| Preface |
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xi | |
| Acknowledgments |
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xiii | |
| About the Author |
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xv | |
| Introduction: The Five-Step Program |
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xvii | |
| Step 1 Set Up Your Study Plan |
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1 What You Need to Know About the AP Calculus AB Exam |
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3 | (5) |
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1.1 What Is Covered on the AP Calculus AB Exam? |
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4 | (1) |
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1.2 What Is the Format of the AP Calculus AB Exam? |
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4 | (1) |
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1.3 What Are the Advanced Placement Exam Grades? |
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5 | (1) |
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How Is the AP Calculus AB Exam Grade Calculated? |
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5 | (1) |
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1.4 Which Graphing Calculators Are Allowed for the Exam? |
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6 | (2) |
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Calculators and Other Devices Not Allowed for the AP Calculus AB Exam |
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7 | (1) |
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Other Restrictions on Calculators |
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7 | (1) |
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8 | (9) |
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2.1 Three Approaches to Preparing for the AP Calculus AB Exam |
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8 | (2) |
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Overview of the Three Plans |
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8 | (2) |
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2.2 Calendar for Each Plan |
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10 | (7) |
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Summary of the Three Study Plans |
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13 | (4) |
| Step 2 Determine Your Test Readiness |
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17 | (20) |
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20 | (1) |
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20 | (5) |
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3.3 Answers to Diagnostic Test |
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25 | (1) |
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3.4 Solutions to Diagnostic Test |
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26 | (8) |
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34 | (3) |
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34 | (1) |
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AP Calculus AB Diagnostic Test |
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34 | (3) |
| Step 3 Develop Strategies for Success |
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4 How to Approach Each Question Type |
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37 | (8) |
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4.1 The Multiple-Choice Questions |
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38 | (1) |
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4.2 The Free-Response Questions |
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38 | (1) |
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4.3 Using a Graphing Calculator |
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39 | (1) |
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40 | (5) |
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What Do I Need to Bring to the Exam? |
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40 | (1) |
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41 | (4) |
| Step 4 Review the Knowledge You Need to Score High |
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45 | (39) |
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46 | (4) |
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46 | (1) |
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46 | (1) |
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Parallel and Perpendicular Lines |
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47 | (3) |
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5.2 Absolute Values and Inequalities |
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50 | (7) |
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50 | (1) |
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Inequalities and the Real Number Line |
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51 | (1) |
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Solving Absolute Value Inequalities |
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52 | (1) |
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Solving Polynomial Inequalities |
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53 | (2) |
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Solving Rational Inequalities |
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55 | (2) |
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57 | (13) |
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57 | (1) |
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58 | (2) |
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60 | (3) |
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Trigonometric and Inverse Trigonometric Functions |
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63 | (3) |
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Exponential and Logarithmic Functions |
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66 | (4) |
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70 | (8) |
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Increasing and Decreasing Functions |
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70 | (2) |
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72 | (1) |
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73 | (2) |
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Shifting, Reflecting, and Stretching Graphs |
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75 | (3) |
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78 | (1) |
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79 | (1) |
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5.7 Cumulative Review Problems |
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80 | (1) |
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5.8 Solutions to Practice Problems |
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80 | (3) |
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5.9 Solutions to Cumulative Review Problems |
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83 | (1) |
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84 | (25) |
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6.1 The Limit of a Function |
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85 | (7) |
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Definition and Properties of Limits |
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85 | (1) |
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85 | (2) |
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87 | (3) |
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90 | (2) |
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6.2 Limits Involving Infinities |
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92 | (7) |
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Infinite Limits (as x right arrow a) |
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92 | (2) |
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Limits at Infinity (as x right arrow ± infinity) |
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94 | (2) |
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Horizontal and Vertical Asymptotes |
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96 | (3) |
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6.3 Continuity of a Function |
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99 | (3) |
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Continuity of a Function at a Number |
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99 | (1) |
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Continuity of a Function over an Interval |
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99 | (1) |
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99 | (3) |
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102 | (1) |
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103 | (1) |
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6.6 Cumulative Review Problems |
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104 | (1) |
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6.7 Solutions to Practice Problems |
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105 | (2) |
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6.8 Solutions to Cumulative Review Problems |
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107 | (2) |
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109 | (28) |
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7.1 Derivatives of Algebraic Functions |
