STEP 1 Set Up Your Study Plan 1 What You Need to Know About the AP Calculus BC Exam 3 1.1 What Is Covered on the AP Calculus BC Exam？ 4 1.2 What Is the Format ofthe AP Calculus BC Exam？ 4 1.3 What Are the Advanced Placement Exam Grades？ 5 How Is the AP Calculus BC 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 BC Exam 7 Other Restrictions on Calculators 7 2 How to Plan Your Time 8 2.1 Three Approaches to Preparing for the AP Calculus BC Exam 8 Overview ofthe Three Plans 8 2.2 Calendar for Each Plan 10 Summary ofthe Three Study Plans 13 STEP 2 Determine Your Test Readiness 3 Take a Diagnostic Exam 17 3.1 GettingStarted！ 21 3.2 Diagnostic Test 21 3.3 Answers to DiagnosticTest 27 3.4 Solutions to DiagnosticTest 28 3.5 Calculate Your Score 38 Short—Answer Questions 38 AP Calculus BC Diagnostic Exam 38 STEP 3 Develop Strategies for Success 4 How to Approach Each Question Type 41 4.1 The Multiple—Choice Questions 42 4.2 The Free—Response Questions 42 4.3 Using a Graphing Calculator 43 4.4 Taking the Exam 44 What Do I Need to Bring to the Exam？ 44 Tips for Taking the Exam 45 STEP 4 Review the Knowledge You Need to Score High 5 Limits and Continuity 49 5.1 The Limit ofa Function 50 Deflnition and Properties ofLimits 50 Evaluating Limits 50 One—Sided Limits 52 Squeeze Theorem 55 5.2 Limitslnvolvinglnflnities 57 Inflnite Limits（as x a）57 Limits at InFmity（as x 00）59 Horizontal and VerticaIAsymptotes 61 5.3 ContinuityofaFunction 64 Continuity of a Function at a Number 64 Continuiry of a Function over an Interval 64 Theorems on Continuity 64 5.4 Rapid Review 67 5.5 Practice Problems 69 5.6 Cumulative Review Problems 70 5.7 Solutions to Practice Problems 70 5.8 Solutions to Cumulative Review Problems 73 6 Differentiation 75 6.1 Derivatives ofAlgebraicFunctions 76 Deflnition ofthe Derivative ofa Function 76 Power Rule 79 The Sum，Difference，Product，and Quotient Rules 80 The Chain Rule 81 6.2 Derivatives ofTrigonometric，lnverse Trigonometric，Exponential，and Logarithmic Functions 82 Derivatives ofTrigonometric Functions 82 Derivatives oflnverse Trigonometric Functions 84 Derivatives ofExponential and Logarithmic Functions 85 6.3 Impliat Differentiation 87 Procedure for Implicit Differentiation 87 6.4 Approximating a Derivative 90 6.5 Derivatives oflnverse Functions 92 6.6 Higher Order Derivatives 94 6，7 Indeterminate Forms 95 L'Hopitals Rule for Indeterminate Forms 95 6.8 Rapid Review 95 6.9 Practice Problems 97 6.10 Cumulative Review Problems 98 6.11 Solutions to Practice Problems 98 6.12 Solutions to Cumulative Review Problems 101 7 Graphs ofFunctions and Derivatives 103 7.1 Rolle's Theorem，Mean Value Theorem，and Extreme Value Theorem 103 Rolle's Theorem 104 Mean Value Theorem 104 Extreme Value Theorem 107 7.2 Determining the Behavior ofFunctions 108 Test for Increasing and Decreasing Functions 108 First Derivative Test and Second Derivative Test for Relative Extrema 111 Test for ConCavity and Points oflnfiection 114 7.3 Sketchingthe.Graphs ofFunctions 120 Graphing without Calculators 120 Graphing with Calculators 121 7.4 Graphs ofDerivatives 123 7.5 Parametric，Polar，and Vector Representations 128 Parametric Curves 128 Polar Equations 129 Types ofPolar Graphs 129 Symmetry ofPolar Graphs 130 Vectors 131 VectorArithmetic 132 7.6 Rapid Review 133 7.7 Practice Problems 137 7.8 Cumulative ReviewProblems 139 7.9 Solutions to Practice Problems 140 7.10 Solutions to Cumulative Review Problems 147 8 Applications ofDerivatives 149 8.1 Related Rate 149 General Procedure for Solving Related Rate Problems 149 Common Related Rate Problems 150 Inverted Cone（Water Tank）Problem 151 Shadow Problem 152 Angle ofElevation Problem 153 8.2 Applied Maximum and Minimum Problems 155 General Procedure for Solving Applied Maximum and Minimum Problems 155 Distance Problem 155 Area and Volume Problem 156 Business Problems 159 8.3 Rapid Review 160 8.4 Practice Problems 161 8.5 Cumulative Review Problems 163 8.6 Solutions to Practice Problems 164 8.7 Solutions to Cumulative Review Problems 171 9 MoreApplications ofDerivatives 174 9.1 TangentandNormalLines 174 Tangent Lines 174 NormalLines 180 9.2 LinearApproximations 183 Tangent Line Approximation（or Linear Approximation）183 Estimating the nth Root ofa Number 185 Estimating the Value ofa Trigonometric Function of an Angle 185 9.3 MotionAlong a Line 186 Instantaneous Velociry and Acceleration 186 VerticaIMotion 188 