AP Calculus (AB)

Goals:

• Students should be able to work with functions represented in a variety of ways: They should understand the connections .
• 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.