qualify to join the service branch of your choice or don't qualify for the job you want,
you haven't technically failed, but you may have to take the test again (after some study
sessions) to get into the branch of service your heart desires.

But if you avoid the mistakes outlined in this chapter, you can improve your chances of
qualifying for enlistment and getting the military job of your dreams.

Choosing Not to Study at All

Many people think that they don't need to study for the ASVAB. They assume that because
they studied many of the subjects in high school, they'll do fine even if they just wing it.

This train of thought isn't true (and it's kind of crazy). Why wouldn't you study? At the very
least, brushing up on vocabulary and math concepts definitely helps you score higher on
the ASVAB. Using a calculator is a no-no on the ASVAB, so you may want to revisit some
math tricks for doing calculations by hand. Auto, Shop, and Mechanical Comprehension
aren't required high school courses, so these subjects may be completely new to you and
require additional attention.

Using study guides like this one not only gives you an idea of what to expect but also allows
you to sharpen some skills that may have gotten a little dull.

Failing to Realize Hotf Scores Are Used

The military powers that be use the nine subtests on the ASVAB to determine which mili-
tary jobs you qualify for. If you don't know how the scores are used, you can't decide which
parts of the exam are most important for you to study.

Check out Chapters 1 and 2 for an explanation of how the military uses ASVAB subtest
scores to determine your qualifications. Also head to Appendix A to see the scores that you
need to get into the various branches of and careers in the military.

366

Part VI: The Part of Tens

Studying (or Unnecessary Subtests

If you don't want to be a mechanic in the military, what are you doing studying for the Auto
& Shop Information subtest? You should be spending your time on the math and vocabulary
review, because the math and vocabulary subtests of the ASVAB are used to compute the
all-important AFQT score, which determines whether you can join the military branch of
your choice.

It's easier to study subject areas that you find easy or have an interest in, but if you're already
an electronics whiz, don't waste your time studying a subject area that you're already going to
ace. Spend your time studying subject areas that you aren't quite so confident of.

Losing Focus

I'm not going to sugarcoat this: The ASVAB is tiring. You have to take nine subtests that
cover some really diverse subjects. You have about three hours to complete the actual test,
so if you lose focus while you're taking the test, time has a tendency of slipping away, and
you may not get to all the questions. It's hard, but keep your mind focused on the task at
hand throughout the whole test. It'll be over soon.

Here are some tips that can help you maintain focus:

v* Arrive at the test location with time to spare. This gives you a few minutes to sit and
relax before you have to dive into the test questions.

J*" Leave your baggage at the door. Don't worry about whether you'll get the military job
you want or whether you'll pass the physical the next morning. You'll have plenty of
time to worry about that after you've finished the test.

v* Concentrate on one subtest at a time. Don't waste time rehashing the questions on the
previous subtest or trying to anticipate the questions on the next subtest. Focus on the
subtest you're taking at the time.

v* Take a few moments to relax and refocus between subtests. If you finish a subtest
with time to spare, close your eyes for a bit and take some deep breaths before you
begin the next subtest.

When you answer the final question on one subtest on the CAT-ASVAB, you move immedi-
ately to the next subtest. If the timer on the computer screen says you have a few minutes
of time left on the subtest, use that time to relax and refocus before submitting that final
answer.

Panicking 0</er Time

Yes, you have only a limited time to do the test, but don't worry about it. The more you panic,
the more likely you are to make mistakes. Just work at a steady pace, and you'll do fine.

Don't spend too much time on any single question. If you're drawing a blank, make a guess
and move on. (See "Making Wild Guesses or Not Guessing at All," later in this chapter.)

Chapter 24: Ten Surefire Ways to Fail the ASVAB 2 A "J

If you're taking the CAT-ASVAB, there will be a timer on the computer screen, counting
down the number of minutes you have to finish that subtest. If you're taking the pencil and
paper version of the test, check the clock on the wall. The proctor will generally write the
start and finish time for the current subtest on a chalkboard. Keep your eye on the time
remaining, but don't panic over it.

Deciding Not to Check the Answers

You should always double-check your answers before you commit to them — you don't
want to be tripped up by silly mistakes. Don't mark your answer and then check your work.
Check your work first.

Do not second-guess yourself (see "Changing Answers," later in this chapter). Just check for
accuracy (like in mathematical equations). Be sure to mark your answer sheet correctly,
too, verifying that the number of the question matches the number on your answer sheet
(you don't have to worry about this with the computerized version of the ASVAB). Getting
just one question off can mess up the rest of the answer sheet.

