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Part I Using This Book to Improve Your AP Score |
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1 | (1) |
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Preview: Your Knowledge, Your Expectations |
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2 | (1) |
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Your Guide to Using This Book |
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2 | (1) |
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3 | (4) |
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7 | (2) |
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9 | (27) |
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36 | (1) |
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37 | (22) |
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Part III About the AP Calculus AB Exam |
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59 | (8) |
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AB Calculus versus BC Calculus |
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60 | (1) |
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The Structure of the Calculus Exam |
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60 | (1) |
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How the AP Calculus AB Exam is Scored |
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61 | (1) |
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Overview of Content Topics |
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62 | (2) |
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General Overview of This Book |
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64 | (2) |
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66 | (1) |
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Designing Your Study Plan |
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66 | (1) |
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Part IV Test-Taking Strategies for the AP Calculus AB Exam |
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67 | (10) |
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1 How to Approach Multiple-Choice Questions |
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69 | (4) |
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2 How to Approach Free-Response Questions |
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73 | (4) |
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Part V Content Review for the AP Calculus AB Exam |
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77 | (432) |
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79 | (1) |
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Introducing Calculus: Can Change Occur at an Instant? |
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80 | (1) |
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Defining Limits Using Limit Notation |
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80 | (2) |
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Estimating Limit Values from Graphs |
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82 | (1) |
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Estimating Limit Values from Tables |
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83 | (1) |
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Determining Limits Using Algebraic Properties of Limits |
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84 | (1) |
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Determining Limits Using Algebraic Manipulation |
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85 | (2) |
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Selecting Procedures for Determining Limits |
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87 | (3) |
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Determining Limits Using the Squeeze Theorem |
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90 | (2) |
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Connecting Multiple Representations of Limits |
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92 | (3) |
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Exploring Types of Discontinuities |
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95 | (4) |
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Defining Continuity at a Point |
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99 | (2) |
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Confirming Continuity Over an Interval |
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101 | (1) |
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102 | (1) |
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Connecting Infinite Limits and Vertical Asymptotes |
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102 | (3) |
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Connecting Limits at Infinity and Horizontal Asymptotes |
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105 | (1) |
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Working with the Intermediate Value Theorem (IVT) |
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106 | (5) |
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4 Differentiation: Definition and Basic Derivative Rules |
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111 | (1) |
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Defining Average and Instantaneous Rates of Change at a Point |
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112 | (1) |
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Defining the Derivative of a Function and Using Derivative Notation |
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113 | (6) |
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Estimating Derivatives of a Function at a Point |
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119 | (3) |
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Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist |
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122 | (1) |
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123 | (1) |
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Derivative Rules: Constant, Sum, Difference, and Constant Multiple |
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124 | (2) |
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Derivatives of cos x, sin x, ex and In x |
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126 | (7) |
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133 | (1) |
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134 | (2) |
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Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions |
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136 | (5) |
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5 Differentiation: Composite, Implicit, and Inverse Functions |
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141 | (1) |
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142 | (6) |
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148 | (6) |
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Differentiating Inverse Functions |
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154 | (4) |
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Differentiating Inverse Trigonometric Functions |
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158 | (2) |
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Selecting Procedures for Calculating Derivatives |
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160 | (2) |
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Calculating Higher-Order Derivatives |
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162 | (7) |
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6 Contextual Applications of Differentiation |
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169 | (1) |
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Interpreting the Meaning of the Derivative in Context |
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170 | (1) |
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Straight-Line Motion: Connecting Position, Velocity, and Acceleration |
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170 | (6) |
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Rates of Change in Applied Contexts Other Than Motion |
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176 | (1) |
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Introduction to Related Rates |
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176 | (1) |
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Solving Related Rates Problems |
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177 | (6) |
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Approximating Values of a Function Using Local Linearity and Linearization |
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183 | (10) |
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Using L'Hospital's Rule for Determining Limits of Indeterminate Forms |
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193 | (8) |
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7 Analytical Applications of Differentiation |
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201 | (1) |
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Using the Mean Value Theorem |
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202 | (5) |
