Goals Of AP-Calculus

Students who are enrolled in AP Calculus AB are expected to

• Work with functions represented in multiple 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 use derivatives to solve problems. 

•  Understand the meaning of the definite integral as a limit of Riemann sums and as the net accumulation of change and use integrals to solve problems.

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

• Communicate mathematics and explain solutions to problems verbally and in writing.

• Model a written description of a physical situation with a function, a differential equation, or an integral.

• Use technology to solve problems, experiment, interpret results, and support 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.