描述
开 本: 16开纸 张: 胶版纸包 装: 平装-胶订是否套装: 否国际标准书号ISBN: 9787560562018
越来越多的高中生选择出国攻读大学课程，参加AP考试并取得优异的成绩不仅可以提高大学申请成功率，还可以在一定程度上减免昂贵的大学学费。
本系列AP考试丛书引进自美国知名教育出版公司McGraw-Hill Education，由AP考试相关领域专家编写，是美国本土大学课堂使用教材，可以帮助考生提前适应全英学习模式。此系列中，AP各学科分册紧扣考试命题特点，以“五步”方案为学习框架，囊括与考试相关的学科要点。同时，还精选针对性练习以及全真模拟试题，配以准确答案和详尽解析，利于考生巩固所学。此外，考生还可在App Store中搜索“AP Planner”免费下载App，量身定制个性化学习日程。
《AP微积分AB 5分制胜》共分5步，帮助考生了解AP考试以及自身水平，培养考试技巧，复习重点难点，建立应考信心。
全书详细介绍了AP考试特点，并提供了三种不同的备考方案，方便考生根据自身情况制定复习计划。诊断测试附有详细答案和解析，方便考生查缺补漏。此外，还为各种类型的考题提供了应试技巧，让考生备考事半功倍。考点复习部分共有十章，涵盖所有AP微积分AB考点，每章包括微积分概念释义以及详细例题解析，考生复习可做到有的放矢。书后配有三套模拟测试，方便考生考前练习。
与微积分BC不同的是，本书包括了进行微积分学习之前的复习章节，能够让学生们在进入微积分学习前夯实基础，考生可以根据自己的需求，选择微积分AB或者微积分BC备考。
STEP 1 Set Up Your Study Plan
1 What You Need to Know About the AP
Calculus AB Exam 3
1.1 What Is Covered on the AP Calculus
Exam? 4
1.2 What Is the Format of the AP Calculus
AB Exam? 4
1.3 What Are the Advanced Placement Exam
Grades? 5
How Is the AP Calculus AB Exam Grade Calculated? 5
1.4 Which Graphing Calculators Are Allowed
for the Exam? 6
Calculators and Other Devices Not Allowed for the AP Calculus AB
Exam 7
Other Restrictions on Calculators 7
2 How to Plan Your Time 8
2.1 Three Approaches to Preparing for the
AP Calculus AB Exam 8
Overview of the Three Plans 8
2.2 Calendar for Each Plan 10
Summary of the Three Study Plans 13
STEP 2 Determine Your Test Readiness
3 Take a Diagnostic Exam 17
3.1 Getting Started! 20
3.2 Diagnostic Test 20
3.3 Answers to Diagnostic Test 26
3.4 Solutions to Diagnostic Test 27
3.5 Calculate Your Score 35
Short-Answer Questions 35
AP Calculus AB Diagnostic Exam 35
STEP 3 Develop Strategies for Success
4 How to Approach Each Question Type 39
4.1 The Multiple-Choice Questions 40
4.2 The Free-Response Questions 40
4.3 Using a Graphing Calculator 41
4.4 Taking the Exam 42
What Do I Need to Bring to the Exam? 42
Tips for Taking the Exam 43
STEP 4 Review the Knowledge You Need to
Score High
5 Review of Precalculus 47
5.1 Lines 48
Slope of a Line 48
Equations of a Line 48
Parallel and Perpendicular Lines 49
5.2 Absolute Values and Inequalities 52
Absolute Values 52
Inequalities and the Real Number Line 53
Solving Absolute Value Inequalities 54
Solving Polynomial Inequalities 55
Solving Rational Inequalities 57
5.3 Functions 59
Definition of a Function 59
Operations on Functions 60
Inverse Functions 62
Trigonometric and Inverse Trigonometric Functions 65
Exponential and Logarithmic Functions 68
5.4 Graphs of Functions 72
Increasing and Decreasing Functions 72
Intercepts and Zeros 74
Odd and Even Functions 75
Shifting, Reflecting, and Stretching Graphs 77
5.5 Rapid Review 80
5.6 Practice Problems 81
5.7 Cumulative Review Problems 82
5.8 Solutions to Practice Problems 82
5.9 Solutions to Cumulative Review Problems
85
6 Limits and Continuity 86
6.1 The Limit of a Function 87
Definition and Properties of Limits 87
Evaluating Limits 87
One-Sided Limits 89
Squeeze Theorem 92
6.2 Limits Involving Infinities 94
Infinite Limits (as x → a) 94
Limits at Infinity (as x → ±∞) 96
Horizontal and Vertical Asymptotes 98
6.3 Continuity of a Function 101
