﻿ ﻿AP Examinations - Calculus AB and Calculus BC

## AP Examinations - Calculus AB and Calculus BC

Introduction

DIAGNOSTIC TESTS

Diagnostic Test Calculus AB

Diagnostic Test Calculus BC

CHAPTER 1 Functions

A. DEFINITIONS

B. SPECIAL FUNCTIONS

C. POLYNOMIAL AND OTHER RATIONAL FUNCTIONS

D. TRIGONOMETRIC FUNCTIONS

E. EXPONENTIAL AND LOGARITHMIC FUNCTIONS

F. PARAMETRICALLY DEFINED FUNCTIONS

G. POLAR FUNCTIONS

Practice Exercises

CHAPTER 2 Limits and Continuity

A. DEFINITIONS AND EXAMPLES

B. ASYMPTOTES

C. THEOREMS ON LIMITS

D. LIMIT OF A QUOTIENT OF POLYNOMIALS

E. OTHER BASIC LIMITS

F. CONTINUITY

Practice Exercises

CHAPTER 3 Differentiation

A. DEFINITION OF DERIVATIVE

B. FORMULAS

C. THE CHAIN RULE; THE DERIVATIVE OF A COMPOSITE FUNCTION

D. DIFFERENTIABILITY AND CONTINUITY

E. ESTIMATING A DERIVATIVE

F. DERIVATIVES OF PARAMETRICALLY DEFINED FUNCTIONS

G. IMPLICIT DIFFERENTIATION

H. DERIVATIVE OF THE INVERSE OF A FUNCTION

I. THE MEAN VALUE THEOREM

J. INDETERMINATE FORMS AND L’HÔPITAL’S RULE

K. RECOGNIZING A GIVEN LIMIT AS A DERIVATIVE

Practice Exercises

CHAPTER 4 Applications of Differential Calculus

A. SLOPE; CRITICAL POINTS

B. TANGENTS AND NORMALS

C. INCREASING AND DECREASING FUNCTIONS

D. MAXIMUM, MINIMUM, AND INFLECTION POINTS: DEFINITIONS

E. MAXIMUM, MINIMUM, AND INFLECTION POINTS: CURVE SKETCHING

F. GLOBAL MAXIMUM OR MINIMUM

G. FURTHER AIDS IN SKETCHING

H. OPTIMIZATION: PROBLEMS INVOLVING MAXIMA AND MINIMA

I. RELATING A FUNCTION AND ITS DERIVATIVES GRAPHICALLY

J. MOTION ALONG A LINE

K. MOTION ALONG A CURVE: VELOCITY AND ACCELERATION VECTORS

L. TANGENT-LINE APPROXIMATIONS

M. RELATED RATES

N. SLOPE OF A POLAR CURVE

Practice Exercises

CHAPTER 5 Antidifferentiation

A. ANTIDERIVATIVES

B. BASIC FORMULAS

C. INTEGRATION BY PARTIAL FRACTIONS

D. INTEGRATION BY PARTS

E. APPLICATIONS OF ANTIDERIVATIVES; DIFFERENTIAL EQUATIONS

Practice Exercises

CHAPTER 6 Definite Integrals

A. FUNDAMENTAL THEOREM OF CALCULUS (FTC); DEFINITION OF DEFINITE INTEGRAL

B. PROPERTIES OF DEFINITE INTEGRALS

C. INTEGRALS INVOLVING PARAMETRICALLY DEFINED FUNCTIONS

D. DEFINITION OF DEFINITE INTEGRAL AS THE LIMIT OF A SUM: THE FUNDAMENTAL THEOREM AGAIN

E. APPROXIMATIONS OF THE DEFINITE INTEGRAL; RIEMANN SUMS

F. INTERPRETING ln x AS AN AREA

G. AVERAGE VALUE

Practice Exercises

CHAPTER 7 Applications of Integration to Geometry

A. AREA

B. VOLUME

C. ARC LENGTH

D. IMPROPER INTEGRALS

Practice Exercises

CHAPTER 8 Further Applications of Integration

A. MOTION ALONG A STRAIGHT LINE

B. MOTION ALONG A PLANE CURVE

C. OTHER APPLICATIONS OF RIEMANN SUMS

D. FTC: DEFINITE INTEGRAL OF A RATE IS NET CHANGE

Practice Exercises

CHAPTER 9 Differential Equations

A. BASIC DEFINITIONS

B. SLOPE FIELDS

C. EULER’S METHOD

D. SOLVING FIRST-ORDER DIFFERENTIAL EQUATIONS ANALYTICALLY

E. EXPONENTIAL GROWTH AND DECAY

Practice Exercises

CHAPTER 10 Sequences and Series

A. SEQUENCES OF REAL NUMBERS

B. INFINITE SERIES

C. POWER SERIES

Practice Exercises

CHAPTER 11 Miscellaneous Multiple-Choice Practice Questions

CHAPTER 12 Miscellaneous Free-Response Practice Exercises

AB PRACTICE EXAMINATIONS

AB Practice Examination 1

AB Practice Examination 2

AB Practice Examination 3

BC PRACTICE EXAMINATIONS

BC Practice Examination 1

BC Practice Examination 2

BC Practice Examination 3

Appendix: Formulas and Theorems for Reference