Master SAT II Math 1c and 2c 4th ed (Arco Master the SAT Subject Test: Math Levels 1 & 2)

405 Pages·2006·1.67 MB·English

ARCO
M
ASTER THE
SAT* S T :
UBJECT EST
M L
ATH EVELS
1 2
AND
4th Edition
Mark N. Weinfeld
Lalit A. Ahuja
David Alan Miller
AnARCOBook
ARCOisaregisteredtrademarkofThomsonLearning,Inc.,andisusedhereinunderlicense
byThomsonPeterson’s.
AboutThomsonPeterson’s
ThomsonPeterson’s(www.petersons.com)isaleadingproviderofeducationinformationandadvice,withbooksand
onlineresourcesfocusingoneducationsearch,testpreparation,andfinancialaid.ItsWebsiteofferssearchable
databasesandinteractivetoolsforcontactingeducationalinstitutions,onlinepracticetestsandinstruction,andplanning
toolsforsecuringfinancialaid.ThomsonPeterson’sserves110millioneducationconsumersannually.
Formoreinformation,contactThomsonPeterson’s,2000LenoxDrive,Lawrenceville,NJ08648;
800-338-3282;orfindusontheWorldWideWebatwww.petersons.com/about.
©2006ThomsonPeterson’s,apartofTheThomsonCorporation
ThomsonLearning™isatrademarkusedhereinunderlicense.
PreviouseditionspublishedasSATIISuccessMath1CandIIC©2000,2001,2004
SpecialthankstoJoanMarieRosebush
Editor:WallieWalkerHammond;ProductionEditor:AlyshaBullock;Manufacturing
Manager:RaymondGolaszewski;CompositionManager:GaryRozmierski
ALLRIGHTSRESERVED.Nopartofthisworkcoveredbythecopyrighthereinmaybe
reproducedorusedinanyformorbyanymeans—graphic,electronic,ormechanical,
includingphotocopying,recording,taping,Webdistribution,orinformationstorageand
retrievalsystems—withoutthepriorwrittenpermissionofthepublisher.
Forpermissiontousematerialfromthistextorproduct,submitarequestonlineat
www.thomsonrights.com
Anyadditionalquestionsaboutpermissionscanbesubmittedbye-mailto
[email protected]
ISBN13:978-0-7689-2304-9
ISBN10:0-7689-2304-2
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1 08 07 06
FourthEdition
Contents
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Before You Begin ................................. vii
How This Book Is Organized .......................... vii
Comprehensive Answer Explanations ................... viii
Special Study Features ................................ viii
You’re Well on Your Way to Success ................... ix
Top 10 Ways to Raise Your Score ...................... x
PART I: SAT SUBJECT TEST BASICS
1 All About the SAT Subject Test: Math Levels 1
and 2 ............................................. 3
Get to Know the Exam Format......................... 3
When to Use Calculators .............................. 4
How the Test Is Scored ............................... 4
Some Test-wise Strategies for SAT Subject Test Success.... 4
Educated Guessing Will Boost Your Score!............... 6
Getting Ready: The Night Before and the Day of the Test .. 6
Summing It Up ...................................... 8
PART II: DIAGNOSING STRENGTHS AND
WEAKNESSES
2 Practice Test 1: Diagnostic Level 1................. 11
Preparing to Take the Diagnostic Test................... 11
Practice Test 1: Diagnostic Level 1...................... 11
Reference Information ................................ 12
Answer Key and Explanations ......................... 21
3 Practice Test 2: Diagnostic Level 2................. 25
Preparing to Take the Diagnostic Test................... 25
Practice Test 2: Diagnostic Level 2...................... 25
Reference Information ................................ 26
Answer Key and Explanations ......................... 35
iii
iv Contents
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
.
.
.PART III: SAT SUBJECT TEST: MATH REVIEW
.
.
.4 Multiple-Choice Math Strategies .............................. 43
.
