Master the AP Calculus AB and BC Test

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You've worked hard all year long in your AP course, and you deserve the most comprehensive and well-regarded test-preparation guide available. Written by an experienced AP teacher, Master the AP Calculus AB & BC Test is filled with invaluable subject review, expert test-taking techniques, and practice questions just like the actual test questions. You'll learn to relax and earn the high scores you need for early college credit.
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Overview

You've worked hard all year long in your AP course, and you deserve the most comprehensive and well-regarded test-preparation guide available. Written by an experienced AP teacher, Master the AP Calculus AB & BC Test is filled with invaluable subject review, expert test-taking techniques, and practice questions just like the actual test questions. You'll learn to relax and earn the high scores you need for early college credit.
Read More Show Less

Product Details

  • ISBN-13: 9780768909890
  • Publisher: Peterson's
  • Publication date: 11/25/2002
  • Series: Master the AP Ser.
  • Edition description: 3RD
  • Edition number: 3
  • Pages: 661
  • Product dimensions: 8.30 (w) x 10.80 (h) x 1.70 (d)

Table of Contents

Part 11
Introduction: How to Use this Book 3
The Chess Dilemma 3
Understanding Versus Mastering: Calculus Reform 4
What Makes This Book Different 4
The Game Pieces 5
Conclusion 6
AP Calculus Formulas 7
Chapter 1 Digging In 9
Frequently Asked Questions About the AP Calculus Test 9
Part 215
Chapter 2 Calculus Prerequisites 17
Functions and Relations 17
Function Properties 25
Inverse Functions 29
Transforming Functions: Hands-on Activity 2.1 34
Trigonometry 41
Parametric Equations (BC Topic only) 50
Polar Equations (BC Topic Only) 55
Vectors and Vector Equations (BC Topic Only) 61
Technology: Solving Equations with a Graphing Calculator 66
Practice Problems 67
Solutions 68
Chapter 3 Limits and Continuity 71
What is a Limit?: Hands on Activity 3.1 71
Evaluating Limits Analytically 77
Continuity 81
The Extreme Value Theorem: Hands-on Activity 3.2 87
The Intermediate Value Theorem: Hands-on Activity 3.3 91
Limits Involving Infinity 96
Special Limits 101
Technology: Evaluating Limits with a Graphing Calculator 105
Practice Problems 108
Solutions 110
Chapter 4 Differentiating 115
Derivative as a Rate of Change 115
The Power Rule 120
Derivatives to Memorize 124
The Chain Rule 129
The Product Rule 133
The Quotient Rule 136
A Word about Respecting Variables 139
Implicit Differentiation 141
Hands-on Activity 4.1: Approximating Derivatives 147
Technology: Finding Numerical Derivatives with the Graphing Calculator 150
Practice Problems 152
Solutions 154
Chapter 5 Advanced Topics in Differentiation 159
The Derivative of an Inverse Function 159
Hands-on Activity 5.1: Linear Approximations 163
L'Hopital's Rule (BC Topic Only) 167
Parametric Derivatives (BC Topic Only) 171
Polar Derivatives (BC Topic Only) 177
Technology: Finding Polar and Parametric Derivatives with Your Calculator (BC Topic Only) 182
Practice Problems 184
Solutions 185
Chapter 6 Applications of the Derivative 191
Related Rates 191
Hands-on Activity 6.1: Rolle's and Mean Value Theorems 199
Hands-on Activity 6.2: The First Derivative Test 205
Concavity 212
Motion 217
Motion in the Plane (BC Topic Only) 222
Optimization 225
Technology: Modeling a Particle's Movement with a Graphing Calculator 233
Practice Problems 235
Solutions 238
Chapter 7 Integration 245
Basic Antiderivatives 245
Hands-on Activity 7.1: Approximating Area with Riemann Sums 253
The Trapezoidal Rule 260
The Fundamental Theorem of Calculus 265
Hands-on Activity 7.2: Accumulation Functions 276
The Mean Value Theorem for Integration, Average Value of a Function 282
U-Substitution 287
Integrating Inverse Trigonometric Functions 297
Technology: Evaluating Definite Integrals with Your Graphing Calculator 301
Practice Problems 303
Solutions 304
Chapter 8 Advanced Methods of Integration 311
Miscellaneous Methods of Integration 311
Parts (BC Topic Only) 317
Powers of Trigonometric Functions (BC Topic Only) 322
Partial Fractions (BC Topic Only) 327
Improper Integrals (BC Topic Only) 331
Technology: Drawing Derivative and Integral Graphs with Your Calculator 338
Practice Problems 341
Solutions 342
Chapter 9 Applications of Integration 347
Hands-on Activity 9.1: Area Between Curves 347
The Disk and Washer Methods 356
The Shell Method 364
Finding the Volume of Regions with Known Cross Sections 371
Arc Length (BC Topic Only) 377
Polar Area (BC Topic Only) 381
Technology: Using Your Calculator Efficiently 388
Practice Problems 390
Solutions 390
Chapter 10 Differential Equations 399
Hands-on Activity 10.1: Separation of Variables 399
Hands-on Activity 10.2: Slope Fields 406
Euler's Method (BC Topic Only) 413
Exponential Growth and Decay 420
Logistic Growth (BC Topic Only) 425
Technology: A Differential Equations Calculator Program 431
Practice Problems 435
Solutions 437
Chapter 11 Sequences and Series (BC Topics Only) 441
Introduction to Sequences and Series, Nth Term Divergence Test 441
Convergence Tests for Infinite Series 447
Power Series 466
Taylor and Maclaurin Series 474
Technology: Viewing and Calculating Sequences and Series with a Graphing Calculator 482
Practice Problems 485
Solutions 486
Part 3 Practice AP Exams 491
Chapter 12 First Model AP Calculus AB Exam 495
Section I Part A 495
Section I Part B 506
Section II Part A 512
Section II Part B 514
Answer Key 516
Solutions 517
Chapter 13 Second Model AP Calculus AB Exam 539
Section I Part A 539
Section I Part B 549
Section II Part A 555
Section II Part B 557
Answer Key 559
Solutions 560
Chapter 14 First Model AP Calculus BC Exam 587
Section I Part A 587
Section I Part B 597
Section II Part A 603
Section II Part B 605
Answer Key 607
Solutions 608
Chapter 15 Second Model AP Calculus BC Exam 627
Section I Part A 627
Section I Part B 637
Section II Part A 642
Section II Part B 644
Answer Key 646
Solutions 647
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