Master the AP Calculus AB and BC Test Book

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