The following is an outline of the topics we cover and a typical sequence in which those topics are covered. The following are major AP calculus goals:
For each major idea the students will examine the concept graphically, numerically, and symbolically, and the class will illustrate connections among the three.
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.
Student should understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of a rate of change and should be able to us integrals to solve a variety of problems.
Student 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 both orally and in well-written sentences and should be able to explain solutions to problems.
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 verify conclusions.
Student should be able to determine the reasonableness of solutions, including sign, size, relative, accuracy, and units of measurement.