Continuity of a Function at a Number 101
Continuity of a Function over an Interval 101
Theorems on Continuity 101
6.4 Rapid Review 104
6.5 Practice Problems 105
6.6 Cumulative Review Problems 106
6.7 Solutions to Practice Problems 107
6.8 Solutions to Cumulative Review Problems
109
7 Differentiation 111
7.1 Derivatives of Algebraic Functions 112
Definition of the Derivative of a Function 112
Power Rule 115
The Sum, Difference, Product, and Quotient Rules 116
The Chain Rule 117
7.2 Derivatives of Trigonometric, Inverse
Trigonometric,
Exponential, and Logarithmic Functions 118
Derivatives of Trigonometric Functions 118
Derivatives of Inverse Trigonometric Functions 120
Derivatives of Exponential and Logarithmic Functions 121
7.3 Implicit Differentiation 123
Procedure for Implicit Differentiation 123
7.4 Approximating a Derivative 126
7.5 Derivatives of Inverse Functions 128
7.6 Higher Order Derivatives 130
7.7 Rapid Review 131
7.8 Practice Problems 132
7.9 Cumulative Review Problems 132
7.10 Solutions to Practice Problems 133
7.11 Solutions to Cumulative Review
Problems 136
8 Graphs of Functions and Derivatives 138
8.1 Rolle’s Theorem, Mean Value Theorem,
and Extreme Value Theorem 138
Rolle’s Theorem 139
Mean Value Theorem 139
Extreme Value Theorem 142
8.2 Determining the Behavior of Functions
143
Test for Increasing and Decreasing Functions 143
First Derivative Test and Second Derivative Test for Relative
Extrema 146
Test for Concavity and Points of Inflection 149
8.3 Sketching the Graphs of Functions 155
Graphing without Calculators 155
Graphing with Calculators 156
8.4 Graphs of Derivatives 158
8.5 Rapid Review 163
8.6 Practice Problems 165
8.7 Cumulative Review Problems 168
8.8 Solutions to Practice Problems 168
8.9 Solutions to Cumulative Review Problems
175
9 Applications of Derivatives 177
9.1 Related Rate 177
General Procedure for Solving Related Rate Problems 177
Common Related Rate Problems 178
Inverted Cone (Water Tank) Problem 179
Shadow Problem 180
Angle of Elevation Problem 181
9.2 Applied Maximum and Minimum Problems
183
General Procedure for Solving Applied Maximum and Minimum Problems
183
Distance Problem 183
Area and Volume Problems 184
Business Problems 187
9.3 Rapid Review 188
9.4 Practice Problems 189
9.5 Cumulative Review Problems 191
9.6 Solutions to Practice Problems 192
9.7 Solutions to Cumulative Review Problems
199
10 More Applications of Derivatives 202
10.1 Tangent and Normal Lines 202
Tangent Lines 202
Normal Lines 208
10.2 Linear Approximations 211
Tangent Line Approximation (or Linear Approximation) 211
Estimating the nth Root of a Number 213
Estimating the Value of a Trigonometric Function of an Angle 213
10.3 Motion Along a Line 214
Instantaneous Velocity and Acceleration 214
Vertical Motion 216
Horizontal Motion 216
10.4 Rapid Review 218
10.5 Practice Problems 219
10.6 Cumulative Review Problems 220
10.7 Solutions to Practice Problems 221
10.8 Solutions to Cumulative Review
Problems 225
11 Integration 227
11.1 Evaluating Basic Integrals 228
Antiderivatives and Integration Formulas 228
