Calculus AB is designed to be taught over a full high school
academic year. It is possible to spend some time on elementary functions
and still cover the Calculus AB curriculum within a year. However, if
students are to be adequately prepared for the Calculus AB examination,
most of the year must be devoted to topics in differential and integral
calculus. These topics are the focus of the AP Exam.
AP Calculus AB Course 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.
- understand the meaning of the derivative in terms of a rate of
change and local linear approximation and they should be able to use
derivatives to solve a variety of problems.
- 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.
- understand the relationship between the derivative and the definite
integral as expressed in both parts of the Fundamental Theorem of
Calculus.
- communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems.
- model a written description of a physical situation with a function, a differential equation, or an integral.
- use technology to help solve problems, experiment, interpret results, and verify conclusions.
- determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
- develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishmen.
AP Calculus AB Syllabus
