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1、ARCOMASTER THESAT* SUBJECT TEST: MATH LEVELS1AND 24th EditionMark N. Weinfeld Lalit A. Ahuja David Alan MillerAn ARCO BookARCO is a registered trademark of Petersons, and is used herein under license by Petersons.About Petersons, a Nelnet companyPetersons () is a leading provider of education inform

2、ation and advice, with books and onlineresources focusing on education search, test preparation, and final aid. Its Web site offers searchable databases andinteractive tools for contacting educational institutions, online practice tests and instruction, and planning tools forsecuring final aid. Pete

3、rsons serves 110 million education consumers annually.For more information, contact Petersons, 2000 Lenox Drive, Lawrenceville, NJ 08648; or find us on the World Wide Web at.© 2006 Petersons, a Nelnet companyPrevious editions published as SAT II Success Math 1C and IIC © 2000, 2001, 2004Sp

4、ecial thanks to Joan Marie RosebushEditor: Wallie Walker Hammond; Production Editor: Alysha Bullock; Manufacturing Manager: Raymond Golaszewski; Composition Manager: Gary Rozmierski. No part of this work covered by the copyright herein may be reproduced or used in any form or by any meansgraphic, el

5、ectronic, or mechanical,including photocopying, recording, ta, Web distribution, or information storage andretrieval systemswithout the prior written permission of the publisher.For permission to use material from this text or product, complete the PermissionRequest Form at.ISBN-13: 978-0-7689-2304-

6、9ISBN-10: 0-7689-2304-2Printed in the United States of America10 9 8 7 6 5 4 3 208 07 06Fourth EditionContents. . Before You Begin . How This Book Is Organized . viivii viii viii ix xCompensive Answer Explanations . Special Study Features . Youre Well on Your Way to Success . Top 10 Ways to Raise Yo

7、ur Score . PART I: SAT SUBJECT TEST BASICS1All About the SAT Subject Test: Math Levels 1and 2 . Get to Know the Exam Format. When to Use Calculators . 33444668How theScored . Some Test-wise Strategies for SAT Subject Test Success . Educated Guessing Will Boost Your Score! . Getting Sumy: The Night B

8、efore and the Day of the Test . . It Up . PART II:DIAGNOSING STRENGTHS AND WEAKNESSES2Practice Test 1: Diagnostic Level 1 . Preparing to Take the Diagnostic Test. Practice Test 1: Diagnostic Level 1. Reference Information . Answer Key and Explanations . Practice Test 2: Diagnostic Level 2 . Preparin

9、g to Take the Diagnostic Test. Practice Test 2: Diagnostic Level 2. Reference Information . Answer Key and Explanations . 111111122125252526353iiiivContents. PART III: SAT SUBJECT TEST: MATH REVIEW4Multiple-Choice Math Strategies . Solving Multiple-choice Math Questions . Know When to Use Your Calcu

10、lator . Learn the Most Important Multiple-choice Math Tips . 43434545596161646566697273747778798186878990919899100103104105108109110SumIt Up . 5Numbers and Operations Review. Properties of Numbers . Exercise: Properties of Numbers. Answers and Explanations . Whole Numbers . Operations with Whole Num

11、bers . Exercise: Whole Numbers . Answers and Explanations . Operations with Fractions . Exercise: Fractions . Answers and Explanations . Operations with Decimals . Decimals and Fractions. Exercise: Decimals and Fractions . Answers and Explanations . Operations with Percents . Exercise: Percents . An

12、swers and Explanations . Exercise: Percent Word Problems. Answers and Explanations . Systems of Measurements . Exercise: Systems of Measurement . Answers and Explanations . Signed Numbers . Exercise: Signed Numbers . Answers and Explanations . SumIt Up . 6Algebra and Functions Review111Powers, Expon

13、ents, and Roots112Exercise: Exponents, Powers, and Roots117Answers and Explanations118Algebra119Exercise: Algebra127Answers and Explanations128Exercise: Equations131Answers and Explanations132. Contentsv. Exercise: Word Problems Involving One Unknown. Answers and Explanations . Exercise: Equation-So

14、lving . Answers and Explanations . Exercise: Linear Inequalities and Equations. Answers and Explanations . Functions and Their Graphs . Exercise: Functions. Answers and Explanations . 138139147148156157164172173175SumIt Up . 7Geometry and Measurement Review177Plane Geometry . Three-dimensional Geome

15、try. Exercise: Geometry. Answers and Explanations . Coordinate Geometry . Exercise: Coordinate Geometry. Answers and Explanations . Trigonometry . Exercise: Trigonometry . Answers and Explanations . 177206208210212216217219224225228234235241242243245248249251255256258Trigonometric Functions of teral

16、 Angle. Exercise: Trigonometric Functions . Answers and Explanations . Exercise: Trigonometric Identity and Equations . Answers and Explanations . Solving Triangles . Scalars and Vectors . Exercise: Triangles . Answers and Explanations . Graphs of Trigonometric Functions . Exercise: Graphs of the Tr

17、igonometric Functions . Answers and Explanations . SumIt Up . 8Data Analysis, Statistics, Probability, and AdvancedMath Review259Set Theory259Exercise: Sets262Answers and Explanations263Probability264Exercise: Probability267Answers and Explanations268. viContents. Permutations and Combinations . Exe