. Solving Multiple-choice Math Questions ............................. 43
.
. Know When to Use Your Calculator ................................ 45
.
Learn the Most Important Multiple-choice Math Tips .................. 45
.
. Summing It Up .................................................. 59
.
.
.5 Numbers and Operations Review............................. 61
.
. Properties of Numbers............................................ 61
.
. Exercise: Properties of Numbers................................ 64
.
. Answers and Explanations..................................... 65
.
Whole Numbers ................................................. 66
.
. Operations with Whole Numbers................................... 69
.
. Exercise: Whole Numbers ..................................... 72
.
. Answers and Explanations..................................... 73
.
Operations with Fractions ......................................... 74
.
. Exercise: Fractions ........................................... 77
.
. Answers and Explanations..................................... 78
.
. Operations with Decimals ......................................... 79
.
Decimals and Fractions............................................ 81
.
. Exercise: Decimals and Fractions ............................... 86
.
. Answers and Explanations..................................... 87
.
. Operations with Percents ......................................... 89
.
Exercise: Percents............................................ 90
.
. Answers and Explanations..................................... 91
.
. Exercise: Percent Word Problems............................... 98
.
. Answers and Explanations..................................... 99
.
Systems of Measurements ......................................... 100
.
. Exercise: Systems of Measurement.............................. 103
.
. Answers and Explanations..................................... 104
.
. Signed Numbers ................................................. 105
.
Exercise: Signed Numbers ..................................... 108
.
. Answers and Explanations..................................... 109
.
. Summing It Up .................................................. 110
.
.
.6 Algebra and Functions Review................................111
.
. Powers, Exponents, and Roots ..................................... 112
.
. Exercise: Exponents, Powers, and Roots......................... 117
.
. Answers and Explanations..................................... 118
.
Algebra ......................................................... 119
.
. Exercise: Algebra............................................. 127
.
. Answers and Explanations..................................... 128
.
. Exercise: Equations........................................... 131
.
Answers and Explanations..................................... 132
.
.
.
.
.www.petersons.com
.
.
.
.
.
.
.
Contents v
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
.
.
Exercise: Word Problems Involving One Unknown................ 138
.
Answers and Explanations..................................... 139 .
.
Exercise: Equation-Solving .................................... 147 .
.
Answers and Explanations..................................... 148 .
.
Exercise: Linear Inequalities and Equations....................... 156
.
Answers and Explanations..................................... 157 .
.
Functions and Their Graphs ....................................... 164 .
.
Exercise: Functions........................................... 172 .
.
Answers and Explanations..................................... 173
.
Summing It Up .................................................. 175 .
.
.
7 Geometry and Measurement Review .........................177 .
.
.
Plane Geometry.................................................. 177
.
Three-dimensional Geometry....................................... 206 .
.
Exercise: Geometry........................................... 208 .
.
Answers and Explanations..................................... 210 .
.
Coordinate Geometry............................................. 212
.
Exercise: Coordinate Geometry................................. 216 .
.
Answers and Explanations..................................... 217 .
.
Trigonometry.................................................... 219 .
.
Exercise: Trigonometry ....................................... 224
.
Answers and Explanations..................................... 225 .
.
Trigonometric Functions of the General Angle........................ 228 .
.
Exercise: Trigonometric Functions.............................. 234 .
.
Answers and Explanations..................................... 235
.
Exercise: Trigonometric Identity and Equations................... 241 .
.
Answers and Explanations..................................... 242 .
.
Solving Triangles................................................. 243 .
.
Scalars and Vectors............................................... 245
.
Exercise: Triangles ........................................... 248 .
.
Answers and Explanations..................................... 249 .
.
Graphs of Trigonometric Functions ................................. 251 .
.
Exercise: Graphs of the Trigonometric Functions ................. 255
.
Answers and Explanations..................................... 256 .
.
Summing It Up .................................................. 258 .
.
.
8 Data Analysis, Statistics, Probability, and Advanced .
.
