## Course Outline (taken from the College Board website)

**Goals**

• Students should be able to work with functions represented in a variety of ways: graphical, numerical, analytical or verbal. They should understand the connections among these representations.

• Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation and should be able to use derivatives to solve a variety of problems.

• Students should understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems.

• Students should understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.

• Students should be able to communicate mathematics and explain solutions to problems both verbally and in written sentences.

• Students should be able to model a written description of a physical situation with a function, a differential equation or an integral.

• Students should be able to use technology to help solve problems, experiment, interpret results and support conclusions.

• Students should be able to determine the reasonableness of solutions, including sign, size, relative accuracy and units of measurement.

• Students should develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment and know the values of the trigonometric functions.

__Topic Outline for Calculus AB__**I. Functions, Graphs and Limits**

· Analysis of graphs. Limits of functions (including one-sided limits)

· Limits of functions (including one-sided limits)

· Asymptotic and unbounded behavior

· Continuity as a property of functions

**II. Derivatives**

· Concept of the Derivative

· Derivative at a point

· Derivative as a function

· Application of Derivatives

· Computation of derivatives

**III. Integrals**

· Interpretations and properties of definate integrals

· Applications of integrals.

· Fundamental Theorem of Calculus

· Techniques of antidifferentiation

· Applications of antidifferentiation

· Numerical approximations to definite integrals.