ARCO Master the AP Calculus AB and BC Test

( 1 )


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. It begs the question: "For the love of humanity, why?" The answer is easy. None of the books on the market offered what I needed as an AP Calculus teacher.

Some of those books are incredibly ...

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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. It begs the question: "For the love of humanity, why?" The answer is easy. None of the books on the market offered what I needed as an AP Calculus teacher.

Some of those books are incredibly rigorous and way too difficult for the average student to understand. Furthermore, the answers they offer to their exercises are often as illuminating as "(C) hint: divide." Other books are very readable, but there is no variety in the problems, so they don't really reflect just how amazingly difficult some AP Test problems really are. Some of the books didn't even include any Free Response questions in their practice exams, and they make up half of the test! All of the books shared one common trait, though: they're not really very funny. If I have learned one thing as a public school teacher, it's that learning is much more entertaining with humor.

And then there was light.

Master the AP Calculus AB and BC Tests" offers everything you could ever want (short of money tucked between the pages):

  • In-depth explanations of everything on the AP Test, written so that you can actually understand every step of each solution—the book teaches you how to do all of the math
  • A wide variety of problems that mirror the problem types asked on the AP test
  • Hands-on activities which allow you to discover the simpler topics on your own—less memorizing and more understanding
  • Extremely detailed answers to EVERY SINGLE problem in the textbook from the easiest example to the hardest AP sample problem
  • Four complete sample AP tests—two AB and two BC tests, plus the sample tests contain outstanding practice Free Response questions designed with past AP tests in mind
  • Technology sections in every chapter which teach you how to use your TI-83 or TI-83+ calculator (the most popular by far at the current time) on the AP test, including step-by-step directions
  • (Believe it or not) humor! Look at the following sample problem from the related rates section

During a Circus of the Stars presentation, Angela Lansbury displays her athletic prowess by skydiving out of a hovering helicopter 100 feet away from a cliff. However, the chutes unfortunately fail, and the proud actress plummets to certain disaster (Tragedy, She Wrote). If her position, in feet, is given by s(t), find the rate of change of her angle of depression (no pun intended). *Note: A fall from a helicopter that high in the sky is not only dangerous but nearly impossible. It should only be attempted by a trained professional or someone REALLY famous.

This book contains everything you need to not only pass the AP test, but also everything you need to understand calculus, whether you are in high school or even college.

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Product Details

  • ISBN-13: 9780764561818
  • Publisher: Peterson's
  • Publication date: 1/28/2001
  • Series: ARCO Master the AP Series
  • Pages: 608
  • Product dimensions: 8.52 (w) x 10.91 (h) x 1.43 (d)

Table of Contents

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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  • Anonymous

    Posted April 28, 2001

    The Absolute, Without a Doubt, Best Prep for the AP Calc Exam

    I am an AP Calc teacher who has searched for an extraordinary resource to help prepare my students for the exam. This is it!! My students have found Mr. Kelley's explanations to be clear, concise, and easy to follow. The Hands On Activities have been very successful with my students in explaining a concept in the simplest of terms. A huge bonus to both my students and me is the fabulous humor that is interjected in the explanations and text. Mr. Kelley definitely knows his calculus and knows how to write to appeal to students! If you can only purchase one book, this must be THE ONE!!!

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