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110 | (6) |
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Definition of the Derivative of a Function |
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110 | (3) |
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113 | (1) |
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The Sum, Difference, Product, and Quotient Rules |
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114 | (1) |
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115 | (1) |
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7.2 Derivatives of Trigonometric, Inverse Trigonometric, Exponential, and Logarithmic Functions |
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116 | (5) |
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Derivatives of Trigonometric Functions |
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116 | (2) |
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Derivatives of Inverse Trigonometric Functions |
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118 | (1) |
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Derivatives of Exponential and Logarithmic Functions |
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119 | (2) |
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7.3 Implicit Differentiation |
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121 | (3) |
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Procedure for Implicit Differentiation |
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121 | (3) |
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7.4 Approximating a Derivative |
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124 | (2) |
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7.5 Derivatives of Inverse Functions |
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126 | (2) |
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7.6 Higher Order Derivatives |
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128 | (1) |
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7.7 L'Hopital's Rule for Indeterminate Forms |
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129 | (1) |
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129 | (2) |
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131 | (1) |
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7.10 Cumulative Review Problems |
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132 | (1) |
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7.11 Solutions to Practice Problems |
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132 | (3) |
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7.12 Solutions to Cumulative Review Problems |
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135 | (2) |
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8 Graphs of Functions and Derivatives |
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137 | (40) |
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8.1 Rolle's Theorem, Mean Value Theorem, and Extreme Value Theorem |
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138 | (4) |
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138 | (1) |
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138 | (3) |
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141 | (1) |
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8.2 Determining the Behavior of Functions |
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142 | (12) |
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Test for Increasing and Decreasing Functions |
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142 | (3) |
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First Derivative Test and Second Derivative Test for Relative Extrema |
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145 | (3) |
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Test for Concavity and Points of Inflection |
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148 | (6) |
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8.3 Sketching the Graphs of Functions |
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154 | (3) |
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Graphing without Calculators |
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154 | (1) |
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Graphing with Calculators |
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155 | (2) |
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8.4 Graphs of Derivatives |
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157 | (5) |
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162 | (2) |
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164 | (3) |
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8.7 Cumulative Review Problems |
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167 | (1) |
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8.8 Solutions to Practice Problems |
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167 | (7) |
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8.9 Solutions to Cumulative Review Problems |
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174 | (3) |
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9 Applications of Derivatives |
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177 | (25) |
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177 | (6) |
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General Procedure for Solving Related Rate Problems |
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178 | (1) |
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Common Related Rate Problems |
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178 | (1) |
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Inverted Cone (Water Tank) Problem |
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179 | (1) |
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180 | (1) |
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Angle of Elevation Problem |
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181 | (2) |
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9.2 Applied Maximum and Minimum Problems |
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183 | (5) |
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General Procedure for Solving Applied Maximum and Minimum Problems |
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183 | (1) |
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183 | (1) |
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184 | (3) |
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187 | (1) |
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188 | (1) |
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189 | (2) |
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9.5 Cumulative Review Problems |
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191 | (1) |
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9.6 Solutions to Practice Problems |
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192 | (7) |
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9.7 Solutions to Cumulative Review Problems |
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199 | (3) |
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10 More Applications of Derivatives |
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202 | (25) |
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10.1 Tangent and Normal Lines |
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202 | (9) |
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202 | (6) |
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208 | (3) |
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10.2 Linear Approximations |
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211 | (3) |
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Tangent Line Approximation (or Linear Approximation) |
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211 | (2) |
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Estimating the nth Root of a Number |
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213 | (1) |
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Estimating the Value of a Trigonometric Function of an Angle |
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213 | (1) |
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214 | (4) |
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Instantaneous Velocity and Acceleration |
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214 | (2) |
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216 | (1) |
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216 | (2) |
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218 | (1) |
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219 | (1) |
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10.6 Cumulative Review Problems |
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220 | (1) |
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10.7 Solutions to Practice Problems |
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221 | (4) |
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10.8 Solutions to Cumulative Review Problems |
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225 | (2) |
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Big Idea 3: Integrals and the Fundamental Theorems of Calculus |
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227 | (20) |
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11.1 Evaluating Basic Integrals |
