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新東方 SAT數學專項突破與模擬試題

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本叢書由新東方從美國巴朗教育出版公司獨家引進，是備考SAT考試的必備輔導用書。本書是關于數學部分的專項指南，介紹了數學考試的總體特點，針對數學各部分知識內容分析解題技巧，總結備考策略。同時，書中還提供大量練習題和全真模考題，并配有詳盡的解析。本書適用于備考新SAT數學考試的所有考生，幫助考生實現全面突破。

2016年，SAT迎來了全新變革：重回1600分制，循證式閱讀和文法，作文改為選考，選錯選項不再扣分等。相信正在備考新SAT的同學們對這些變化已經了然于心，唯獨缺少針對新SAT的備考資料。新東方在*時間獨家引進了巴朗NEW SAT系列叢書，為同學們提供及時的備考指導與豐富習題。

本書根據2016年改革后的SAT考試內容編寫而成，深入分析了新SAT考試數學部分的考查重點和題型特點，并提供考試策略及解題思路。詳細講解重要的數學概念、運算技巧及特殊題型的處理方法，歸納總結數學常考要點，方便考生查漏補缺。每課結束后還設有跟進練習，并附有詳細的答案解析，幫助考生及時鞏固所學。另外，本書精選了數百道選擇題和主觀填空題，同時含有2套數學全真模擬題，供考生自測及考前練兵。直擊新SAT數學考試，幫助考生實現全面突破！

本書根據2016年改革后的SAT考試（以下簡稱新SAT考試）內容編寫而成。如果正在備考SAT考試數學部分，那么以下簡單易行的四步學習計劃正是考生所需了解與掌握的：

STEP 1. Know what to expect on test day.

STEP 2. Become testwise.

STEP 3. Review SAT Math topics and SAT-type questions.

STEP 4. Take practice exams under test conditions.

STEP 1 KNOW WHAT TO EXPECT ON TEST DAY

第一章介紹SAT考試數學部分的形式、類型和題目要求。在正式考試中，這些信息不僅會為考生節約寶貴的時間，還會增加自信，避免因為沒有充分理解題目要求而出現錯誤。

STEP 2 BECOME TESTWISE

第二章是極其重要的一章，主要講解了SAT考試數學部分的基本解題技巧。學習這些解題技巧以及整本書中穿插的數學知識點將會幫助考生提高做題速度和正確率，進而取得高分。此外，本章還介紹了新SAT考試數學部分中新增的考點。

STEP 3 REVIEW SAT MATH TOPICS AND SAT-TYPE QUESTIONS

新SAT考試數學部分依然注重高中課本上的基本概念，但解題技巧與策略卻有所不同。第三章至第六章是一個簡短的數學復習課程。在這些章節中，考生可以發現大量按章節知識點設置的數學題目，它們都是圍繞新SAT考試數學部分四大核心內容展開的：代數核心內容、問題求解與數據分析、高數基礎以及其他一些基本的數學問題（如幾何關系和三角關系）。因此，無論是自主復習，還是參加補習班進行復習，簡單易行的概念介紹和課程設置都使得本書成為SAT考生的理想伴侶。同時，對于練習題目和樣題，書中還附有詳細的答案和解題思路。

STEP 4 TAKE PRACTICE EXAMS UNDER TEST CONDITIONS

俗話說：熟能生巧！本書最后一章提供了兩套完整的新SAT考試數學模擬試題，并且附有答案和詳細的解析。考生最好能模擬考試環境來完成這些試題，以便在實際考試中很好地把握答題時間。此外，這些試題也可以幫助考生發現并消除復習過程中的任何薄弱環節和知識漏洞。

Lawrence S. Leff

Preface .....................................................................................................................................iii

LEARNING ABOUT SAT MATH

1 Know What Youre Up Against ..........................................................................................3

Lesson 1-1 Getting Acquainted with the Redesigned SAT ......................................................4

Lesson 1-2 Multiple-Choice Questions ....................................................................................9

Lesson 1-3 Grid-In Questions ..................................................................................................14

2 SAT Math Strategies ...........................................................................................................21

Lesson 2-1 SAT Math Strategies You Need to Know .............................................................22

Lesson 2-2 Guessing and Calculators on the SAT ...................................................................71

THE FOUR MATHEMATICS CONTENT AREAS

3 Heart of Algebra..................................................................................................................81

Lesson 3-1 Some Beginning Math Facts .................................................................................82

Lesson 3-2 Solving Linear Equations ......................................................................................91

Lesson 3-3 Equations with More Than One Variable .............................................................100

Lesson 3-4 Polynomials and Algebraic Fractions ...................................................................106

Lesson 3-5 Factoring................................................................................................................114

Lesson 3-6 Quadratic Equations..............................................................................................122

Lesson 3-7 Systems of Equations ............................................................................................127

Lesson 3-8 Algebraic Inequalities ...........................................................................................138

Lesson 3-9 Absolute Value Equations and Inequalities ..........................................................144

Lesson 3-10 Graphing in the xy-Plane ....................................................................................149

Lesson 3-11 Graphing Linear Systems ...................................................................................168

Lesson 3-12 Working with Functions .....................................................................................177

Answer Key for Chapter 3 Tune-Up Exercises ......................................................................189

4 Problem Solving and Data Analysis .................................................................................193

Lesson 4-1 Working with Percent ..........................................................................................194

Lesson 4-2 Ratio and Variation ..............................................................................................200

Lesson 4-3 Rate Problems ......................................................................................................209

Lesson 4-4 Converting Units of Measurement .......................................................................215

Lesson 4-5 Linear and Exponential Functions ........................................................................220

Lesson 4-6 Graphs and Tables ................................................................................................234

Lesson 4-7 Scatterplots and Sampling ....................................................................................245

Lesson 4-8 Summarizing Data Using Statistics ......................................................................253

Answer Key for Chapter 4 Tune-Up Exercises ......................................................................261

5 Passport To Advanced Math ............................................................................................263

Lesson 5-1 Rational Exponents .............................................................................................264

Lesson 5-2 More Advanced Algebraic Methods ...................................................................270

Lesson 5-3 Complex Numbers ..............................................................................................280

Lesson 5-4 Completing The Square ......................................................................................285

Lesson 5-5 The Parabola and Its Equations ..........................................................................292

Lesson 5-6 Reflecting and Translating Function Graphs ......................................................305

Answer Key for Chapter 5 Tune-Up Exercises .....................................................................316

6 Additional Topics in Math ..............................................................................................317

Lesson 6-1 Reviewing Basic Geometry Facts.......................................................................318

Lesson 6-2 Area of Plane Figure...........................................................................................328

Lesson 6-3 Circles and Their Equations ...............................................................................339

Lesson 6-4 Solid Figures.......................................................................................................355

Lesson 6-5 Basic Trigonometry ...........................................................................................365

Lesson 6-6 The Unit Circle ...................................................................................................377

Answer Key for Chapter 6 Tune-Up Exercises ....................................................................386

SOLUTIONS FOR TUNE-UP EXERCISES

Worked out solutions for Chapters 36.................................................................................391

TAKING PRACTICE TESTS

Practice Test 1......................................................................................................................483

Answer Key ...........................................................................................................................506

Answer Explanations for Practice Test 1..............................................................................508

Practice Test 2......................................................................................................................521

Answer Key ...........................................................................................................................545

Answer Explanations for Practice Test 2...............................................................................547

How to Evaluate Your Performance on a Practice Test...................................................559

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