Kaplan AP Calculus AB & BC 2007

by Tamara Lefcourt Ruby; James Sellers; Lisa Korf; Van Horn Van Horn; Mike Munn

• ISBN13: 9781419550782
• ISBN10: 1419550780
• Format: Paperback
• Copyright: 2006-12-26
• Publisher: Kaplan

Summary

-Complete review of essential topics on the AP Calculus AB and BC topic outline-3 full-length practice tests (2 AB, 1 BC)-A diagnostic quiz helps students determine which topics they should spend the most time reviewing-Complete test information and resources-Kaplan's proven AP score-raising strategies-A chapter devoted to using a graphing calculator-Sample free-response questions, answers, and walk-through explanations for all key topics

Table of Contents

About the Authors	p. xi
Kaplan Panel of AP Experts	p. xiii
The Basics
Inside the AP Calculus Exam	p. 3
Introduction to the AP Calculus Exam	p. 4
Overview of the Test Structure	p. 4
How the Exam is Scored	p. 6
Registration and Fees	p. 6
Additional Resources	p. 6
Strategies for Success: It's Not Always How Much You Know	p. 7
General Test-Taking Strategies	p. 7
How This Book Can Help, Plus Specific AP Calculus Exam Strategies	p. 9
Using a Calculator on the AP Calculus Exam	p. 9
How to Approach the Multiple-Choice Questions	p. 10
How to Approach the Free-Response Questions	p. 13
Stress Management	p. 15
Countdown to the Test	p. 17
Calculator Basics	p. 19
How Much Computing Power Do You Need?	p. 19
Using Calculators with This Book	p. 21
When Can You Use Your Graphing Calculator?	p. 22
Calculator...Friend or Foe?	p. 24
Diagnostic Tests
Diagnostic Test AB	p. 29
Answers and Explanations	p. 36
Correlation Chart for Diagnostic Test AB	p. 41
Diagnostic Test BC	p. 43
Answers and Explanations	p. 52
Correlation Chart for Diagnostic Test BC	p. 60
AP Calculus Review
Graphing with a Calculator	p. 63
Using Your Calculator to Graph a Function	p. 63
Graphing More than One Function	p. 65
Graphing in Action on the AP Exam	p. 67
Review Questions	p. 72
Answers and Explanations	p. 75
Equation Solving with a Calculator	p. 79
Solving Equations by Finding the Zero of a Graph	p. 79
Solver Utility	p. 81
Equation Solving in Action on the AP Exam	p. 83
Review Questions	p. 86
Answers and Explanations	p. 89
Operations with Functions on a Calculator	p. 97
Evaluating a Function	p. 98
Evaluating a Derivative at a Point	p. 100
Computing a Definite Integral	p. 102
Other Utilities	p. 104
Function Operations in Action on the AP Exam	p. 104
Review Questions	p. 109
Answers and Explanations	p. 114
Limits	p. 121
Basic Definitions and Understanding Limits Graphically	p. 121
Evaluating Limits Computationally	p. 125
Evaluating Limits Algebraically	p. 126
Some Important Limits	p. 128
Review Questions	p. 131
Answers and Explanations	p. 134
Asymptotes	p. 137
Infinite Limits	p. 137
Vertical Asymptotes; Understanding Infinite Limits Graphically	p. 139
Limits Approaching Infinity	p. 142
Horizontal Asymptotes	p. 143
Using Asymptotes to Sketch a Graph	p. 144
Rates of Growth	p. 147
Review Questions	p. 149
Answers and Explanations	p. 155
Continuous Functions	p. 159
Continuity and Limits	p. 159
Building Continuous Functions	p. 162
Properties of Continuous Functions	p. 163
Review Questions	p. 167
Answers and Explanations	p. 172
Functions, Graphs, and Limits	p. 175
Parametric Functions	p. 175
Polar Functions	p. 177
Vector Functions	p. 180
Review Questions	p. 181
Answers and Explanations	p. 182
The Concept Of The Derivative	p. 183
A Physical Interpretation of the Derivative: Velocity	p. 183
A Geometric Interpretation: The Derivative as a Slope	p. 186
The Relationship between Differentiability and Continuity	p. 187
Review Questions	p. 189
Answers and Explanations	p. 199
Computation Of Derivatives	p. 205
Derivative of a Constant Function	p. 206
Derivative of x[superscript n]	p. 206
Derivative of [Characters not reproducible]	p. 208
Rules for Computing Derivatives	p. 208
Derivatives of Trigonometric Functions	p. 212
Chain Rule	p. 213
Exponential and Logarithmic Functions	p. 216
The Derivative of Inverse Functions	p. 218
Implicit Differentiation	p. 220
Derivatives of Parametric, Polar, and Vector Functions	p. 223
Table of Derivative Formulas	p. 224
Review Questions	p. 227
Answers and Explanations	p. 238
The Derivative At A Point	p. 243
Computing the Derivative as the Limit of the Difference Quotient	p. 243
The Derivative Function	p. 244
The Slope of a Curve at a Point	p. 247
Local Linear Approximation	p. 247
Approximating Derivative Using Tables and Graphs	p. 249
