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新东方·GRE数学备考策略与模拟试题

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新东方·GRE数学备考策略与模拟试题

Name: 新东方·GRE数学备考策略与模拟试题
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《GRE数学备考策略与模拟试题》
全面介绍GRE数学测试部分的考查内容、题目类型、评分方式等。
分类详解GRE数学基本概念，并辅以大量练习和详细解析。
针对GRE数学常考题型，提供实用高效的解题策略。
精编2套数学模拟题，便于考生诊断自测，查漏补缺。

Content Description

《GRE数学备考策略与模拟试题》引进自美国巴朗教育出版公司，根据改革后GRE数学考试的特点编写而成。书中详细介绍GRE数学测试中算术、代数、数据分析、几何等相关数学知识，穿插相应的解题技巧和备考策略，同时提供大量练习题目及2套完整的数学测试试题，帮助考生提高解题技能，实现高效备考。

Catalogue

To the Student vii

Guide to Using This Book ix

1 The GRE General Math Exam 1

Exam Structure 1

Question Types 2

Multiple-Choice Questions 2

Multiple-Answer Questions 3

Quantitative Comparison Questions 3

Numeric Entry Questions 4

Topics and Scoring 5

Calculator Use 6

Problems 8

Solutions 9

2 STRATEGIES AND PROBLEM SOLVING 13

Test-Taking Strategies 13

Problem Solving 14

General Strategies 16

Use a Diagram 16

Pay Attention to Units 20

Use Numbers Instead of Variables 21

Strategies for Multiple-Choice Questions 22

Test Answers Starting with C 22

Use Numbers Instead of Variables 22

Eliminate Choices, Then Guess 23

Strategies for Data Interpretation Questions 24

Estimate, Don’t Calculate 25

Try to Visualize Rather Than Calculate 25

Strategies for Quantitative Comparison

Questions 26

Do the Same Thing to Each Quantity 26

Compare, Don’t Calculate 27

Replace Variables with Numbers 27

Choose a Good Number for the Whole 28

Guess 29

Strategies for Numeric Entry Questions 30

Don’t Simplify Fractions 30

Strategies for Multiple-Answer Questions 31

Problems 31

Solutions 34

3 NUMBERS 39

Numbers 40

Operations 40

Basic Properties 40

Absolute Value 42

Order of Operations: PEMDAS 43

Problems 45

Basic Problems 45

GRE Problems 45

Integers 46

Consecutive Integers 48

Problems 48

Basic Problems 48

GRE Problems 50

Number Theory 52

Divisibility Rules 52

Odds and Evens 54

Prime Numbers 55

Greatest Common Factor and Lowest Common Multiple 57

Problems 58

Basic Problems 58

GRE Problems 59

Fractions 61

Equivalent Fractions 62

Mixed Fractions 64

Operations on Fractions 65

Simplifying Complex Fractions 68

Solving Fraction Problems with Diagrams 69

Problems 70

Basic Problems 70

GRE Problems 72

Decimals 74

Converting Between Fractions and Decimals 75

Comparing Decimal Numbers 76

Operations on Decimals 76

Multiplying or Dividing by Problems 77

Basic Problems 77

GRE Problems 78

Radicals and Exponents 79

Simplifying Radicals 80

Defining Powers 81

Rules for Working with Powers 82

Problems 83

Basic Problems 83

GRE Problems 84

Solutions 86

Numbers 86

Integers 87

Number Theory 90

Fractions 94

Decimals 98

Radicals and Exponents 100

4 ALGEBRA 103

Polynomials and Factoring 103

Problems 107

Basic Problems 107

GRE Problems 108

Solving Equations 110

Solving Systems of Linear Equations 113

Problems 115

Basic Problems 115

GRE Problems 117

Inequalities 119

Problems 122

Basic Problems 122

GRE Problems 123

Functions 125

Problems 127

Basic Problems 127

GRE Problems 128

Solutions 129

Polynomials and Factoring 129

