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In 2016-17, updates to the AP Calculus BC course and exam take effect. For more information about the changes, visit AP Central.

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

AP Calculus BC is a course in single-variable calculus that includes all the topics of AP Calculus AB (techniques and applications of the derivative, techniques and applications of the definite integral and the Fundamental Theorem of Calculus) plus additional topics in differential and integral calculus (including parametric, polar and vector functions) and series. According to surveys of comparable curricula at four-year colleges and universities, it is equivalent to at least a year (two semesters) 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 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 and explain solutions to problems both verbally and in written sentences.
  • 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 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
  • Parametric, polar and vector functions


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


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

Polynomial Approximations and Series

  • Concept of series
  • Series of constants
  • Taylor series

Read the full course and exam description and exam information with sample questions.