AP Calculus Course Syllabus
Unit 1: Pre-Calculus Review
A. Brief history
B. Set notation
C. Inequalities
a. Double
b. Quadratic
c. Absolute value
D. Distance
E. Trigonometry
a. Unit circle
b. Calculator
c. Graphs
d. Domain and range
e. Transformations
F. Representation
a. Analytic
b. Geometric
c. Numeric
G. Intercepts
H. Symmetry
I. Points of intersection
J. Slope
a. Rate of change
b. Parallel and Perpendicular Lines
c. Equations of lines
K. Functions and graphs
a. Domain and range
b. Piecewise
c. Library of curves
d. Transformations
e. Elementary and transcendental
f. Even and odd
g. Composite
h. Fitting models to data
Unit 2: Limits and Continuity
A. Limits
a. Tables
b. Formal definition
c. Failure to exist
d. One-sided
e. Properties
B. Continuity
a. At a point
b. Open interval
c. Everywhere
d. Discontinuity
i. Removable
ii. Non-Removable
e. Properties
C. Limits involving infinity
a. Vertical asymptotes
b. Horizontal asymptotes
c. Slant asymptotes
Unit 3: The Derivative
A. Definition of the derivative
B. Instantaneous rate of change
C. Local linearity
D. Differentiability
E. Derivatives of algebraic functions
F. Derivatives of Trigonometric functions
G. Rates of change
H. Higher order derivatives
I. Chain Rule
J. Implicit differentiation
K. Related rates
L. Derivatives of logarithms and exponentials
a. Explicit
b. Implicit
M. Derivatives of inverse trigonometric functions
Unit 4: Applications of Differentiation
A. Extrema
a. Critical numbers
b. Absolute
c. Relative
B. Rolle’s Theorem
C. Mean Value Theorem
D. First derivative test
a. Increasing intervals
b. Decreasing intervals
c. Monotonic curves
E. Second derivative
a. Points of Inflection
b. Concavity
c. Second derivative test for extrema
F. Curve sketching
G. Linear Approximations
H. Differentials
Unit Five: Integration
A. Definition of antiderivative
B. Constant of Integration
C. Indefinite Integrals
a. General solution
b. Initial conditions – particular solutions
D. Sigma notation
E. Summation formulas
F. Approximating area under a curve
a. Riemann sums
b. Trapezoidal Rule
G. Definite integrals
a. Area under a curve
H. Fundamental Theorem of Calculus
I. Integration by substitution
Unit 6: Differential Equations
A. Separable differential equations
a. Slope fields
b. Growth and decay
Unit 7: Applications Integration
A. Area between two curves
B. Volume of revolution
a. Disc method
b. Washer method
c. Solid with known cross sections
C. Particle motion
References and Materials
Major text
Larson, Ron, Robert P. Hostetler, and Bruce H. Edwards. Calculus of
a Single Variable. 8th ed. Boston: Houghton Mifflin Company, 2006.
Reference Books
Finney, Ross L., Franklin D. Demana, Bert K. Waits, and Daniel
Kennedy. Calculus - Graphical, Numerical, Algebraic. 1st ed.
Needham, MA.: Pearson, 2003.
Himonas, Alex, and Alan Howard. Calculus – Ideas and
Applications. 1st ed. John Wiley & Sons, Inc, 2003.
Lederman, David. Multiple-Choice & Free-Response Questions in
Preparation for the AP Calculus (AB) Examination. 8th ed. D & S
Marketing Systems, 2004.
Stewart, James. Calculus. 5th ed. Australia: Thomson, Brooks/Cole,
2003.