AP Calculus v3.0

*Materials Required* By the end of the course the student will 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 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 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 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