Evaluating Integrals 230
11.2 Integration by U-Substitution 233
The U-Substitution Method 233
U-Substitution and Algebraic Functions 233
U-Substitution and Trigonometric Functions 235
U-Substitution and Inverse Trigonometric Functions 236
U-Substitution and Logarithmic and Exponential Functions 238
11.3 Rapid Review 241
11.4 Practice Problems 242
11.5 Cumulative Review Problems 243
11.6 Solutions to Practice Problems 244
11.7 Solutions to Cumulative Review
Problems 246
12 Definite Integrals 247
12.1 Riemann Sums and Definite Integrals
248
Sigma Notation or Summation Notation 248
Definition of a Riemann Sum 249
Definition of a Definite Integral 250
Properties of Definite Integrals 251
12.2 Fundamental Theorems of Calculus 253
First Fundamental Theorem of Calculus 253
Second Fundamental Theorem of Calculus 254
12.3 Evaluating Definite Integrals 257
Definite Integrals Involving Algebraic Functions 257
Definite Integrals Involving Absolute Value 258
Definite Integrals Involving Trigonometric, Logarithmic,
and Exponential Functions 259
Definite Integrals Involving Odd and Even Functions 261
12.4 Rapid Review 262
12.5 Practice Problems 263
12.6 Cumulative Review Problems 264
12.7 Solutions to Practice Problems 265
12.8 Solutions to Cumulative Review
Problems 268
13 Areas and Volumes 270
13.1 The Function F(x) =fxaf (t)dt 271
13.2 Approximating the Area Under a Curve
275
Rectangular Approximations 275
Trapezoidal Approximations 279
13.3 Area and Definite Integrals 280
Area Under a Curve 280
Area Between Two Curves 285
13.4 Volumes and Definite Integrals 289
Solids with Known Cross Sections 289
The Disc Method 293
The Washer Method 298
13.5 Rapid Review 301
13.6 Practice Problems 303
13.7 Cumulative Review Problems 305
13.8 Solutions to Practice Problems 305
13.9 Solutions to Cumulative Review
Problems 312
14 More Applications of Definite Integrals
315
14.1 Average Value of a Function 316
Mean Value Theorem for Integrals 316
Average Value of a Function on [a, b] 317
14.2 Distance Traveled Problems 319
14.3 Definite Integral as Accumulated Change
322
Business Problems 322
Temperature Problem 323
Leakage Problems 324
Growth Problem 324
14.4 Differential Equations 325
Exponential Growth/Decay Problems 325
Separable Differential Equations 327
14.5 Slope Fields 330
14.6 Rapid Review 334
14.7 Practice Problems 335
14.8 Cumulative Review Problems 337
14.9 Solutions to Practice Problems 338
14.10 Solutions to Cumulative Review
Problems 342
STEP 5 Build Your Test-Taking Confidence
AP Calculus AB Practice Exam 1 347
AP Calculus AB Practice Exam 2 373
AP Calculus AB Practice Exam 3 401
Appendix 427
Bibliography and Websites 431
AP项目（Advanced Placement Program）始于1955年，由美国大学理事会（the College Board）主持，是在高中阶段开设的具有大学水平的课程，即大学预修课程。AP项目目前设有34门课程和考试，它可以使有余力、有能力、成绩优秀的高中生有机会先修部分美国大学基础课程以获得大学学分，因此吸引了很多成绩优秀的学生选修。目前，已有60多个国家的几千所大学把AP学分作为其入学参考标准，其中包括哈佛大学、耶鲁大学、牛津大学、剑桥大学等世界知名大学。
美国每年约有200万高中毕业生，他们都要参加美国高考SAT和AP课程的考试。美国高中生会在11年级时完成SAT考试，在12年级（高中后一年）完成两件大事：，根据SAT的考试成绩申请大学和奖学金；第二，选修AP课程，并进行备考。在高中选修AP课程和通过AP考试不仅是对学生能力和学业水平的证明，还可以使学生：1.
