Cracking the AP Calculus AB & BC, 2000-2001 Edition

by KAHN, DAVID

• ISBN13: 9780375754999
• ISBN10: 0375754997
• Additional ISBN(s): 9780375752858, 9780375762222
• Edition: 4th
• Format: Trade Paper
• Copyright: 2000-02-01
• Publisher: Princeton Review
• More Book Details
• Purchase Benefits

Summary

The Book That Gets You Results Sharpen your skills with more than 900 practice questions We Know the AP Calculus AB & BC Exams The experts at The Princeton Review study the AP Claculus exam and other standardized tests each year to make sure you get the most up-to-date, thouroughly researched books possible. We Know Students Each year we help more than two million students score high with our courses, bestselling books, and award-winning software. We Get Results Students who take our courses for the SAT, GRE, LSAT, and many other tests see score improvements that have been verified by independent accounting firms. The proven techniques we teach in our courses are in this book. And If It's on the AP Calculus Exam, It's in This Book We don't try to teach you everything there is to know about calculus--only the facts and techniques you'll need to know to score higher on the Advanced Placement exam. There's a big difference. InCracking the AP Calculus AB & BC, 2000-2001 Edition, you will learn to think like the test-makers and *Review and practice the calculus concepts that are covered on the exam *Score higher by mastering a few essential problem-solving techniques *Immediately recognize problem types and recall the techniques that are needed to solve them *Memorize important formulas so you won't have to rely on your calculator *Become a test-taking expert by practicing on the more than 900 problems in this book Practice your skills on the four full-length sample tests inside (two each for the AB and BC exams). The questions are just like the ones you'll see on the actual AP Calculus exam, and we fully explain every answer.

Table of Contents

Introduction	p. xiii
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. 46
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. 62
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 ln 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. 153
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. 178
The Mean Value Theorem for Integrals	p. 178
The Second Fundamental Theorem of Calculus	p. 180
Practice Problem Set 23	p. 182
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
Practice Problem Set 27	p. 223
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
Differential Equations	p. 255
Separation of Variables	p. 255
Euler's Method	p. 260
Slope Fields	p. 266
Practice Problem Set 33	p. 269
Infinite Series	p. 271
Sequences and Series	p. 271
Geometric Series	p. 273
The Ratio Test	p. 275
Alternating Series	p. 276
Integral Test	p. 277
Comparison Test	p. 278
Power Series	p. 279
Taylor Series and Polynomials	p. 280
Practice Problem Set 34	p. 284
Answers to Practice Problems	p. 285
The Princeton Review AP Calculus AB Diagnostic Exam 1	p. 301
Answers and Explanations to the AB Diagnostic Exam 1	p. 327
The Princeton Review AP Calculus AB Diagnostic Exam 2	p. 369
Answers and Explanations to the AB Diagnostic Exam 2	p. 395
The Princeton Review AP Calculus BC Diagnostic Exam 1	p. 429
Answers and Explanations to the BC Diagnostic Exam 1	p. 455
The Princeton Review AP Calculus BC Diagnostic Exam 2	p. 501
Answers and Explanations to the BC Diagnostic Exam 2	p. 529
Appendix	p. 565
Derivatives and Integrals That You Should Know	p. 566
Prerequisite Mathematics	p. 567
Using the TI-83 Calculator	p. 570
About the Author	p. 581
About this Book	p. 583
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