beginning of content:

## About the updated AP Calculus AB course and exam (2016-17 and beyond)

AP Calculus AB is a course in single-variable calculus that includes techniques and applications of the derivative, techniques and applications of the definite integral and the Fundamental Theorem of Calculus. According to surveys of comparable curricula at four-year colleges and universities, it is equivalent to a semester of calculus at most colleges and universities. Algebraic, numerical and graphical representations are emphasized throughout the course. AP Calculus BC is an extension of AP Calculus AB rather than an enhancement; common topics require a similar depth of understanding.

At the conclusion of both courses, students should have the ability to:

• Work with functions represented in a variety of ways — graphical, numerical, analytical, and 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 and explain solutions to problems both verbally and in written sentences.
• Use technology to help solve problems, experiment, interpret results and support conclusions.
• Determine the reasonableness of solutions, including sign, size, relative accuracy and units of measurement.
• Appreciate calculus as a coherent body of knowledge and as a human accomplishment.

## Topics covered on the exam include:

### Functions, Graphs and Limits

• Analysis of graphs
• Limits of functions (including one-sided limits)
• Asymptotic and unbounded behavior
• Continuity as a property of functions

### Derivatives

• Concept of the derivative
• Derivative at a point
• Derivative as a function
• Second derivatives
• Applications of derivatives
• Computation of derivatives

### Integrals

• Interpretations and properties of definite integrals
• Applications of integrals
• Fundamental Theorem of Calculus
• Techniques of antidifferentiation
• Applications of antidifferentiation
• Numerical approximations to definite integrals