Review Questions	p. 252
Answers and Explanations	p. 257
The Derivative As A Function	p. 263
Increasing and Decreasing Behavior of f and the Sign of f'	p. 263
Critical Points and Local Extrema	p. 265
Global Extrema	p. 268
The First Derivative Test	p. 269
Corresponding Characteristics of the Graphs of f and f'	p. 271
The Mean Value Theorem	p. 273
Equations Involving Derivatives: Translating Between Verbal Descriptions and Equations Involving Derivatives	p. 274
Review Questions	p. 276
Answers and Explanations	p. 281
Second Derivatives	p. 285
Concavity and the Sign of f"	p. 285
Inflection Points	p. 289
Review Questions	p. 292
Answers and Explanations	p. 299
Applications of Derivatives	p. 305
Graphing Using Derivatives	p. 305
Optimization	p. 310
Related Rates	p. 313
Interpreting the Derivative as a Rate of Change	p. 315
Differential Equations	p. 319
Differential Equations Via Euler's Method	p. 321
L'hopital's Rule	p. 323
Review Questions	p. 327
Answers and Explanations	p. 334
Interpretation of Integrals	p. 343
Computing Distance Traveled	p. 344
Finding the Area Under a Curve	p. 345
Riemann Sums	p. 348
Introducing the Definite Integral	p. 349
Rates of Change and the Definite Integral	p. 350
Properties of the Definite Integral	p. 351
Review Questions	p. 354
Answers and Explanations	p. 358
Applications of Integrals	p. 363
Area Between Two Curves	p. 364
Area Bounded by Curves	p. 368
Volumes of Solids	p. 370
Solids of Revolution	p. 372
Accumulated Change	p. 375
Distance Traveled by a Particle Along a Line	p. 378
Average Value of a Function	p. 378
Review Questions	p. 380
Answers and Explanations	p. 384
Antiderivatives-The Indefinite Integral	p. 389
What is an Antiderivative?	p. 389
The Indefinite Integral	p. 390
Properties of the Antiderivative	p. 391
Review Questions	p. 392
Answers and Explanations	p. 395
The Fundamental Theorem of Calculus	p. 397
The Fundamental Theorem of Calculus (FTC)	p. 397
What's So Fundamental? The Connection Between Integrals and Derivatives	p. 400
Interpreting the Fundamental Theorems Graphically	p. 402
Review Questions	p. 404
Answers and Explanations	p. 407
Techniques of Antidifferentiation	p. 411
Finding Antiderivatives	p. 411
Computing Antiderivatives Directly	p. 413
When F is Complicated: The Substitution Game	p. 414
Integration by Parts	p. 419
Antiderivatives by Simple Partial Fractions	p. 422
Antiderivatives by Improper Integrals	p. 423
Review Questions	p. 426
Answers and Explanations	p. 430
Applications of Antidifferentiation	p. 437
Initial Conditions-What is C?	p. 437
Accumulation Functions and Antiderivatives	p. 438
Differential Equations	p. 439
Separable Differential Equations	p. 440
Solving Logistic Differential Equations and Using Them in Modeling	p. 443
Review Questions	p. 445
Answers and Explanations	p. 448
Numerical Approximations	p. 453
Approximating Area Under the Curve Using Riemann Sums	p. 454
Trapezoidal Approximation	p. 457
Approximating the Area Under Functions Given Graphically or Numerically	p. 458
Review Questions	p. 460
Answers and Explanations	p. 64
The Concept of Series	p. 469
The Concept of Series	p. 469
From Sequences to Series Via Partial Sums	p. 471
To Converge or Not to Converge	p. 472
Review Questions	p. 474
Answers and Explanations	p. 478
The Properties of Series	p. 481
The Geometric Series, [Characters not reproducible], with Applications	p. 481
The Harmonic Series, [Characters not reproducible]	p. 483
The Integral Test and The Convergence of P-Series, [Characters not reproducible]	p. 484
Comparing Series to Test for Convergence or Divergence	p. 487
Alternating Series with Error Bound	p. 488
Absolutely Convergent Series	p. 491
The Ratio Test for Convergence and Divergence	p. 491
Review Questions	p. 494
Answers and Explanations	p. 498
Taylor Series	p. 501
From Series to Power Series	p. 501
Taylor Polynomial Approximation	p. 504
Maclaurin Series for Special Functions	p. 507
Shortcuts Using Taylor/Maclaurin Series	p. 508
Functions Defined by Power Series	p. 510
How Close is Close Enough? The Lagrange Error Bound	p. 511
Review Questions	p. 515
Answers and Explanations	p. 520
Practice Tests
How to Take the Practice Tests	p. 526
How to Compute Your Score	p. 527
	p. 529
Answer Key	p. 546
Answers and Explanations	p. 547
	p. 563
Answer Key	p. 578
Answers and Explanations	p. 579
Practice Test 3 BC	p. 597
Answer Key	p. 611
Answers and Explanations	p. 612
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