HorizontaIMotion 188 9.4 Parametric，Polar，and Vector Derivatives 190 Derivatives ofParametric Equations 190 Position，Speed，and Acceleration 191 Derivatives ofPolar Equations 191 Velocity and Acceleration ofVector Functions 192 9.5 Rapid Review 195 9.6 Practice Problems 196 9.7 Cumulative Review Problems 198 9.8 Solutions to Practice Problems 199 9.9 Solutions to Cumulative Review Problems 204 10 Integration 207 10.1 EvaluatingBasiclntegrals 208 Antiderivatives and Integration Formulas 208 Evaluatinglntegrals 210 10.2 Integration byU—Substitution 213 The U—Substitution Method 213 U—Substiturion and Algebraic Functions 213 U—Substitution and Trigonometric Functions 215 U—Substitution and Inverse Trigonometric Functions 216 U—Substitution and Logarithmic and Exponential Functions 218 10.3 Techniques oflntegration 221 Integration by Parts 221 Integration by Partial Fractions 222 10.4 Rapid Review 223 10.5 Practice Problems 224 10.6 Cumulative Review Problems 225 10.7 Solutions to Practice Problems 226 10.8 Solutions to Cumulative Review Problems 229 11 Definitelntegrals 231 11.1 Riemann Sums and DeFinite Integrals 232 Sigma Notation or Summation Notation 232 DeFmition ofa Riemann Sum 233 DeFinition ofa DeFinite Integral 234 Properties ofDeFmite Integrals 235 11.2 FundamentaITheorems ofCalculus 237 First FundamentaITheorem ofCalculus 237 Second FundamentaITheorem ofCalculus 238 11.3 Evaluating Definite Integrals 241 Definite Integrals Involving Algebraic Functions 241 Definite Integrals Involving Absolute Value 242 Definite Integrals Involving Trigonometric，Logarithmic， and Exponential Functions 243 Def Inite Integrals Involving Odd and Even Functions 245 11.4 Improperlntegrals 246 Infinite Intervals oflntegration 246 InFinite Discontinuities 247 11.5 Rapid Review 248 11.6 Practice Problems 249 11.7 Cumulative Review Problems 250 11.8 Solutions to Practice Problems 251 11.9 Solutions to Cumulative Review Problems 254 12 Areas andVolumes 257 12.1 TheFunction F（x）=（ax f（t）dt 258 12.2 Approximating the Area Under a Curve 262 Rectangular Approximations 262 TrapezoidaI Approximations 266 12.3 Areaand DeFinite Integrals 267 Area Under a Curve 267 Area Between Two Curves 272 12.4 Volumes and DeFinite Integrals 276 Solids with Known Cross Sections 276 The Disc Method 280 The Washer Method 285 12.5 Integration ofParametric，Polar，and Vector Curves 289 Area，Arc Length，and Surface Area for Parametric Curves 289 Area and Arc Length for Polar Curves 290 Integration ofa Vector—Valued Function 291 12.6 Rapid Review 292 12.7 Practice Problems 295 12.8 Cumulative Review Problems 296 12.9 Solutions to Practice Problems 297 12.10 Solutions to Cumulative Review Problems 305 13 MoreApplications ofDefinitelntegrals 309 13.1 Average Value ofa Function 310 Mean Value Theorem for Integrals 310 Average Value ofa Function on（a，b）311 13.2 Distance Traveled Problems 313 13.3 DeFmitelntegralasAccumulated Change 316 Business Problems 316 Temperature Problem 317 Leakage Problems 318 Growth Problem 318 13.4 DifferentiaIEquations 319 Exponential Growth／Decay Problems 319 Separable Differential Equations 321 13.5 Slope Fields 324 13.6 Logistic DifferentiaIEquations 328 13.7 Euler's Method 330 Approximating Solutions of Differential Equations by Euler's Merhod 330 13.8 Rapid Review 332 13.9 Practice Problems 334 13.10 Cumulative Review Problems 336 13.11 Solutions to Practice Problems 337 13.12 Solutions to Cumulative Review Problems 343 14 Series 346 14.1 Sequencesand Series 347 Convergence 347 14.2 Types ofSeries 348 p—Series 348 Harmonic Series 348 Geometric Series 348 DecimaIExpansion 349 14.3 ConvergenceTests 350 IntegraITest 350 Ratio Test 351 Comparison Test 351 Limit Comparison Test 352 14.4 AlternatingSeries 353 Error Bound 354 Absolute Convergence 354 14.5 Power Series 354 Radius and Interval ofConvergence 355 14.6 TaylorSeries 355 Taylor Series and MacLaurin Series 355 Common MacLaurin Series 357 14.7 Operations on Series 357 Substitution 357 Differentiation and Integration 358 Error Bounds' 359 14.8 Rapid Review 360 14.9 Practice Problems 362 14.10 Cumulative Review Problems 363 14.11 Solutions to Practice Problems 363 14.12 Solutions to Cumulative Review Problems 366 STEP 5 Bruld Your Test—Taking Confidence AP Calculus BC Practice Exam 1371 AP Calculus BC Practice Exam 2401 AP Calculus BC Practice Exam 3433 Formulas and Theorems 463 Bibliography and Websites 471
