新东方 SAT数学专项突破与模拟试题

      本书根据2016年改革后的SAT考试内容编写而成，深入分析了新SAT考试数学部分的考查重点和题型特点，并提供考试策略及解题思路。详细讲解重要的数学概念、运算技巧及特殊题型的处理方法，归纳总结数学常考要点，方便考生查漏补缺。每课结束后还设有跟进练习，并附有详细的答案解析，帮助考生及时巩固所学。另外，本书精选了数百道选择题和主观填空题，同时含有2套数学全真模拟题，供考生自测及考前练兵。直击新SAT数学考试，帮助考生实现全面突破！ 

     本丛书由新东方从美国巴朗教育出版公司独家引进，是备考SAT考试的辅导用书。本书是关于数学部分的专项指南，介绍了数学考试的总体特点，针对数学各部分知识内容分析解题技巧，总结备考策略。同时，书中还提供大量练习题和全真模考题，并配有详尽的解析。本书适用于备考新SAT数学考试的所有考生，帮助考生实现全面突破。

Lawrence S. Leff：美国纽约市富兰克林罗斯福高中前助理校长和数学部主席。从事数学教育多年，是美国资深的SAT考试与教育专家。

Preface
…………………………………………………………………………………………………………………….iii

 

LEARNING ABOUT SAT MATH

1 Know What You’re 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 3–6………………………………………………………………………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

      本书根据2016年改革后的SAT考试（以下简称新SAT考试）内容编写而成。如果正在备考SAT考试数学部分，那么以下简单易行的“四步”学习计划正是考生所需了解与掌握的：

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

      章介绍SAT考试数学部分的形式、类型和题目要求。在正式考试中，这些信息不仅会为考生节约宝贵的时间，还会增加自信，避免因为没有充分理解题目要求而出现错误。

 

STEP 2 BECOME TESTWISE

      第二章是极其重要的一章，主要讲解了SAT考试数学部分的基本解题技巧。学习这些解题技巧以及整本书中穿插的数学知识点将会帮助考生提高做题速度和正确率，进而取得高分。此外，本章还介绍了新SAT考试数学部分中新增的考点。

 

STEP 3 REVIEW SAT MATH TOPICS AND
SAT-TYPE QUESTIONS

      新SAT考试数学部分依然注重高中课本上的基本概念，但解题技巧与策略却有所不同。第三章至第六章是一个简短的数学复习课程。在这些章节中，考生可以发现大量按章节知识点设置的数学题目，它们都是围绕新SAT考试数学部分四大核心内容展开的：代数核心内容、问题求解与数据分析、高数基础以及其他一些基本的数学问题（如几何关系和三角关系）。因此，无论是自主复习，还是参加补习班进行复习，简单易行的概念介绍和课程设置都使得本书成为SAT考生的理想伴侣。同时，对于练习题目和样题，书中还附有详细的答案和解题思路。

 

STEP 4 TAKE PRACTICE EXAMS UNDER
TEST CONDITIONS

      俗话说：熟能生巧！本书后一章提供了两套完整的新SAT考试数学模拟试题，并且附有答案和详细的解析。考生好能模拟考试环境来完成这些试题，以便在实际考试中很好地把握答题时间。此外，这些试题也可以帮助考生发现并消除复习过程中的任何薄弱环节和知识漏洞。

Lawrence S. Leff