Math Review..................................................259 .
.
Set Theory ...................................................... 259 .
.
Exercise: Sets................................................ 262
.
Answers and Explanations..................................... 263 .
.
Probability ...................................................... 264 .
.
Exercise: Probability.......................................... 267 .
.
Answers and Explanations..................................... 268
.
.
.
.
.
.
www.petersons.com .
.
.
.
.
.
.
.
vi Contents
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
.
.
Permutations and Combinations.................................... 270
.
. Exercise: Permutations and Combinations........................ 273
.
. Answers and Explanations..................................... 274
.
. Statistics ........................................................ 275
.
Exercise: Statistics............................................ 279
.
. Answers and Explanations..................................... 280
.
. Exponents and Logarithms......................................... 281
.
. Exercise: Exponents and Logarithms ............................ 286
.
Answers and Explanations..................................... 288
.
. Logic........................................................... 289
.
. Exercise: Logic............................................... 294
.
. Answers and Explanations..................................... 295
.
Systems of Numbers.............................................. 296
.
. Exercise: Systems of Numbers.................................. 299
.
. Answers and Explanations..................................... 300
.
. Complex Numbers ............................................... 301
.
Exercise: Complex Numbers................................... 304
.
. Answers and Explanations..................................... 305
.
. Sequences....................................................... 306
.
. Exercise: Sequences .......................................... 310
.
Answers and Explanations..................................... 311
.
. Summing It Up .................................................. 313
.
.
.
.
.PART IV: FOUR PRACTICE TESTS
.
.
. Practice Test 3: Level 1 ........................................317
.
.
Reference Information ............................................ 318
.
. Answer Key and Explanations ..................................... 329
.
.
. Practice Test 4: Level 1 ........................................339
.
. Reference Information ............................................ 340
.
. Answer Key and Explanations ..................................... 351
.
.
. Practice Test 5: Level 2 ........................................357
.
. Reference Information ............................................ 358
.
. Answer Key and Explanations ..................................... 369
.
.
. Practice Test 6: Level 2 ........................................377
.
. Reference Information ............................................ 378
.
. Answer Key and Explanations ..................................... 388
.
.
.
.
.
.
.
.
.
.
.
.www.petersons.com
.
.
.
.
.
.
.
Before You Begin
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
HOW THIS BOOK IS ORGANIZED
Almost a quarter of a million students take SAT Subject Tests every year. In
the past, these tests were known as the College Board Achievement Tests.
These tests are important for several reasons. Because many of the colleges
requireSATSubjectTests,theseareimportantexamsforyou.Thepurposeof
these tests is to measure and demonstrate your knowledge and/or skills in
specific subjects and to test your ability to apply that knowledge to each
particular examination. The better your score is, the better your application
will look to the colleges of your choice.
If you’re reading this book, it’s likely that you are preparing for the SAT
Subject Test Mathematics—either Level 1 or Level 2. We have tried to make
this a workable book. In other words, the book is set up so that regardless of
thelevelexamyou’retaking,youwillbeabletofindthematerialnecessaryto
study and to take those tests that are most applicable to your level.
As a further enhancement to your ability to prepare for this exam, we have
prepared in-depth mathematics review material and highlighted those areas
that are required primarily for Level 2, so that those studying for the Level 1
test can focus on only those areas that are appropriate.
Dividedintosections,thebookbeginswithtwodiagnosticexams.Thereisone
each for Level 1 and Level 2. Take these exams (and all of the tests) under
simulatedexamconditions,ifyoucan.Findaquietplaceinwhichtowork,set
up a clock, and take the test without stopping. When you are finished, take a
break and then go back and check your answers. Always reread those
questions you got wrong, since sometimes your errors come from merely
misreadingthequestion.Again,double-checkyouranswers,andifthey’restill
not clear, read the appropriate section in the review material.