18、rcise: Permutations and Combinations. Answers and Explanations . Statistics . Exercise: Statistics . Answers and Explanations . Exponents and Logarithms. Exercise: Exponents and Logarithms . Answers and Explanations . Logic . Exercise: Logic. Answers and Explanations . Systems of Numbers . Exercise:

19、 Systems of Numbers. Answers and Explanations . Complex Numbers . Exercise: Complex Numbers . Answers and Explanations . Sequences. Exercise: Sequences . Answers and Explanations . 270273274275279280281286288289294295296299300301304305306310311313SumIt Up . PART IV: FOUR PRACTICE TESTSPractice Test

20、3: Level 1317Reference Information318Answer Key and Explanations329Practice Test 4: Level 1339Reference Information340Answer Key and Explanations351Practice Test 5: Level 2357Reference Information358Answer Key and Explanations369Practice Test 6: Level 2377Reference Information378Answer Key and Expla

21、nations388. Before You Begin. . HOW THIS BOOK IS ORGANIZEDAlmost a quarter of a millions take SAT Subject Tests every year. Inthe past, these tests were known as the CollegAchievement Tests.These tests are important for several reasons. Because many of the colleges require SAT Subject Tests, these a

22、re important exams for you. The purpose of 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 applicationwill look to the colleges of yo

23、ur choice.If youreing this book, its likely that you are preparing for the SATSubject Test Mathematicseither 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 the level exam youre taking, you will be able to find the material nec

24、essary to 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

25、Level 1 test can focus on only those areas that are appropriate.Divided into sections, the book begins with two diagnostic exams. There is one each for Level 1 and Level 2. Take these exams (and all of the tests) undersimulated exam conditions, if you can. Find a quiet place in which to work, setup

26、a clock, and take the test without stopbreak and then go back and check your questions you got wrong, since sometimes. When you are finished, take aanswers. Always rethoseyour errors come from merelymising the question. Again, double-check your answers, and if theyre stillnot clear,the appropriate s

27、ection in the review material.Once youve completed your diagnostic test(s), its time to move on to thereview section. Study the material carefully, but feelof the review section that is easy for you.to skim the portionviiviiiBefore You Begin. Then, take the actual practice tests. These simulated exa

28、ms are designed to give you a broad spectrum of question types that are similar to those you will find on the actual SAT Subject Tests: Mathematics. We suggest that, regardless of the level exam you are planning to take, it would be extremely helpful to take all of the tests in the book . If you are

29、 taking Level 2, taking the lower-level test will give you that much more practice for the exam. And if you are taking Level 1, it would be helpful to test your skills and stretch your thinking to give you a stronger grounding for the Level 1 exam.As you complete each exam, take some time to review

30、your answers. We think youll 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 still dont understand the material, go to your teacher for help.COMPENSIVE ANSWE

31、R EXPLANATIONSAt the end of each practice session,all the answers and explanations, even for thequestions that you answered correctly. There are compensive explanations for every one ofthe books 1,000+ questions! Bymistakes.ing the answer explanations, you can learn from yourOur objective is to help

32、 you dramatically raise your scores so that you canize thelikelihood of getting into the college of your choice. And if you use this book properly, we canhelp you reach that goal.SPECIAL STUDY FEATURESARCO Master the SAT Subject Test: Math Levels 1 and 2 is designed to be as user-friendly as it is c

33、omplete. To this end, it includes several features to make your preparation much more efficient.OverviewEach 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.SumIt UpEach chapter

34、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 form

35、s:. Before You Beginix. NoteNotes highlight critical information about the SAT Subject Test formatfor example, that the answers in the test always go from smaller to larger.TipTips draw your attention to valuable concepts, advice and shortcuts for tackling Math:Levels 1 and 2. Bying the tips you wil

36、l 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, youll find an Alert!. This information reveals and eliminates the misperceptions and wrong t

37、urns so many people take on the exam. By taking full advantage of all features presented in ARCO Master the SAT 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.YOURE WELL ON YOUR WAY TO SUCCESSRemember th

38、at knowledge is power. By using ARCO Master the SAT Subject Test: MathLevels 1 and 2 you will be studying the most compensive SAT Subject Tests preparationguide available and you will become extremely knowledgeable about the SAT. We look forwardto helyou raise your scores and improve your college pr

39、ospects. 10To p 10 Waysto Raise Your ScoreWhen it comes to taking the SAT, some test-taking skills will do you more good than others. There are concepts you can learn, techniques you can follow, and tricks you can use that will help you to do your very best. Here are our picks for the top 10 ways to

40、 raise your score:1. Regardless of w hich plan you w ill follo w, get started bying Chapter 1 to familiarize yourself w ith the test format.2. Take the diagnostic practice tests.3. Compute your category percentages to assess your relative strengths and areas for improvement.4. If you have time,the b

41、ook from cover to cover. Start at the beginning or start with the kind of question or the topic that you find most difficult.5. Complete the exercises in each chapter youand assess your performanceyour diagnostic scores.6. When you are one third of the w ay through your preparation, take apractice test. Compare your scores with your original results. Make sure you are applying new test-taking strategies.7. Revisit problematic chapters and chapter summaries.Then additional chapters, do exercises, and