Material Covered
AP Calculus AB Ch. 1: Functions and Models 1.1 Four Ways to Represent a Function
Verbally, Numerically, Visually, Algebraically.
Definition of a Function
Domain, Range, Independent and Dependent variables
Vertical Line Test
Piecewise Functions
Absolute Value
Symmetry – Even and Odd Functions
Increasing and Decreasing Functions
1.2 Mathematical Models: A Catalog of Essential Functions
Polynomials—Degree of a Polynomial
Graphs of f(x) = xn for n=1,2,3,4,5
Graphs of root functions
Graph of the reciprocal function ( f(x) = 1/x)
Rational Functions
Trigonometric Functions
Exponential Functions
Logarithmic Functions
1.3 New Functions from Old Functions
Transformation of Functions
Vertical and Horizontal Shifts, Stretching and Reflecting
Combinations of Functions—Algebra of Functions
Composition of Functions
*Know how to use your graphing calculator to examine graphs of functions.
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws2.4 The Precise Definition of a Limit Infinite Limits
2.5 ContinuityDefinition of a continuous function
Definition of a discontinuous function
Infinite, Jump, and Removable Discontinuities
The Intermediate Value Theorem
2.6 Tangents, Velocities, and Other Rates of Change
The Tangent Line
The Derivative of a Function at a Number a
Interpretation of the Derivative as the Slope of a Tangent
Interpretation of the Derivative as a Rate of Change
Instantaneous Rate of Change
3.2 The Derivative as a Function
Graphing the Derivative Given the Original Function
Finding the Derivative
Determining Where a Function is Differentiable
How Can a Function Fail to be Differentiable
3.3 Differentiation Formulas
Derivative of a Constant
Power Functions
The Constant Multiple Rule
The Sum Rule
The Difference Rule
The Product Rule
The Quotient Rule
3.4 Rates of Change in the Natural and Social Sciences
Physics
Chemistry
Biology
Economics
3.5 Derivatives of Trigonometric Functions
Definitions for Derivatives of Trigonometric Functions
Trigonometric Functions Determined from a Graph
3.6 The Chain Rule
3.7 Implicit Differentiation
3.8 Higher Derivatives3.9 Related Rates
3.10 Linear Approximations and Differentials
Chapter 4: Applications of Differentiation
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 How Derivatives Affect the Shape of a Graph
4.4 Limits at Infinity; Horizontal Asymptotes
4.5 Summary of Curve Sketching
4.6 Graphing with Calculus and Calculators
4.7 Optimization Problems
4.8 Applications to Business and Economics
4.9 Newton’s Method
4.10 Antiderivatives
Material currently being covered:
Chapter 5: Integrals
5.1 Areas and Distances
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
5.5 The Substitution Rule
Chapter 6: Applications of Integration
6.1 Areas Between Curves
