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

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  • Format: Trade Paper
  • Copyright: 1/10/2006
  • Publisher: Princeton Review
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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

Introductionp. xi
Limitsp. 1
What Is a Limit?p. 1
Limits of Trigonometric Functionsp. 6
Practice Problem Set 1p. 10
Continuityp. 13
The Definition of Continuityp. 14
Types of Discontinuitiesp. 16
Practice Problem Set 2p. 21
The Definition of the Derivativep. 23
Deriving the Formulap. 23
The Slope of a Curvep. 25
The Secant and the Tangentp. 25
Differentiabilityp. 28
Practice Problem Set 3p. 31
Basic Differentiationp. 33
Notationp. 33
The Power Rulep. 34
The Addition Rulep. 36
Higher Order Derivativesp. 37
Practice Problem Set 4p. 38
The Product Rulep. 39
The Quotient Rulep. 41
The Chain Rulep. 42
Practice Problem Set 5p. 47
Derivatives of Trig Functionsp. 48
Practice Problem Set 6p. 52
Implicit Differentiationp. 55
How to Do Itp. 55
Second Derivativesp. 61
Practice Problem Set 7p. 65
Basic Applications of the Derivativep. 67
Equations of Tangent Lines and Normal Linesp. 67
Practice Problem Set 8p. 73
The Mean Value Theorem for Derivativesp. 74
Rolle's Theoremp. 76
Practice Problem Set 9p. 78
Maxima and Minimap. 79
Applied Maxima and Minima Problemsp. 79
Practice Problem Set 10p. 90
Curve Sketchingp. 91
Practice Problem Set 11p. 104
Motionp. 105
Related Ratesp. 105
Practice Problem Set 12p. 110
Position, Velocity, and Accelerationp. 111
Practice Problem Set 13p. 115
Exponential and Logarithmic Functions, Part Onep. 117
The Derivative of In xp. 118
The Derivative of e[superscript x]p. 119
The Derivative of log[subscript a]xp. 119
The Derivative of a[superscript x]p. 120
Practice Problem Set 14p. 124
Other Topics in Differential Calculusp. 125
The Derivative of an Inverse Functionp. 125
Practice Problem Set 15p. 128
Derivatives of Parametric Functionsp. 129
Practice Problem Set 16p. 133
L'Hopital's Rulep. 134
Practice Problem Set 17p. 138
Differentialsp. 138
Practice Problem Set 18p. 141
Logarithmic Differentiationp. 142
Practice Problem Set 19p. 147
The Integralp. 149
The Antiderivativep. 149
Integrals of Trig Functionsp. 151
Addition and Subtractionp. 152
Practice Problem Set 20p. 156
U-Substitutionp. 157
Practice Problem Set 21p. 162
Definite Integralsp. 163
Area Under a Curvep. 163
The Fundamental Theorem of Calculusp. 170
The Trapezoid Rulep. 171
Practice Problem Set 22p. 177
The Mean Value Theorem for Integralsp. 177
The Second Fundamental Theorem of Calculusp. 179
Practice Problem Set 23p. 181
Exponential and Logarithmic Functions, Part Twop. 183
More Integrals of Trig Functionsp. 184
Integrating e[superscript x] and a[superscript x]p. 186
Practice Problem Set 24p. 190
The Area Between Two Curvesp. 191
Vertical Slicesp. 192
Horizontal Slicesp. 195
Practice Problem Set 25p. 200
The Volume of a Solid of Revolutionp. 201
Washers and Disksp. 202
Cylindrical Shellsp. 207
Volumes of Solids with Known Cross-Sectionsp. 211
Practice Problem Set 26p. 218
Integration By Partsp. 219
The Formulap. 219
Practice Problem Set 27p. 224
Trig Functionsp. 225
Inverse Trig Functionsp. 225
Practice Problem Set 28p. 231
Advanced Integrals of Trig Functionsp. 232
Practice Problem Set 29p. 238
Other Applications of the Integralp. 239
Length of a Curvep. 239
Parametric Functionsp. 241
Practice Problem Set 30p. 243
The Method of Partial Fractionsp. 244
Practice Problem Set 31p. 249
Improper Integralsp. 250
Practice Problem Set 32p. 254
Calculus of Polar Curvesp. 255
Practice Problem Set 33p. 259
Differential Equationsp. 261
Separation of Variablesp. 261
Euler's Methodp. 266
Slope Fieldsp. 272
Practice Problem Set 34p. 275
Infinite Seriesp. 277
Sequences and Seriesp. 277
Geometric Seriesp. 279
The Ratio Testp. 281
Alternating Seriesp. 282
Integral Testp. 283
Comparison Testp. 284
Power Seriesp. 285
Taylor Series and Polynomialsp. 286
Practice Problem Set 35p. 290
Answers to Practice Problem Setsp. 291
The Princeton Review AP Calculus AB Practice Test 1p. 307
Answers and Explanations to AB Practice Test 1p. 331
The Princeton Review AP Calculus AB Practice Test 2p. 369
Answers and Explanations to AB Practice Test 2p. 395
The Princeton Review AP Calculus AB Practice Test 3p. 429
Answers and Explanations to AB Practice Test 3p. 459
The Princeton Review AP Calculus BC Practice Test 1p. 497
Answers and Explanations to BC Practice Test 1p. 523
The Princeton Review AP Calculus BC Practice Test 2p. 567
Answers and Explanations to BC Practice Test 2p. 599
Appendixp. 639
Derivatives and Integrals That You Should Knowp. 640
Prerequisite Mathematicsp. 641
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