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Part 11 | ||
Introduction: How to Use this Book | 2 | |
The Chess Dilemma | 2 | |
Understanding Versus Mastering: Calculus Reform | 2 | |
What Makes This Book Different | 2 | |
The Game Pieces | 4 | |
Conclusion | 5 | |
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 | 95 | |
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 | 128 | |
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 | 161 |
The Derivative of an Inverse Function | 161 | |
Hands-on Activity 5.1: Linear Approximations | 165 | |
L'Hopital's Rule (BC Topic Only) | 169 | |
Parametric Derivatives (BC Topic Only) | 173 | |
Polar Derivatives (BC Topic Only) | 178 | |
Technology: Finding Polar and Parametric Derivatives with your Calculator (BC Topic Only) | 183 | |
Practice Problems | 185 | |
Solutions | 186 | |
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) | 221 | |
Optimization | 225 | |
Technology: Modeling a Particle's Movement with a Graphing Calculator | 233 | |
Practice Problems | 235 | |
Solutions | 237 | |
Chapter 7 | Integration | 245 |
Basic Antiderivatives | 245 | |
Hands-on Activity 7.1: Approximating Area with Riemann Sums | 253 | |
The Trapezoidal Rule | 259 | |
The Fundamental Theorem of Calculus | 265 | |
Hands-on Activity 7.2: Accumulation Functions | 275 | |
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 | 302 | |
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) | 328 | |
Improper Integrals | 332 | |
Technology: Drawing Derivative and Integral Graphs with your Calculator | 339 | |
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 | 389 | |
Practice Problems | 390 | |
Solutions | 391 | |
Chapter 10 | Differential Equations | 399 |
Hands-on Activity 10.1: Separation of Variables | 399 | |
Hands-on Activity 10.2: Slope Fields (BC Topic Only) | 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 (BC Topic Only) | 431 | |
Practice Problems | 435 | |
Solutions | 436 | |
Chapter 11 | Sequences and Series (BC Topic 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 | 485 | |
Part 3491 | ||
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 | 556 | |
Section II Part B | 558 | |
Answer Key | 560 | |
Solutions | 561 | |
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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Add Master the AP Calculus AB and BC Test, There are a lot of AP Calculus books on the market. In fact, if you laid them end to end starting at your bedroom door, it'd probably be hard to make your way to the bathroom with the lights off. However, that did not stop me from writing yet another. , Master the AP Calculus AB and BC Test to the inventory that you are selling on WonderClubX
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Add Master the AP Calculus AB and BC Test, There are a lot of AP Calculus books on the market. In fact, if you laid them end to end starting at your bedroom door, it'd probably be hard to make your way to the bathroom with the lights off. However, that did not stop me from writing yet another. , Master the AP Calculus AB and BC Test to your collection on WonderClub |