﻿ ﻿Master AP Calculus AB & BC

## Master AP Calculus AB & BC

QUICK REFERENCE GUIDE

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

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

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)

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

Practice Test 2: AP Calculus AB