Solving Equations 131

Inequalities 134

Functions 137

5 DATA ANALYSIS 139

Percentages 139

Problems 142

Averages 144

Problems 148

Charts and Graphs 150

Problems 153

Counting 157

Venn Diagrams 158

Partitions 159

Counting Commas 160

Problems 161

Basic Problems 161

GRE Problems 162

Probability 163

Problems 165

Solutions 168

Percentages 168

Averages 169

Charts and Graphs 171

Counting 173

Probability 175

6 GEOMETRY 179

Perimeter 180

Problems 183

Basic Problems 183

GRE Problems 184

Angles 186

Problems 189

Basic Problems 189

GRE Problems 190

Triangles 192

Triangle Inequality 194

Pythagorean Theorem 195

Problems 197

Basic Problems 197

GRE Problems 199

Polygons 201

Regular Polygons 202

Quadrilaterals 204

Problems 206

Basic Problems 206

GRE Problems 207

Area 209

Connecting Area and Perimeter 212

Problems 213

Basic Problems 213

GRE Problems 214

Surface Area and Volume 217

Surface Area 217

Volume 219

Problems 221

Basic Problems 221

GRE Problems 222

Solutions 224

Perimeter 224

Angles 227

Triangles 229

Polygons 231

Area 234

Surface Area and Volume 237

7 SAMPLE EXAMS AND SOLUTIONS 241

Sample Test 1 245

Sample Test 2 253

Answers and Complete Solutions to Sample Exams 259

Appendix: Suggested Facts to Memorize 271

Index 273

Introduction

To the Student
亲爱的考生：
相信现在的你一定有些兴奋！你已经或者即将取得学士学位，并正在考虑进入更高阶段的学习——攻读研究生无疑是一段令人兴奋的、高要求、高回报的学习经历。
或许此时，你还没有准备好去迎接另一场考试，但你的GRE成绩将是影响你进入理想学校的关键因素之一；更为重要的是，它还决定了你就读期间可能获得的奖学金。因此，花一点时间用心准备GRE考试绝对是明智的选择。
我们建议要以严肃认真的态度对待GRE考试，并且每周都安排时间进行备考训练。每周花几个小时学习远比考试前临时突击20个小时更有效。如果你需要激励或者额外的帮助，不妨报名参考附近的GRE培训班。对很多考生来说，能和其他考生一起学习，且有老师指点，复习的过程会更容易。
每个考生的情况都不同。你可能是个物理专业的高手，只需再稍微完善一下数学技能就达到理想学校所要求的165分。你也可能是个心理专业的学生，高中之后就没再接触过数学，必须努力提高数学水平，才能达到理想学校所要求的155分。为避免不必要的失望，以及为自己设定合理的目标，建议考生提前联系打算申请的学校，咨询录取所需的分数标准（你甚至可以咨询获得一等奖学金所需的分数）。
本书将帮助你复习GRE数学必考内容。鉴于整个高中阶段的数学和知识都在考试范围之内，本书并不能完全取代高中数学教材。不过不要担心，即使你对数学不自信，也会在复习过程中逐渐回忆起那些最基本的数学概念。因此，本书将带你回顾那些学过的数学知识，并告诉你考试中最常见的考点。
祝学习开心、考试顺利！
编者
Guide to Using This Book
本书第一章介绍了GRE考试数量推理（Quantitative Reasoning）部分的考试形式。考生将了解考试结构、各题型的分析和例题、得分标准以及屏幕计算器的使用技巧等相关信息。第二章展示了针对不同题型的解题策略。这两章都包含了GRE风格的练习题和解析，便于考生训练新学的解题技巧。
第三到六章介绍了攻克GRE数量推理部分所需的数学技能。这些章节的每个部分都包含了基础习题（Basic problems）和GRE习题（GRE problems），供考生练习。基础习题重点考查考生在每部分学到的知识点；在一些情况下，这些问题不太可能出现在实际的GRE考试中。GRE习题更有难度，且更接近实际的考试，考查内容也不局限于考生在本部分学到的技能。每章最后都附有对所有题目的详细解析。
第七章包含两套数量推理模拟测试题，并附有答案解析。通过进行模拟训练，并对照答案进行评估，考生可以找到学习中的不足，并将这些不足作为未来复习的重点。
附录部分列出了一系列数学常识，如简分数及其对应小数、常见无理数平方根及其对应小数、不等式和代数式等，建议考生铭记于心。
Choose the Study Plan that is Right for You
不管对自己的数学水平是否有信心，制订复习计划都是非常重要的，这个复习计划应该可以帮你充分利用学习时间，并能满足你的个人需求。
如果你对自己的数学能力有信心，则可以：
√ 阅读第一、二章，重点关注其中提到的解题策略。这些策略能提高你的答题速度，并帮助你处理那些无法很快知道如何求解的问题。
√ 阅读第三到六章，重点关注每章出现的“TIPS”，以及更具难度的例题。做完所有的GRE习题，遇到不熟悉的考点就回过头复习相应章节中的知识点。
√ 阅读附录部分，并将你尚未记住的数学常识铭记于心。
√ 利用第七章的模拟题进行模拟练习，并对照答案核对每道题。标记那些没有顺利求解的问题，并带着问题复习书中相应的章节。
如果你对自己的数学能力没有信心，那么：
√ 阅读第一章，熟悉GRE数学的考试题型。
√ 阅读第三到六章，重点关注其中的基本技巧和例题。使用基础习题进行练习，碰到问题就复习相应的章节。
√ 阅读第二章，重点关注其中提到的解题策略。这些策略能提高你的答题速度，并帮助你处理那些无法很快知道如何求解的问题。
√ 重读第三到六章，重点关注每章中的提到的“TIPS”和更具难度的问题。仔细解答每道GRE习题。
√ 阅读附录部分，将你尚未记住的数学常识铭记于心。
√ 利用第七章的模拟题进行模拟练习，并对照答案核对每道题。标记那些你没有顺利求解的问题，并带着问题复习书中相应的章节。

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