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Extreme Value Theorem, Global Versus Local Extrema, and Critical Points |
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207 | (1) |
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Determining Intervals on Which a Function Is Increasing or Decreasing |
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208 | (2) |
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Using the First Derivative Test to Determine Relative (Local) Extrema |
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210 | (2) |
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Using the Candidate Test to Determine Absolute (Global) Extrema |
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212 | (2) |
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Determining Concavity of Functions over Their Domains |
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214 | (3) |
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Using the Second Derivative Test to Determine Extrema |
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217 | (3) |
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Sketching Graphs of Functions and Their Derivatives |
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220 | (15) |
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Connecting a Function, Its First Derivative, and Its Second Derivative |
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235 | (6) |
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Introduction to Optimization Problems |
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241 | (1) |
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Solving Optimization Problems |
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242 | (10) |
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Exploring Behaviors and Implicit Relations |
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252 | (3) |
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8 Integration and Accumulation of Change |
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255 | (1) |
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Exploring Accumulations of Change |
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256 | (1) |
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Approximating Areas with Riemann Sums |
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257 | (14) |
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Riemann Sums, Summation Notation, and Definite Integral Notation |
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271 | (1) |
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The Fundamental Theorem of Calculus and Accumulation Functions |
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272 | (2) |
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Interpreting the Behavior of Accumulation Functions Involving Area |
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274 | (4) |
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Applying Properties of Definite Integrals |
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278 | (1) |
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The Fundamental Theorem of Calculus and Definite Integrals |
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279 | (2) |
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Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation |
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281 | (8) |
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Integrating Using Substitution |
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289 | (16) |
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Integrating Functions Using Long Division and Completing the Square |
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305 | (3) |
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Selecting Techniques for Antidifferentiation |
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308 | (5) |
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313 | (1) |
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Modeling Situations with Differential Equations |
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314 | (1) |
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Verifying Solutions for Differential Equations |
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314 | (1) |
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315 | (4) |
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Reasoning Using Slope Fields |
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319 | (2) |
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Finding General Solutions Using Separation of Variables |
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321 | (1) |
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Finding Particular Solutions Using Initial Conditions and Separation of Variables |
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322 | (4) |
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Exponential Models with Differential Equations |
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326 | (5) |
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10 Applications of Integration |
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331 | (1) |
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Finding the Average Value of a Functions on an Interval |
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332 | (2) |
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Connecting Position, Velocity, and Acceleration of Functions Using Integrals |
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334 | (1) |
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Using Accumulation Functions and Definite Integrals in Applied Contexts |
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335 | (1) |
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Finding the Area Between Curves Expressed as Functions of x |
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336 | (2) |
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Finding the Area Between Curves Expressed as Functions of y |
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338 | (4) |
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Finding the Area Between Curves That Intersect at More than Two Points |
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342 | (1) |
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Volumes with Cross Sections: Squares and Rectangles |
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343 | (2) |
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Volumes with Cross Sections: Triangles and Semicircles |
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345 | (1) |
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Volume with Disc Method: Revolving Around x- or Y-Axis |
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346 | (3) |
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Volume with Disc Method: Revolving Around Other Axes |
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349 | (2) |
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Volume with Washer Method: Revolving Around x- or y-Axis |
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351 | (3) |
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Volume with Washer Method: Revolving Around Other Axes |
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354 | (5) |
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11 Answers to Practice Problems Sets |
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359 | (124) |
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12 Answers to End of
Chapter Drills |
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483 | (26) |
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Part VI Practice Tests 2 and 3 |
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509 | (114) |
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511 | (28) |
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Practice Test 2 Answers and Explanations |
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539 | (24) |
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563 | (32) |
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Practice Test 3 Answers and Explanations |
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595 | (28) |
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Part VII Additional Practice Tests |
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623 | (91) |
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625 | (26) |
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Practice Test 4 Answers and Explanations |
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651 | (18) |
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669 | (26) |
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Practice Test 5 Answers and Explanations |
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695 | (19) |
| About the Author |
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714 | |
| Practice Test A Online |
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| Practice Test A Answers and Explanations online |
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| Practice Test B Online |
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| Practice Test B Answers and Explanations online |
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