Course Outline
AP Calculus AB Course Outline
Unit 1: Pre-Calculus Review
A. Lines
1. Slope as rate of change
2. Parallel and perpendicular lines
3. Equations of lines
B. Functions and graphs
1. Functions: parabolas, circles, ellipses, rational expressions, radical equations
a. Characteristics
b. Standard and general forms
c. Completing the square
d. Zeroes, asymptotes, points of interest
2. Domain and range of functions: set notation and interval notation
3. Families of function
4. Piecewise functions
5. Composition of functions
C. Exponential and logarithmic functions
1. Exponential growth and decay
2. Inverse functions
3. Logarithmic functions
4. Properties of logarithms
D. Trigonometric functions
1. Graphs of basic trigonometric functions
a. Domain and range
b. Transformations
c. Inverse trigonometric functions
E. Solving equations
1. Absolute value
2. Using matrices
3. Substitution
4. Factoring
F. Even and odd functions
Review of Refresher Material (practice test)
Refresher Material Solutions to both in-class and take-home portion of test.
Practice Test on Limits at bottom of page (will be posted late 9/27/13)
A. Definition of limit
1. Finding limits graphically and numerically
2. Evaluating limits analytically
Finding Limits Using Difference of Cubes
Finding Limits Using Difference of Cubes II
Finding Limits Using Common Denominator
Finding Limits Using Conjugates
Finding Limits Involving Trig Functions I
Finding Limits Involving Trig Functions II
Finding Limits Involving Trig Functions III
B. Limits at a point
1. Properties of limits
2. Well-known theorems
3. One-sided
4. Two-sided
C. Limits involving infinity
1. Asymptotic behavior
2. End behavior
3. Properties of limits
4. Visualizing limits
D. Continuity
1. Continuous functions
2. Discontinuous functions
a. Removable discontinuity
b. Jump discontinuity (non-removable)
c. Infinite discontinuity (non-removable)
Unit 2: Limits and Continuity
A. Definition of limit
1. Finding limits graphically and numerically
2. Evaluating limits analytically
Finding Limits Using Difference of Cubes
Finding Limits Using Difference of Cubes II
Finding Limits Using Common Denominator
Finding Limits Using Conjugates
Finding Limits Involving Trig Functions I
B. Limits at a point
1. Properties of limits
2. Well-known theorems
3. One-sided
4. Two-sided
C. Limits involving infinity
1. Asymptotic behavior
2. End behavior
3. Properties of limits
4. Visualizing limits
D. Continuity
1. Continuous functions
2. Discontinuous functions
a. Removable discontinuity
b. Jump discontinuity (non-removable)
c. Infinite discontinuity (non-removable)
E. Rates of Change
1. Average rate of change
2. Instantaneous rate of change
F. Intermediate Value Theorem
Unit 3: The Derivative
A. Definition of the derivative
Derivatives Practice Quiz (definition and concept)
B. Differentiability
1. Local linearity
2. Numeric derivatives using the calculator
3. Differentiability and continuity
C. Secant and tangent lines (average versus instantaneous rate of change)
D. Techniques of differentiation
1. Notation
2. Derivatives of polynomial functions
3. Derivatives of trigonometric functions
4. Derivatives of radical functions
E. Derivative rules when combining functions
Guided Notes to Follow Videos (PDF)
Solutions to NOTES from Videos (PDF)
Problems to try on your own (PDF)
1. Power rule
Example 1 (Video) Example 2 (Video) Example 3 (Video) Example 4 (Video) Example 5 (Video)Example 6 (Video) Example 7 (Video) Example 8 (Video) Example 9 (Video)
2. Product Rules
Example 1 (Video) Example 2 (Video) Example 3 (Video) Example 4 (Video)
Example 5 (Video) Example 6 (Video) Example 7 (Video) Example 8 (Video)
3. Quotient Rule
Example 1 (Video) Example 2 (Video) Example 3 (Video) Example 4 (Video)
Example 5 (Video) Example 6 (Video) Example 7 (Video)
4. Chain Rule (Applied across all the rules)
Example 1 (Video) Example 2 (Video) Example 3 (Video) Example 4 (Video) Example 5 (Video)Example 6 (Video) Example 7 (Video) Example 8 (Video) Example 9 (Video)
F. Implicit derivatives
G. Normal lines
H. Related rates
I. Derivatives of logarithmic and exponential functions
Calculus Review of Derivatives
Unit 4: Applications of the Derivative
A. Extreme values
1. Local (relative max / min) extrema
2. Global (absolute max / min) extrema
B. Using the derivative
1. Mean value theorem
2. Rolle’s theorem
C. Applying the first derivative
1. Increasing and decreasing functions (slope of tangents)
2. Velocity
D. Applying the second derivative
1. Concavity
2. Acceleration
E. Analysis of graphs using the first and second derivatives (curve sketching)
1. Critical values
2. First derivative test for extrema
3. Concavity and points of inflection
4. Second derivative test for extrema
5. Slant and horizontal asymptotes
6. End behavior
D. Optimization problems
E. Local linearization models
F. Related rates revisited
G. Particle motion
H. L’Hopital’s Rule
Application of Derivatives Test 2012
Solutions to Optimization Questions (Scale Printing to 85%)
Solutions to Related Rates (Scale Printing to 85%)
Unit 5: The Definite Integral
A. Approximating areas
1. Riemann sums
a. Right sums
b. Left sums
2. Trapezoidal rule
B. Definite integrals and antiderivatives
C. The Fundamental Theorem of Calculus (part 1)
1. Finding areas
2. Average value of a function
D. Integration using u-substitution
E. Integration involving trigonometric functions.
F. Integration using the natural logarithmic function
G. The Fundamental Theorem of Calculus (part 2)
H. Separable differential equations
1. Growth and decay
2. Slope fields
3. General differential equations
Unit 6: Applications of Definite Integrals
A. Area between curves
1. Horizontal slicing
2. Vertical slicing
B. Volumes
1. Volumes of solids with known cross sections.
2. Volumes of solids of revolution
a. Disk method
b. Washer method
c. Shell method
C. Arc length and surfaces of revolution
Current Material
A. Definition of limit
1. Finding limits graphically and numerically
2. Evaluating limits analytically
Finding Limits Using Difference of Cubes
Finding Limits Using Difference of Cubes II
Finding Limits Using Common Denominator
Finding Limits Using Conjugates
Finding Limits Involving Trig Functions I
Finding Limits Involving Trig Functions II
Finding Limits Involving Trig Functions III
B. Limits at a point
1. Properties of limits
2. Well-known theorems
3. One-sided
4. Two-sided
C. Limits involving infinity
1. Asymptotic behavior
2. End behavior
3. Properties of limits
4. Visualizing limits
D. Continuity
1. Continuous functions
2. Discontinuous functions
a. Removable discontinuity
b. Jump discontinuity (non-removable)
c. Infinite discontinuity (non-removable)
E. Rates of Change
1. Average rate of change
2. Instantaneous rate of change
F. Intermediate Value Theorem