Once you’ve completed your diagnostic test(s), it’s time to move on to the
review section. Study the material carefully, but feel free to skim the portion
of the review section that is easy for you.
vii
viii Before You Begin
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
.
.
Then,taketheactualpracticetests.Thesesimulatedexamsaredesignedtogiveyouabroad
.
.
spectrum of question types that are similar to those you will find on the actual SAT Subject
.
.
Tests:Mathematics.Wesuggestthat,regardlessofthelevelexamyouareplanningtotake,it
.
.
wouldbeextremelyhelpfultotakeallofthetestsinthebook.IfyouaretakingLevel2,taking
.
.
thelower-leveltestwillgiveyouthatmuchmorepracticefortheexam.Andifyouaretaking
.
.
Level1,itwouldbehelpfultotestyourskillsandstretchyourthinkingtogiveyouastronger
.
.
grounding for the Level 1 exam.
.
.
.As you complete each exam, take some time to review your answers. We think you’ll find a
.
.marked improvement from taking the diagnostic tests to completing all of the full-length
.
.practice tests. Always take the time to check the review section for clarification, and if you
.
.stilldon’tunderstandthematerial,gotoyourteacherforhelp.
.
.
.
.
.
COMPREHENSIVE ANSWER EXPLANATIONS
.
.
.At the end of each practice session, read all the answers and explanations, even for the
.
.questionsthatyouansweredcorrectly.Therearecomprehensiveexplanationsforeveryoneof
.
.the book’s 1,000+ questions! By reading the answer explanations, you can learn from your
.
.mistakes.
.
.
.Our objective is to help you dramatically raise your scores so that you can maximize the
.
.likelihood of getting into the college of your choice.And if you use this book properly, we can
.
.help you reach that goal.
.
.
.
.
.SPECIAL STUDY FEATURES
.
.
.ARCO Master the SAT Subject Test: Math Levels 1 and 2is designed to be as user-friendly as
.
.it is complete. To this end, it includes several features to make your preparation much more
.
.efficient.
.
.
.
.Overview
.
.Each chapter begins with a bulleted overview listing the topics to be covered in the chapter.
.
.This will allow you to quickly target the areas in which you are most interested.
.
.
.
.Summing It Up
.
.
Each chapter ends with a point-by-point summary that captures the most important points
.
.
contained in the chapter. They are a convenient way to review key points.As you work your
.
.
way through the book, keep your eye on the margins to find bonus information and advice.
.
.
Information can be found in the following forms:
.
.
.
.
.
.
.
.www.petersons.com
.
.
.
.
.
.
.
Before You Begin ix
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
.
.
Note
.
.
NoteshighlightcriticalinformationabouttheSATSubjectTestformat—forexample,thatthe .
.
answers in the test always go from smaller to larger. .
.
.
.
Tip .
.
Tips draw your attention to valuable concepts, advice and shortcuts for tackling Math: .
.
Levels 1 and 2. By reading the tips you will learn how to approach different question types, .
.
use process-of-elimination techniques, pace yourself, and guess most effectively. .
.
.
.
Alert! .
.
.
Wherever you need to be careful of a common pitfall or test-taker trap, you’ll find an Alert!.
.
.
This information reveals and eliminates the misperceptions and wrong turns so many people
.
.
takeontheexam.BytakingfulladvantageofallfeaturespresentedinARCOMastertheSAT
.
.
Subject Test: Math Levels 1 and 2 you will become much more comfortable with the SAT and
.
.
considerably more confident about getting a good score.
.
.
.
.
.
YOU’RE WELL ON YOUR WAY TO SUCCESS .
.
.
Remember that knowledge is power. By using ARCO Master the SAT Subject Test: Math
.
.
Levels 1 and 2 you will be studying the most comprehensive SAT Subject Tests preparation
.
.
guideavailableandyouwillbecomeextremelyknowledgeableabouttheSAT.Welookforward
.
.
to helping you raise your scores and improve your college prospects.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
www.petersons.com .
.
.
.
.
.
.
.