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228 | (5) |
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Antiderivatives and Integration Formulas |
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228 | (2) |
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230 | (3) |
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11.2 Integration by U-Substitution |
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233 | (8) |
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The U-Substitution Method |
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233 | (1) |
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U-Substitution and Algebraic Functions |
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233 | (2) |
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U-Substitution and Trigonometric Functions |
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235 | (1) |
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U-Substitution and Inverse Trigonometric Functions |
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236 | (2) |
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U-Substitution and Logarithmic and Exponential Functions |
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238 | (3) |
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241 | (1) |
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242 | (1) |
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11.5 Cumulative Review Problems |
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243 | (1) |
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11.6 Solutions to Practice Problems |
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244 | (2) |
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11.7 Solutions to Cumulative Review Problems |
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246 | (1) |
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247 | (23) |
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12.1 Riemann Sums and Definite Integrals |
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248 | (5) |
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Sigma Notation or Summation Notation |
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248 | (1) |
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Definition of a Riemann Sum |
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249 | (1) |
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Definition of a Definite Integral |
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250 | (1) |
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Properties of Definite Integrals |
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251 | (2) |
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12.2 Fundamental Theorems of Calculus |
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253 | (4) |
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First Fundamental Theorem of Calculus |
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253 | (1) |
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Second Fundamental Theorem of Calculus |
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254 | (3) |
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12.3 Evaluating Definite Integrals |
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257 | (5) |
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Definite Integrals Involving Algebraic Functions |
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257 | (1) |
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Definite Integrals Involving Absolute Value |
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258 | (1) |
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Definite Integrals Involving Trigonometric, Logarithmic, and Exponential Functions |
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259 | (2) |
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Definite Integrals Involving Odd and Even Functions |
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261 | (1) |
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262 | (1) |
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263 | (1) |
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12.6 Cumulative Review Problems |
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264 | (1) |
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12.7 Solutions to Practice Problems |
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265 | (3) |
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12.8 Solutions to Cumulative Review Problems |
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268 | (2) |
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270 | (45) |
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13.1 The Function F (x) = integralxa f(t)dt |
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271 | (4) |
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13.2 Approximating the Area Under a Curve |
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275 | (5) |
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Rectangular Approximations |
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275 | (4) |
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Trapezoidal Approximations |
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279 | (1) |
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13.3 Area and Definite Integrals |
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280 | (9) |
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280 | (5) |
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285 | (4) |
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13.4 Volumes and Definite Integrals |
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289 | (12) |
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Solids with Known Cross Sections |
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289 | (4) |
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293 | (5) |
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298 | (3) |
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301 | (2) |
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303 | (2) |
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13.7 Cumulative Review Problems |
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305 | (1) |
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13.8 Solutions to Practice Problems |
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305 | (7) |
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13.9 Solutions to Cumulative Review Problems |
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312 | (3) |
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14 More Applications of Definite Integrals |
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315 | |
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14.1 Average Value of a Function |
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316 | (3) |
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Mean Value Theorem for Integrals |
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316 | (1) |
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Average Value of a Function on [ a, b] |
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317 | (2) |
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14.2 Distance Traveled Problems |
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319 | (3) |
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14.3 Definite Integral as Accumulated Change |
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322 | (3) |
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322 | (1) |
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323 | (1) |
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324 | (1) |
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324 | (1) |
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14.4 Differential Equations |
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325 | (5) |
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Exponential Growth/Decay Problems |
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325 | (2) |
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Separable Differential Equations |
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327 | (3) |
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330 | (4) |
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334 | (1) |
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335 | (2) |
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14.8 Cumulative Review Problems |
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337 | (1) |
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14.9 Solutions to Practice Problems |
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338 | (4) |
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14.10 Solutions to Cumulative Review Problems |
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342 | |
| Step 5 Build Your Test-Taking Confidence |
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AP Calculus AB Practice Exam 1 |
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347 | (28) |
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AP Calculus AB Practice Exam 2 |
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375 | (28) |
| Appendix |
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403 | (6) |
| Bibliography |
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409 | (2) |
| Websites |
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411 | |
Lisainfo e-raamatute kohta