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Tables of Contents for Master the Ap Calculus Ab & Bc Tests 2003
Chapter/Section Title
Page #
Page Count
PART 1
1
14
Introduction: How to Use this Book
3
1
The Chess Dilemma
3
1
Understanding Versus Mastering: Calculus Reform
4
1
What Makes This Book Different
4
1
The Game Pieces
5
1
Conclusion
6
1
AP Calculus Formulas
7
2
Digging In
9
6
Frequently Asked Questions About the AP Calculus Test
9
6
PART 2
15
476
Calculus Prerequisites
17
54
Functions and Relations
17
8
Function Properties
25
4
Inverse Functions
29
5
Transforming Functions: Hands-on Activity 2.1
34
7
Trigonometry
41
9
Parametric Equations (BC Topic only)
50
5
Polar Equations (BC Topic Only)
55
6
Vectors and Vector Equations (BC Topic Only)
61
5
Technology: Solving Equations with a Graphing Calculator
66
1
Practice Problems
67
1
Solutions
68
3
Limits and Continuity
71
44
What is a Limit?: Hands on Activity 3.1
71
6
Evaluating Limits Analytically
77
4
Continuity
81
6
The Extreme Value Theorem: Hands-on Activity 3.2
87
4
The Intermediate Value Theorem: Hands-on Activity 3.3
91
5
Limits Involving Infinity
96
5
Special Limits
101
4
Technology: Evaluating Limits with a Graphing Calculator
105
3
Practice Problems
108
2
Solutions
110
5
Differentiating
115
44
Derivative as a Rate of Change
115
5
The Power Rule
120
4
Derivatives to Memorize
124
5
The Chain Rule
129
4
The Product Rule
133
3
The Quotient Rule
136
3
A Word about Respecting Variables
139
2
Implicit Differentiation
141
6
Hands-on Activity 4.1: Approximating Derivatives
147
3
Technology: Finding Numerical Derivatives with the Graphing Calculator
150
2
Practice Problems
152
2
Solutions
154
5
Advanced Topics in Differentiation
159
32
The Derivative of an Inverse Function
159
4
Hands-on Activity 5.1: Linear Approximations
163
4
L'Hopital's Rule (BC Topic Only)
167
4
Parametric Derivatives (BC Topic Only)
171
6
Polar Derivatives (BC Topic Only)
177
5
Technology: Finding Polar and Parametric Derivatives with Your Calculator (BC Topic Only)
182
2
Practice Problems
184
1
Solutions
185
6
Applications of the Derivative
191
54
Related Rates
191
8
Hands-on Activity 6.1: Rolle's and Mean Value Theorems
199
6
Hands-on Activity 6.2: The First Derivative Test
205
7
Concavity
212
5
Motion
217
5
Motion in the Plane (BC Topic Only)
222
3
Optimization
225
8
Technology: Modeling a Particle's Movement with a Graphing Calculator
233
2
Practice Problems
235
3
Solutions
238
7
Integration
245
66
Basic Antiderivatives
245
8
Hands-on Activity 7.1: Approximating Area with Riemann Sums
253
7
The Trapezoidal Rule
260
5
The Fundamental Theorem of Calculus
265
11
Hands-on Activity 7.2: Accumulation Functions
276
6
The Mean Value Theorem for Integration, Average Value of a Function
282
5
U-Substitution
287
10
Integrating Inverse Trigonometric Functions
297
4
Technology: Evaluating Definite Integrals with Your Graphing Calculator
301
2
Practice Problems
303
1
Solutions
304
7
Advanced Methods of Integration
311
36
Miscellaneous Methods of Integration
311
6
Parts (BC Topic Only)
317
5
Powers of Trigonometric Functions (BC Topic Only)
322
5
Partial Fractions (BC Topic Only)
327
4
Improper Integrals (BC Topic Only)
331
7
Technology: Drawing Derivative and Integral Graphs with Your Calculator
338
3
Practice Problems
341
1
Solutions
342
5
Applications of Integration
347
52
Hands-on Activity 9.1: Area Between Curves
347
9
The Disk and Washer Methods
356
8
The Shell Method
364
7
Finding the Volume of Regions with Known Cross Sections
371
6
Arc Length (BC Topic Only)
377
4
Polar Area (BC Topic Only)
381
7
Technology: Using Your Calculator Efficiently
388
2
Practice Problems
390
1
Solutions
390
9
Differential Equations
399
42
Hands-on Activity 10.1: Separation of Variables
399
7
Hands-on Activity 10.2: Slope Fields
406
7
Euler's Method (BC Topic Only)
413
7
Exponential Growth and Decay
420
5
Logistic Growth (BC Topic Only)
425
6
Technology: A Differential Equations Calculator Program
431
4
Practice Problems
435
2
Solutions
437
4
Sequences and Series (BC Topics Only)
441
50
Introduction to Sequences and Series, Nth Term Divergence Test
441
6
Convergence Tests for Infinite Series
447
19
Power Series
466
8
Taylor and Maclaurin Series
474
8
Technology: Viewing and Calculating Sequences and Series with a Graphing Calculator
482
3
Practice Problems
485
1
Solutions
486
5
PART 3 PRACTICE AP EXAMS
491
156
First Model AP Calculus AB Exam
495
44
Section I Part A
495
11
Section I Part B
506
6
Section II Part A
512
2
Section II Part B
514
2
Answer Key
516
1
Solutions
517
22
Second Model AP Calculus AB Exam
539
48
Section I Part A
539
10
Section I Part B
549
6
Section II Part A
555
2
Section II Part B
557
2
Answer Key
559
1
Solutions
560
27
First Model AP Calculus BC Exam
587
40
Section I Part A
587
10
Section I Part B
597
6
Section II Part A
603
2
Section II Part B
605
2
Answer Key
607
1
Solutions
608
19
Second Model AP Calculus BC Exam
627
20
Section I Part A
627
10
Section I Part B
637
5
Section II Part A
642
2
Section II Part B
644
2
Answer Key
646
1
Solutions
647