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Overview
Product Details
| ISBN-13: | 9781260122770 |
|---|---|
| Publisher: | McGraw Hill LLC |
| Publication date: | 08/06/2018 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| Pages: | 448 |
| File size: | 55 MB |
| Note: | This product may take a few minutes to download. |
About the Author
Table of Contents
Preface ix
Acknowledgmentsd xi
About the Author xiii
Introduction: The Five-Step Program xv
Step 1 Set Up Your Study Plan
1 What You Need to Know About the AP Calculus AB Exam 3
1.1 What Is Covered on the AP Calculus AB Exam? 4
1.2 What Is the Format of the AP Calculus AB Exam? 4
1.3 What Are the Advanced Placement Exam Grades? 5
How Is the AP Calculus AB Exam Grade Calculated? 5
1.4 Which Graphing Calculators Are Allowed for the Exam? 6
Calculators and Other Devices Not Allowed for the AP Calculus AB Exam 7
Other Restrictions on Calculators 7
2 How to Plan Your Time 8
2.1 Three Approaches to Preparing for the AP Calculus AB Exam 8
Overview of the Three Plans 8
2.2 Calendar for Each Plan 10
Summary of the Three Study Plans 13
Step 2 Determine Your Test Readiness
3 Take a Diagnostic Exam 17
3.1 Getting Started! 20
3.2 Diagnostic Test 20
3.3 Answers to Diagnostic Test 25
3.4 Solutions to Diagnostic Test 26
3.5 Calculate Your Score 34
Short-Answer Questions 34
AP Calculus AB Diagnostic Test 34
Step 3 Develop Strategies for Success
4 How to Approach Each Question Type 37
4.1 The Multiple-Choice Questions 38
4.2 The Free-Response Questions 38
4.3 Using a Graphing Calculator 39
4.4 Taking the Exam 40
What Do I Need to Bring to the Exam? 40
Tips for Taking the Exam 41
Step 4 Review the Knowledge You Need to Score High
5 Review of Precalculus 45
5.1 Lines 46
Slope of a Line 46
Equations of a Line 46
Parallel and Perpendicular Lines 47
5.2 Absolute Values and Inequalities 50
Absolute Values 50
Inequalities and the Real Number Line 51
Solving Absolute Value Inequalities 52
Solving Polynomial Inequalities 53
Solving Rational Inequalities 55
5.3 Functions 57
Definition of a Function 57
Operations on Functions 58
Inverse Functions 60
Trigonometric and Inverse Trigonometric Functions 63
Exponential and Logarithmic Functions 66
5.4 Graphs of Functions 70
Increasing and Decreasing Functions 70
Intercepts and Zeros 72
Odd and Even Functions 73
Shifting, Reflecting, and Stretching Graphs 75
5.5 Rapid Review 78
5.6 Practice Problems 79
5.7 Cumulative Review Problems 80
5.8 Solutions to Practice Problems 80
5.9 Solutions to Cumulative Review Problems 83
Big Idea 1: Limits
6 Limits and Continuity 84
6.1 The Limit of a Function 85
Definition and Properties of Limits 85
Evaluating Limits 85
One-Sided Limits 87
Squeeze Theorem 90
6.2 Limits Involving Infinities 92
Infinite Limits (as x → a) 92
Limits at Infinity (as x → ±∞) 94
Horizontal and Vertical Asymptotes 96
6.3 Continuity of a Function 99
Continuity of a Function at a Number 99
Continuity of a Function over an Interval 99
Theorems on Continuity 99
6.4 Rapid Review 102
6.5 Practice Problems 103
6.6 Cumulative Review Problems 104
6.7 Solutions to Practice Problems 105
6.8 Solutions to Cumulative Review Problems 107
Big Idea 2: Derivatives
7 Differentiation 109
7.1 Derivatives of Algebraic Functions 110
Definition of the Derivative of a Function 110
Power Rule 113
The Sum, Difference, Product, and Quotient Rules 114
The Chain Rule 115
7.2 Derivatives of Trigonometric, Inverse Trigonometric, Exponential, and Logarithmic Functions 116
Derivatives of Trigonometric Functions 116
Derivatives of Inverse Trigonometric Functions 118
Derivatives of Exponential and Logarithmic Functions 119
7.3 Implicit Differentiation 121
Procedure for Implicit Differentiation 121
7.4 Approximating a Derivative 124
7.5 Derivatives of Inverse Functions 126
7.6 Higher Order Derivatives 128
7.7 L'Hôpital's Rule for Indeterminate Forms 129
7.8 Rapid Review 129
7.9 Practice Problems 131
7.10 Cumulative Review Problems 132
7.11 Solutions to Practice Problems 132
7.12 Solutions to Cumulative Review Problems 135
8 Graphs of Functions and Derivatives 137
8.1 Rolle's Theorem, Mean Value Theorem, and Extreme Value Theorem 138
Rolle's Theorem 138
Mean Value Theorem 138
Extreme Value Theorem 141
8.2 Determining the Behavior of Functions 142
Test for Increasing and Decreasing Functions 142
