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Chapter 1 What You Need to Know About the AP Calculus AB Exam |
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3 | (4) |
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Chapter 2 How to Get the Score You Need |
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7 | (10) |
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Chapter 3 Calculator Basics |
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17 | (6) |
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23 | (26) |
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4.1 Evaluating Limits Graphically |
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27 | (4) |
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4.2 Evaluate Limits Algebraically |
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31 | (4) |
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4.3 Limits of Composite Functions |
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35 | (4) |
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4.4 Limits That Don't Exist |
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39 | (10) |
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Chapter 5 More Advanced Limits |
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49 | (28) |
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53 | (4) |
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57 | (4) |
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5.3 Horizontal and Vertical Asymptotes |
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61 | (4) |
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5.4 Limits Involving Trig Functions |
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65 | (12) |
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77 | (24) |
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6.1 Continuity and Limits |
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81 | (4) |
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6.2 Types of Discontinuities |
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85 | (4) |
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89 | (12) |
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Chapter 7 Derivatives---The Basics |
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101 | (48) |
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7.1 The Limit Definition of the Derivative |
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107 | (4) |
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7.2 Estimating Derivatives from Graphs and Tables |
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111 | (4) |
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115 | (4) |
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7.4 The Product and Quotient Rules |
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119 | (4) |
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123 | (4) |
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7.6 Derivatives of Logarithmic and Exponential Functions |
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127 | (4) |
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131 | (4) |
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7.8 The Intermediate Value, Extreme Value, and Mean Value Theorems |
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135 | (14) |
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Chapter 8 More Advanced Derivatives |
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149 | (32) |
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8.1 Derivatives of Trig Functions |
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153 | (4) |
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8.2 Derivatives of Inverse Trig Functions |
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157 | (4) |
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8.3 Higher Order Derivatives |
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161 | (4) |
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8.4 Implicit Differentiation |
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165 | (6) |
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8.5 Derivatives of Inverse Functions |
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171 | (10) |
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Chapter 9 Applications of the Derivative |
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181 | (38) |
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9.1 The Slope of a Curve at a Point |
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185 | (4) |
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9.2 Tangent Lines and Normal Lines |
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189 | (4) |
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9.3 Local Linear Approximations |
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193 | (4) |
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9.4 Derivatives as Rates of Change |
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197 | (4) |
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9.5 First Derivatives and Curve Sketching |
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201 | (4) |
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9.6 Second Derivatives and Curve Sketching |
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205 | (14) |
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Chapter 10 More Advanced Applications |
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219 | (38) |
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10.1 The Relationship Between Differentiability and Continuity |
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223 | (4) |
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10.2 Using the Graphs of f, f', and f' |
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227 | (6) |
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233 | (6) |
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239 | (4) |
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243 | (14) |
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PART 4 INTEGRALS AND THE FUNDAMENTAL THEOREM OF CALCULUS |
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Chapter 11 Integration---The Basics |
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257 | (34) |
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11.1 Antiderivatives and the Indefinite Integral |
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261 | (4) |
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11.2 Antiderivatives Subject to an Initial Condition |
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265 | (4) |
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11.3 U-Substitution and Algebraic Functions |
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269 | (6) |
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11.4 Integration of Trig Functions |
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275 | (4) |
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11.5 Integration of Exponential and Logarithmic Functions |
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279 | (12) |
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Chapter 12 The Definite Integral |
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291 | (30) |
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12.1 The Fundamental Theorems of Calculus |
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295 | (4) |
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12.2 Riemann Sums and Definite Integrals |
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299 | (4) |
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12.3 Properties of Definite Integrals |
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303 | (4) |
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12.4 U-Substitution and Definite Integrals |
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307 | (4) |
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12.5 Equivalent Forms of Definite Integrals |
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311 | (10) |
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Chapter 13 Geometric Applications of Integration |
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321 | (28) |
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325 | (4) |
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13.2 Area Between or Bounded by Curves |
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329 | (4) |
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13.3 Volumes of Solids with Known Cross Sections |
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333 | (6) |
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13.4 Volumes of Solids of Revolution |
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339 | (10) |
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Chapter 14 Further Applications of Integration |
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349 | (40) |
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14.1 Average Value of a Function |
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353 | (4) |
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14.2 Net Change over an Interval |
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357 | (4) |
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361 | (4) |
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14.4 Differential Equations |
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365 | (4) |
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14.5 Exponential Growth and Decay |
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369 | (4) |
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373 | (16) |
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PART 5 GRAPHING CALCULATORS AND FREE-RESPONSE QUESTIONS |
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Chapter 15 Problems that Require Graphing Calculators |
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389 | (18) |
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15.1 Graphing Functions and Finding Critical Points |
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391 | (6) |
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15.2 Finding a Derivative at a Point |
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397 | (4) |
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15.3 Evaluating a Definite Integral |
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401 | (6) |
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Chapter 16 Answering Free-Response Questions |
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407 | (20) |
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427 | (52) |
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479 | (48) |
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527 | (54) |
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581 | (58) |
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639 | (54) |
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693 | (58) |
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751 | (58) |
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809 | (56) |
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Appendix A Derivative Rules |
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865 | (4) |
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Appendix B Integration Rules |
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869 | |