Making Wild Guesses or Not Guessing at Alt

Take the time to eliminate answers you know are incorrect before choosing among the
remaining answer options. And here's the number one rule: Don't leave any blank spaces. In
most cases, guessing if you have to is the way to go — at least you have a higher chance at
getting the right answer, as opposed to a percent chance if you leave the answer blank. If
you can eliminate answers you know are wrong before guessing, you increase your chances
of answering correctly even more. For tips on smart guessing, see Chapter 3.

Changing Answers

After you double-check your math, decide that Choice (C) is correct, and mark it on the
answer sheet, don't change your answer on the paper version of the ASVAB! You're almost
certain to change a right answer to a wrong one when you play that game. Plus, you can
drive yourself crazy by second-guessing (and third- and fourth-guessing) your decision.
Mark the answer and move on.

Memorizing the Practice Test Questions

Don't waste your time trying to memorize the practice questions in this book. I can almost
guarantee you won't see any of the practice questions in this book (or any other study guide)
on the actual ASVAB. Military test materials are highly controlled items, and no author of an
ASVAB preparation book has access to them. In fact, military members and military civilian
employees who disclose actual ASVAB test questions or answers can go to jail — and I'm not
planning on going to the big house any time soon!

Just use the practice questions in this book as a measurement tool of which subject areas
you should spend your time concentrating on.

3liS

Part VI: The Part of Tens

Misunderstanding the Problem

Make sure that you know what the question wants from you and then give the question
what it wants. If the problem asks for the sum of two numbers, don't multiply the numbers.
Don't mistake a division sign for an addition sign. By familiarizing yourself with the types of
questions on the ASVAB, you'll be able to zero in on what you're supposed to do a lot more
quickly than those poor folks who didn't have the brilliant idea to buy this book.

Chapter 25

Ten Tips for Doing Well on the AFQT

In This Chapter

Using your scratch paper wisely
Reading carefully
Performing math operations
Making sure your answers make sense

■ ommonly referred to as the ASVAB score, the Armed Forces Qualification Test (AFQT)
^^ score is actually computed only from the reading and math skills subtests of the
ASVAB. The AFQT score determines whether you're even qualified to enlist in the service of
your choice. (For the full scoop, see Chapter 1.) The ten concepts presented in this chapter
help you score better on the four subtests of the ASVAB that are used to calculate your
AFQT score.

As Soon as the Test Starts, Write Dou/n
What \lou're Likely to Forget

You can't bring your own scratch paper to the test, but the test proctors will give you as
many sheets of scratch paper as you want. Not only is your scratch paper useful to take the
place of the calculator you're not allowed to use, but you can also use it to write notes at
the very beginning of the test, things that you're worried you may forget. For example, if
you're worried that you'll forget the math order of operations, write it down first thing.

Read All the Answer Choices before bedding

I think that those people who write the ASVAB questions must go through a special course
about being tricky. Many of the answer choices given on the ASVAB are "close but no cigar."
In other words, these tricksters often try to pull a fast one over on you with an incorrect
answer that's almost correct but not quite.

The best defense against this type of trickery is to read each answer choice completely,
even if you think the first or second choice looks plausible. You're looking for the answer
that's most correct.

350

Part VI: The Part of Tens

Don't Expect Perfect Word Matches

jjjftBEfl The Word Knowledge subtest of the ASVAB contains questions that ask you to find the

word that is closest in meaning to a given word. Don't get confused and think that you have
to find the word that means exactly the same thing as the given word. Just follow the direc-
tions. Because some of the answer options may have similar meanings, you need to choose
the answer that's closest in meaning to the given word — the answer that's most right.

Read Passages before the Questions

Some of the Paragraph Comprehension questions can be tricky. The question asks you to
come to a conclusion based on the information presented in the paragraph. The only way
to do this effectively is to understand the entire paragraph and what the author wants to
convey. If you instead read the question first, you may find yourself wasting time by looking
for information that isn't directly stated.

Reread to Find Specific Information

The Paragraph Comprehension subtest often asks you to find specific information in a
passage. Go back and reread the paragraph. You shouldn't have to guess what this informa-
tion is — it's in the passage, or you can easily deduce it from the passage. For instance, if a
paragraph includes the sentence, "Six out of ten smokers will contract some form of
cancer," and a question asks, "How many smokers won't contract some form of cancer?"
you can easily deduce that four is the correct number.

