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AP Calculus

Course Description


This course is equivalent to first semester college calculus in the calculus sequence. The major topics are the limit process, differential and integral calculus. Special emphasis is

given to the properties of functions and their derivatives, differentiation vs. antidifferentiation, and the analysis of moving objects. Applications from physics are studied.

Course Goals


Students should be able to:
  • Work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal and understand the connections among these representations.
  • Understand the meaning of the derivative in terms of a rate of change and local linear approximation and 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 a rate of change and 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 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 accomplishment.