Cracking the AP Calculus AB and BC Exams, 2006-2007 Edition

by PRINCETON REVIEW

• ISBN13: 9780375765261
• ISBN10: 0375765263
• Format: Trade Paper
• Copyright: 2006-01-10
• Publisher: Princeton Review

Summary

The Princeton Review realizes that scoring high on the AP Calculus AB & BC Exams is very different from earning straight A's in school. We don't try to teach you everything there is to know about calculusonly the strategies and information you'll need to get your highest score. In Cracking the AP Calculus AB & BC Exams, we'll teach you how to Use our preparation strategies and test-taking techniques to raise your score Focus on the topics most likely to appear on the test Test your knowledge with review questions for each calculus topic covered This book includes 5 full-length practice AP Calculus AB & BC tests: 3 for AB and 2 for BC. All of our practice questions are just like those you'll see on the actual exam, and we explain how to answer every question.

Table of Contents

Introduction	p. xi
Limits	p. 1
What Is a Limit?	p. 1
Limits of Trigonometric Functions	p. 6
Practice Problem Set 1	p. 10
Continuity	p. 13
The Definition of Continuity	p. 14
Types of Discontinuities	p. 16
Practice Problem Set 2	p. 21
The Definition of the Derivative	p. 23
Deriving the Formula	p. 23
The Slope of a Curve	p. 25
The Secant and the Tangent	p. 25
Differentiability	p. 28
Practice Problem Set 3	p. 31
Basic Differentiation	p. 33
Notation	p. 33
The Power Rule	p. 34
The Addition Rule	p. 36
Higher Order Derivatives	p. 37
Practice Problem Set 4	p. 38
The Product Rule	p. 39
The Quotient Rule	p. 41
The Chain Rule	p. 42
Practice Problem Set 5	p. 47
Derivatives of Trig Functions	p. 48
Practice Problem Set 6	p. 52
Implicit Differentiation	p. 55
How to Do It	p. 55
Second Derivatives	p. 61
Practice Problem Set 7	p. 65
Basic Applications of the Derivative	p. 67
Equations of Tangent Lines and Normal Lines	p. 67
Practice Problem Set 8	p. 73
The Mean Value Theorem for Derivatives	p. 74
Rolle's Theorem	p. 76
Practice Problem Set 9	p. 78
Maxima and Minima	p. 79
Applied Maxima and Minima Problems	p. 79
Practice Problem Set 10	p. 90
Curve Sketching	p. 91
Practice Problem Set 11	p. 104
Motion	p. 105
Related Rates	p. 105
Practice Problem Set 12	p. 110
Position, Velocity, and Acceleration	p. 111
Practice Problem Set 13	p. 115
Exponential and Logarithmic Functions, Part One	p. 117
The Derivative of In x	p. 118
The Derivative of e[superscript x]	p. 119
The Derivative of log[subscript a]x	p. 119
The Derivative of a[superscript x]	p. 120
Practice Problem Set 14	p. 124
Other Topics in Differential Calculus	p. 125
The Derivative of an Inverse Function	p. 125
Practice Problem Set 15	p. 128
Derivatives of Parametric Functions	p. 129
Practice Problem Set 16	p. 133
L'Hopital's Rule	p. 134
Practice Problem Set 17	p. 138
Differentials	p. 138
Practice Problem Set 18	p. 141
Logarithmic Differentiation	p. 142
Practice Problem Set 19	p. 147
The Integral	p. 149
The Antiderivative	p. 149
Integrals of Trig Functions	p. 151
Addition and Subtraction	p. 152
Practice Problem Set 20	p. 156
U-Substitution	p. 157
Practice Problem Set 21	p. 162
Definite Integrals	p. 163
Area Under a Curve	p. 163
The Fundamental Theorem of Calculus	p. 170
The Trapezoid Rule	p. 171
Practice Problem Set 22	p. 177
The Mean Value Theorem for Integrals	p. 177
The Second Fundamental Theorem of Calculus	p. 179
Practice Problem Set 23	p. 181
Exponential and Logarithmic Functions, Part Two	p. 183
More Integrals of Trig Functions	p. 184
Integrating e[superscript x] and a[superscript x]	p. 186
Practice Problem Set 24	p. 190
The Area Between Two Curves	p. 191
Vertical Slices	p. 192
Horizontal Slices	p. 195
Practice Problem Set 25	p. 200
The Volume of a Solid of Revolution	p. 201
Washers and Disks	p. 202
Cylindrical Shells	p. 207
Volumes of Solids with Known Cross-Sections	p. 211
Practice Problem Set 26	p. 218
Integration By Parts	p. 219
The Formula	p. 219
Practice Problem Set 27	p. 224
Trig Functions	p. 225
Inverse Trig Functions	p. 225
Practice Problem Set 28	p. 231
Advanced Integrals of Trig Functions	p. 232
Practice Problem Set 29	p. 238
Other Applications of the Integral	p. 239
Length of a Curve	p. 239
Parametric Functions	p. 241
Practice Problem Set 30	p. 243
The Method of Partial Fractions	p. 244
Practice Problem Set 31	p. 249
Improper Integrals	p. 250
Practice Problem Set 32	p. 254
Calculus of Polar Curves	p. 255
Practice Problem Set 33	p. 259
Differential Equations	p. 261
Separation of Variables	p. 261
Euler's Method	p. 266
Slope Fields	p. 272
Practice Problem Set 34	p. 275
Infinite Series	p. 277
Sequences and Series	p. 277
Geometric Series	p. 279
The Ratio Test	p. 281
Alternating Series	p. 282
Integral Test	p. 283
Comparison Test	p. 284
Power Series	p. 285
Taylor Series and Polynomials	p. 286
Practice Problem Set 35	p. 290
Answers to Practice Problem Sets	p. 291
The Princeton Review AP Calculus AB Practice Test 1	p. 307
Answers and Explanations to AB Practice Test 1	p. 331
The Princeton Review AP Calculus AB Practice Test 2	p. 369
Answers and Explanations to AB Practice Test 2	p. 395
The Princeton Review AP Calculus AB Practice Test 3	p. 429
Answers and Explanations to AB Practice Test 3	p. 459
The Princeton Review AP Calculus BC Practice Test 1	p. 497
Answers and Explanations to BC Practice Test 1	p. 523
The Princeton Review AP Calculus BC Practice Test 2	p. 567
Answers and Explanations to BC Practice Test 2	p. 599
Appendix	p. 639
Derivatives and Integrals That You Should Know	p. 640
Prerequisite Mathematics	p. 641
Table of Contents provided by Ingram. All Rights Reserved.