Master AP Calculus AB & BC

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PART I. AP CALCULUS AB & BC BASICS

CHAPTER 1. All About the AP Calculus AB & BC Tests

PART II. AP CALCULUS AB & BC REVIEW

CHAPTER 2. Calculus Prerequisites

  FUNCTIONS AND RELATIONS

  FUNCTION PROPERTIES

  INVERSE FUNCTIONS

  HANDS-ON ACTIVITY 2.1: TRANSFORMING FUNCTIONS

  TRIGONOMETRY

  PARAMETRIC EQUATIONS (BC TOPIC ONLY)

  POLAR EQUATIONS (BC TOPIC ONLY)

  VECTORS AND VECTOR EQUATIONS (BC TOPIC ONLY)

  TECHNOLOGY: SOLVING EQUATIONS WITH A GRAPHING CALCULATOR

CHAPTER 3. Limits and Continuity

  HANDS-ON ACTIVITY 3.1: WHAT IS A LIMIT?

  EVALUATING LIMITS ANALYTICALLY

  CONTINUITY

  HANDS-ON ACTIVITY 3.2: THE EXTREME VALUE THEOREM

  HANDS-ON ACTIVITY 3.3: THE INTERMEDIATE VALUE THEOREM

  LIMITS INVOLVING INFINITY

  SPECIAL LIMITS

  TECHNOLOGY: EVALUATING LIMITS WITH A GRAPHING CALCULATOR

CHAPTER 4. Differentiating

  DERIVATIVE AS A RATE OF CHANGE

  THE POWER RULE

  DERIVATIVES TO MEMORIZE

  THE CHAIN RULE

  THE PRODUCT RULE

  THE QUOTIENT RULE

  A WORD ABOUT RESPECTING VARIABLES

  IMPLICIT DIFFERENTIATION

  HANDS-ON ACTIVITY 4.1: APPROXIMATING DERIVATIVES

  TECHNOLOGY: FINDING NUMERICAL DERIVATIVES WITH THE GRAPHING CALCULATOR

CHAPTER 5. Advanced Topics in Differentiation

  THE DERIVATIVE OF AN INVERSE FUNCTION

  HANDS-ON ACTIVITY 5.1: LINEAR APPROXIMATIONS

  L’HOPITAL’S RULE (BC TOPIC ONLY)

  PARAMETRIC DERIVATIVES (BC TOPIC ONLY)

  POLAR DERIVATIVES (BC TOPIC ONLY)

  TECHNOLOGY: FINDING POLAR AND PARAMETRIC DERIVATIVES WITH YOUR CALCULATOR (BC TOPIC ONLY)

CHAPTER 6. Applications of the Derivative

  RELATED RATES

  HANDS-ON ACTIVITY 6.1: ROLLE’S AND MEAN VALUE THEOREMS

  HANDS-ON ACTIVITY 6.2: THE FIRST DERIVATIVE TEST

  CONCAVITY

  MOTION

  MOTION IN THE PLANE (BC TOPIC ONLY)

  OPTIMIZATION

  TECHNOLOGY: MODELING A PARTICLES MOVEMENT WITH A GRAPHING CALCULATOR

CHAPTER 7. Integration

  BASIC ANTIDERIVATIVES

  HANDS-ON ACTIVITY 7.1: APPROXIMATING AREA WITH RIEMANN SUMS

  THE TRAPEZOIDAL RULE

  THE FUNDAMENTAL THEOREM OF CALCULUS

  HANDS-ON ACTIVITY 7.2: ACCUMULATION FUNCTIONS

  THE MEAN VALUE THEOREM FOR INTEGRATION, AVERAGE VALUE OF A FUNCTION

  U-SUBSTITUTION

  INTEGRATING INVERSE TRIGONOMETRIC FUNCTIONS

  TECHNOLOGY: EVALUATING DEFINITE INTEGRALS WITH YOUR GRAPHING CALCULATOR

CHAPTER 8. Advanced Methods of Integration

  MISCELLANEOUS METHODS OF INTEGRATION

  PARTS (BC TOPIC ONLY)

  POWERS OF TRIGONOMETRIC FUNCTIONS (BC TOPIC ONLY)

  PARTIAL FRACTIONS (BC TOPIC ONLY)

  IMPROPER INTEGRALS (BC TOPIC ONLY)

  TECHNOLOGY: DRAWING DERIVATIVE AND INTEGRAL GRAPHS WITH YOUR CALCULATOR

CHAPTER 9. Applications of Integration

  HANDS-ON ACTIVITY 9.1: AREA BETWEEN CURVES

  THE DISK AND WASHER METHODS

  THE SHELL METHOD

  FINDING THE VOLUME OF REGIONS WITH KNOWN CROSS SECTIONS

  ARC LENGTH (BC TOPIC ONLY)

  POLAR AREA (BC TOPIC ONLY)

  TECHNOLOGY: USING YOUR CALCULATOR EFFICIENTLY

CHAPTER 10. Differential Equations

  HANDS-ON ACTIVITY 10.1: SEPARATION OF VARIABLES

  HANDS-ON ACTIVITY 10.2: SLOPE FIELDS

  EULER’S METHOD (BC TOPIC ONLY)

  EXPONENTIAL GROWTH AND DECAY

  LOGISTIC GROWTH (BC TOPIC ONLY)

  TECHNOLOGY: A DIFFERENTIAL EQUATIONS CALCULATOR PROGRAM

CHAPTER 11. Sequences and Series (BC Topics Only)

  INTRODUCTION TO SEQUENCES AND SERIES, NTH TERM DIVERGENCE TEST

  CONVERGENCE TESTS FOR INFINITE SERIES

  POWER SERIES

  TAYLOR AND MACLAURIN SERIES

  TECHNOLOGY: VIEWING AND CALCULATING SEQUENCES AND SERIES WITH A GRAPHING CALCULATOR

PART III. FOUR PRACTICE TESTS

  Practice Test 1: AP Calculus AB

  ANSWER KEY AND EXPLANATIONS

  Practice Test 2: AP Calculus AB

  ANSWER KEY AND EXPLANATIONS

  Practice Test 3: AP Calculus BC

  ANSWER KEY AND EXPLANATIONS

  Practice Test 4: AP Calculus BC

  ANSWER KEY AND EXPLANATIONS

APPENDIX. COLLEGE-BY-COLLEGE GUIDE TO AP CREDIT AND PLACEMENT