Base Conclusions Only on What \lou Read

You may have to draw inferences or conclusions from what you've read. You must use only
the information presented in the paragraph to reach this conclusion instead of relying on
your own ideas and opinions. In other words, ask yourself, "Would the author agree with
this statement, based on what he or she has written in this paragraph?" Apply this test to
each answer option to choose the best answer.

Change Percents to Decimals

To perform math operations, you often have to change a percent to a fraction or a decimal.
To change a percent to a fraction, multiply the percent by j^ and drop the percent sign:

KO/ _ c _1 5_

0/0-0 100" 100

To change a percent to a decimal, move the decimal point over two places to the left and
drop the percent sign:

5% = 0.05

Chapter 25: Ten Tips for Doing Well on the AFQT 2^ /

Understand Inverses

Inverse operations are opposite operations. The opposite of addition is subtraction, and vice
versa. And the opposite of multiplication is division, and vice versa.

But when it comes to numbers, the term inverse is not the same as opposite. The opposite of
5 is -5, but the inverse of 5 is -w. When you deal with numbers, think of writing the inverse of

5 1

a number as standing the number on its head: The inverse (reciprocal) of 5, or y, is -?.

Remember Hou) Ratios, Rates,
and Scales Compare

You need to understand the differences among ratios, rates, and scales:

v* Ratio: A ratio represents any relationship between two objects. If Luis invests $10 in
Lotto tickets and Joe invests $20 in Lotto tickets, then for every dollar Luis invests,
Joe invests two. That's a ratio of 1:2.

i*" Rate: A rate is an expression of the relationship between two unlike elements. For exam-
ple, if Anna's car can travel a distance of 450 miles per tank of gas and her gas tank
holds 15 gallons, then her car consumes gas at a rate of 30 miles per gallon, or 30 mpg
(miles and gallons being unlike elements). Mathematically, 450 (miles) * 15 (gallons in
the tank) = 30 miles to the gallon.

j*" Scale: A scale expresses a relationship between two like elements, although the
units of measure may differ. A map drawn to scale may use 1 inch to represent 1 mile.
Although an inch and a mile aren't the same unit of measure, they measure the same
thing (distance).

Make Sure \lour Answers Are Reasonable

On the Arithmetic Reasoning and Mathematics Knowledge subtests, you have a very short
amount of time to answer each question, approximately a minute. But if you use your time
wisely, you should have plenty of time to double-check and make sure you've chosen the
correct answer.

0t&£H

Your answers should make sense, or they're probably wrong. For example, if you're required
to compute the average speed that a car maintains during a 2,000 mile trip and your answer
is 2,000 mph, your answer is probably not correct. If a question includes a formula (such as
2 + x - 10), plug in your answer for the variable and see whether both sides are equal. So if
you answered 8, plug in 8 for x and find that 10 = 10. That means your answer checks out.

Those crazy test-writers who designed the test questions often include wrong answers that
you may chose if you make a common mistake when solving the problem. Double-checking
your answers allows you to catch your errors.

352

Part VI: The Part of Tens

Chapter 26

Ten Ways to Boost Your
Math and English Skills

In This Chapter

Getting used to doing math correctly by hand
Knowing key rules and formulas
Expanding your vocabulary
Becoming a better reader

m he ASVAB includes two math and two English subtests: Mathematics Knowledge,
m Arithmetic Reasoning, Word Knowledge, and Paragraph Comprehension. These four
subtests are probably the most important subtests of the ASVAB, because they comprise
your AFQT score, which is the score that determines whether or not you qualify to join the
branch of your choice. (Check out Chapter 1 for more info on the AFQT and Chapter 22 for
a sample AFQT. You can also peruse my book AFQT For Dummies [published by Wiley].)

Because these four subtests are so important, this chapter includes ten surefire ways to
build your skills in these critical areas before you take the test.

Practice Doing Math Problems

The best way to get a firm grasp of certain types of math is by doing math problems and not
simply reading them. Take advantage of the practice math questions in this book, and visit
the public library to see what kind of high school math textbooks it has to lend. The more
you do math, the better you'll get at it.

Put Au/ay \lour Calculator

You're not allowed to use a calculator when you take the ASVAB, so the time to get used to
solving basic math problems without one is now, not during the test. You may have been
taught to rely on a calculator for high school math, but you have to leave your calculator at
home. Practice working out problems by hand, and make sure you know your multiplication
tables and other basic calculations. The ASVAB math questions are written by people who
know how to compute 2 + 2 in their heads.