First Derivative Test and Second Derivative Test for Relative Extrema 145
Test for Concavity and Points of Inflection 148
8.3 Sketching the Graphs of Functions 154
Graphing without Calculators 154
Graphing with Calculators 155
8.4 Graphs of Derivatives 157
8.5 Rapid Review 162
8.6 Practice Problems 164
8.7 Cumulative Review Problems 167
8.8 Solutions to Practice Problems 167
8.9 Solutions to Cumulative Review Problems 174
9 Applications of Derivatives 177
9.1 Related Rate 177
General Procedure for Solving Related Rate Problems 178
Common Related Rate Problems 178
Inverted Cone (Water Tank) Problem 179
Shadow Problem 180
Angle of Elevation Problem 181
9.2 Applied Maximum and Minimum Problems 183
General Procedure for Solving Applied Maximum and Minimum Problems 183
Distance Problem 183
Area and Volume Problems 184
Business Problems 187
9.3 Rapid Review 188
9.4 Practice Problems 189
9.5 Cumulative Review Problems 191
9.6 Solutions to Practice Problems 192
9.7 Solutions to Cumulative Review Problems 199
10 More Applications of Derivatives 202
10.1 Tangent and Normal Lines 202
Tangent Lines 202
Normal Lines 208
10.2 Linear Approximations 211
Tangent Line Approximation (or Linear Approximation) 211
Estimating the nth Root of a Number 213
Estimating the Value of a Trigonometric Function of an Angle 213
10.3 Motion Along a Line 214
Instantaneous Velocity and Acceleration 214
Vertical Motion 216
Horizontal Motion 216
10.4 Rapid Review 218
10.5 Practice Problems 219
10.6 Cumulative Review Problems 220
10.7 Solutions to Practice Problems 221
10.8 Solutions to Cumulative Review Problems 225
Big Idea 3: Integrals and the Fundamental Theorems of Calculus
11 Integration 227
11.1 Evaluating Basic Integrals 228
Antiderivatives and Integration Formulas 228
Evaluating Integrals 230
11.2 Integration by U-Substitution 233
The U-Substitution Method 233
U-Substitution and Algebraic Functions 233
U-Substitution and Trigonometric Functions 235
U-Substitution and Inverse Trigonometric Functions 236
U-Substitution and Logarithmic and Exponential Functions 238
11.3 Rapid Review 241
11.4 Practice Problems 242
11.5 Cumulative Review Problems 243
11.6 Solutions to Practice Problems 244
11.7 Solutions to Cumulative Review Problems 246
12 Definite Integrals 247
12.1 Riemann Sums and Definite Integrals 248
Sigma Notation or Summation Notation 248
Definition of a Riemann Sum 249
Definition of a Definite Integral 250
Properties of Definite Integrals 251
12.2 Fundamental Theorems of Calculus 253
First Fundamental Theorem of Calculus 253
Second Fundamental Theorem of Calculus 254
12.3 Evaluating Definite Integrals 257
Definite Integrals Involving Algebraic Functions 257
Definite Integrals Involving Absolute Value 258
Definite Integrals Involving Trigonometric, Logarithmic, and Exponential Functions 259
Definite Integrals Involving Odd and Even Functions 261
12.4 Rapid Review 262
12.5 Practice Problems 263
12.6 Cumulative Review Problems 264
12.7 Solutions to Practice Problems 265
12.8 Solutions to Cumulative Review Problems 268
13 Areas and Volumes 270
13.1 The Function F (x) = ∫ax f (t)dt 271
13.2 Approximating the Area Under a Curve 275
Rectangular Approximations 275
Trapezoidal Approximations 279
13.3 Area and Definite Integrals 280
Area Under a Curve 280
Area Between Two Curves 285
13.4 Volumes and Definite Integrals 289
Solids with Known Cross Sections 289
The Disc Method 293
The Washer Method 298
13.5 Rapid Review 301
13.6 Practice Problems 303
13.7 Cumulative Review Problems 305
13.8 Solutions to Practice Problems 305
13.9 Solutions to Cumulative Review Problems 312
14 More Applications of Definite Integrals 315
14.1 Average Value of a Function 316
Mean Value Theorem for Integrals 316
Average Value of a Function on [a, b] 317
14.2 Distance Traveled Problems 319
14.3 Definite Integral as Accumulated Change 322
Business Problems 322
Temperature Problem 323
Leakage Problem 324
Growth Problem 324
14.4 Differential Equations 325
Exponential Growth/Decay Problems 325
Separable Differential Equations 327
14.5 Slope Fields 330
14.6 Rapid Review 334
14.7 Practice Problems 335
14.8 Cumulative Review Problems 337
14.9 Solutions to Practice Problems 338
14.10 Solutions to Cumulative Review Problems 342
Step 5 Build Your Test-Taking Confidence
AP Calculus AB Practice Exam 1 347
AP Calculus AB Practice Exam 2 375
Appendix 403
Bibliography 409
Websites 411