Master AP Calculus AB & BC
TOP 10 STRATEGIES TO RAISE YOUR SCORE
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
HANDS-ON ACTIVITY 2.1: TRANSFORMING FUNCTIONS
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
HANDS-ON ACTIVITY 3.2: THE EXTREME VALUE THEOREM
HANDS-ON ACTIVITY 3.3: THE INTERMEDIATE VALUE THEOREM
TECHNOLOGY: EVALUATING LIMITS WITH A GRAPHING CALCULATOR
CHAPTER 4. Differentiating
DERIVATIVE AS A RATE OF CHANGE
A WORD ABOUT RESPECTING VARIABLES
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
HANDS-ON ACTIVITY 6.1: ROLLE’S AND MEAN VALUE THEOREMS
HANDS-ON ACTIVITY 6.2: THE FIRST DERIVATIVE TEST
MOTION IN THE PLANE (BC TOPIC ONLY)
TECHNOLOGY: MODELING A PARTICLES MOVEMENT WITH A GRAPHING CALCULATOR
CHAPTER 7. Integration
HANDS-ON ACTIVITY 7.1: APPROXIMATING AREA WITH RIEMANN SUMS
THE FUNDAMENTAL THEOREM OF CALCULUS
HANDS-ON ACTIVITY 7.2: ACCUMULATION FUNCTIONS
THE MEAN VALUE THEOREM FOR INTEGRATION, AVERAGE VALUE OF A FUNCTION
INTEGRATING INVERSE TRIGONOMETRIC FUNCTIONS
TECHNOLOGY: EVALUATING DEFINITE INTEGRALS WITH YOUR GRAPHING CALCULATOR
CHAPTER 8. Advanced Methods of Integration
MISCELLANEOUS METHODS OF INTEGRATION
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
FINDING THE VOLUME OF REGIONS WITH KNOWN CROSS SECTIONS
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)
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
TECHNOLOGY: VIEWING AND CALCULATING SEQUENCES AND SERIES WITH A GRAPHING CALCULATOR
PART III. FOUR PRACTICE TESTS
Practice Test 1: AP Calculus AB
Practice Test 2: AP Calculus AB
Practice Test 3: AP Calculus BC
Practice Test 4: AP Calculus BC
APPENDIX. COLLEGE-BY-COLLEGE GUIDE TO AP CREDIT AND PLACEMENT