351*

Part VI: The Part of Tens

As you solve math problems by hand, you can get a feel for what works and what doesn't.
For instance, some questions ask you to find the square root of a number, which you may
find hard without a calculator. But a little logic can help. If you know the square root of 9 is
3 (3 x 3 = 9) and you know the square root of 16 is 4 (4 x 4 = 16), then you can conclude that
the square root of 12 falls between 3 and 4.

Memorize the Order of Operations

0t&£H

Mathematical equations with multiple steps must be solved in a specific order. Otherwise,
you won't get the correct answer. Memorize the order in which you do certain calculations
when you're solving equations, and practice applying these rules well before test day.

When solving an equation involves multiple steps, the correct order of operations is

1. Whatever's within parentheses (and other grouping symbols)

If you have multiple parentheses nested inside each other, do the innermost set first.
On the ASVAB, the other grouping symbols you run across are the fraction bar and the
square root sign. Do what's beneath the square root bar before taking the root. Do
any operation above the fraction bar and any operation below the fraction bar before
dividing.

2. Exponents

3. Multiplication and division

Operate from left to right.

4. Addition and subtraction

Again, work from left to right.

For example, 3 + 2x3 isn't equal to 5 x 3, or 15. The correct answer is 9. You first do the
multiplication and then the addition. You can remember order of operations as "Please
Excuse My Dear Aunt Sally," or PEMDAS. Check out Chapter 7 for more explanation.

Knou) l/our Geometry Formulas

You encounter some math questions that require you to calculate area, perimeter, and
volume on the ASVAB. Memorize the following area formulas:

u* Area of a rectangle: For any rectangle, Area = Length x Width: A - Iw.

v* Area of a triangle: For triangles, Area = Base x Height (or altitude) divided by 2:
A = ^bh.

e* Area of a circle: For circles, area is n (approximately 3.14) times the radius squared: Anr 2 .

Know these perimeter and circumference formulas:

v* Perimeter of polygon (a shape with straight sides): Calculate the perimeter of any
quadrilateral (four-sided figure) or triangle by adding the lengths of all the sides
together.

v* Circumference of a circle: Find the circumference of a circle by multiplying n times the
diameter: C = nd. Note: Diameter equals 2 times the radius.

Chapter 26: Ten Ways to Boost Your Math and English Skills $55

And know these formulas for the volume of 3-D solids:

j*" Volume of a box: Find the volume of a rectangular solid by multiplying Length x Width x
Height: V=lwh.

U* Volume of a cylinder: Find the volume of a cylinder by multiplying the area of the
circular base (n times the base's radius squared) by the cylinder's height: V= tuP-h.

Keep a Word List

The English language has well over 200,000 words in it, so nobody expects you to know
them all. However, the ASVAB writers do expect you to have a good grasp of many vocabu-
lary words. One way to improve your vocabulary is to keep a word list.

How does a word list work? As you read, write down the words that you don't know. Quickly
look them up in the dictionary. You can then apply your word list in your day-to-day life. Of
course, you can't remember every single word, but you can focus on mastering one new
word every day and using it in conversation. Check out Chapter 4 for more tips on building
your vocabulary.

Don't waste your time and choose little-known words, such as absquatulate (which means to
leave hurriedly or secretly). You're unlikely to see obscure words on the ASVAB, but you
should make a practice of learning the meaning of as many common English words as possible.

Study Latin and Greek

You can skip the grammar and pronunciation, but you should get to know some of the
roots, prefixes, and suffixes that English has borrowed from Latin and Greek. These word
parts are the building blocks of much of the English language, and they can give you clues
about what words mean.

If you see an unfamiliar word on the Word Knowledge section, try to figure out its root.
For example, if you know the meaning of mercy, you can figure out the meaning of merciful.
Remember that prefixes and suffixes can be added onto a root to change the word's mean-
ing or function. Here are some examples:

v* Changing meaning: The prefix a- usually means opposite, so the word atypical means
the opposite of typical, not a typical thing.

v* Changing parts of speech: Establish is a verb meaning to make stable or to prove,

whereas establishment (with a suffix) is a noun meaning a thing that has been established.

For a list of common word parts you should know, check out Chapter 4.

Use Flashcards

Flashcards help you remember important facts through the process of spaced repetition.
Learning psychologists agree that this is one of the most effective methods of memorizing
new information. Plus, it's cheap — all you need is a set of blank index cards and a pen to
create your very own studying machine.

356

Part VI: The Part of Tens

You can use flashcards to improve both your mental math and vocabulary — write down
vocab words, roots, prefixes, and suffixes, practice matching square roots and square num-
bers, or just make sure you know your math formulas.

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