在申请大学时具有很大的优势。美国大学把学生在AP考试中的表现作为衡量其是否能够顺利完成大学学业的依据。从美国大学录取顾问委员会公布的影响大学录取因素的比较分析可以看出，AP成绩以80.3%的影响力位居，因为它向学校充分展示了学生的才智、专长及学习能力。2.
进入大学后，可以获得大学学分，免修同类课程，提早选修更高级的课程或跳级。3. 提前毕业。4. 节省大学学费。在美国，初等教育是免费的，但高等教育是收费的。选修的AP课程越多，免修的大学课程也就越多，节省的学费也就越多。另外，对中国学生而言，除了可以获得美国大学学分、省时省钱外，还可以在国内提前适应美国大学课程。
AP考试成绩的评定为5分制，满分5分表示极为优秀，4分为优秀，3分相当于合格，即可为大多数学校所接受，2分为可能有资格，1分则不予推荐。 AP考试在每年5月份举行一次，为期两周。每门课程的考试时间约为2～3个小时，考试费用为每科1100元人民币或者1790港币左右。
更多信息可查询以下网站：
AP考试官网：http://www.collegeboard.com
AP国内报名网站：http://apchina.net.cn
香港考务局报名网址：https://www2.hkeaa.edu.hk
为满足国内考生对AP考试资料日益增长的需求，我们从美国知名教育出版公司McGraw-Hill Education引进了本系列AP考试丛书，共包括7本，分别为《AP微观经济学5分制胜》、《AP宏观经济学5分制胜》、《AP微积分AB
5分制胜》、《AP微积分BC 5分制胜》、《AP美国历史5分制胜》、《AP化学5分制胜》和《AP生物5分制胜》。AP各学科分册由AP考试相关领域专家编写，精准把握考试命题特点，设计“五步”高效学习方案，总结与考试相关的学科内容和要点，精选针对性练习以及全真模拟试题，并配以答案和准确详尽的解析。本系列丛书适用于备考AP的所有考生，便于考生巩固所学，紧抓重点，取得高分。
本书为其中的《AP微积分AB 5分制胜》。
恭喜你！成为了一名AP微积分考生。众所周知，AP微积分是高中挑战性的科目之一，你学习的数学概念曾经改变了世界。不久以前，微积分课程还只对大学生开放，而现在和你一样勤奋努力的考生在高中就开始了微积分学习。如果你在AP微积分AB考试中取得3分或以上的成绩，大多数大学都会给予学分。
怎样才能在AP微积分考试中取得优异成绩呢？怎样才能得到满分5分呢？其实你已经开始步了，因为你正在阅读这本书。你需要做的下一步就是确保读懂书中内容并做完全部习题。近年来，AP微积分考试发生了许多改变。例如，现在的试题不再强调冗长枯燥的代数运算，而是期望考生具备解决各种问题的能力，包括以图表或文字的形式出现的题目。对于很多题目，你都可以使用计算器来得出答案。
我们拥有多年AP微积分的教学经验，并与考生和其他教师有过很多交流，十分了解考生在AP微积分考试中会遇到的一些困难。例如，有些考生抱怨不能读懂题目的含义，也有考生说即使给出了解题方法，他们还是无法理解解题步骤。遇到这样的情况，谁能不感觉到沮丧呢？本书将为考生解决这些问题。书中的题目能附图表的都附有图表，解题方法会逐一呈现。本书从关于极限与连续的章节开始。这部分内容通常在初级微积分课程中教授。如果你对这些概念已经十分熟悉，那就可以略过这些内容，从第六章开始学习。
那么，怎样才能在AP微积分AB考试中取得满分5分呢？
步：从本书第二章中给出的三个学习计划中挑选一个适合你自己的。
第二步：利用第三章的诊断测试（Diagnostic Exam）来检测你的备考程度。
第三步：通过学习第四章提供的应试技巧，研究考试成功的策略。
第四步：通过学习第五章至第十四章的全部内容来巩固获取高分所必需的知识点。
第五步：利用本书提供的模拟测试（Practice Exams）来树立考试信心。
正如大部分AP考试专家所说的那样，“首先必须理解，然后练习。”
祝你好运！
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