William Ma：资深AP教学与考试专家，拥有多年AP微积分教学经验，曾出版多本AP微积分教材，熟知AP考试特点，曾任纽约赫里克斯学校数学部主任。
目錄：
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 Rolles Theorem, Mean Value Theorem, and Extreme Value Theorem 138
Rolles 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 Fx =fxaf tdt 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 GrowthDecay 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
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