Calculus BC can be offered by schools that are able to complete all the prerequisites before the course. Calculus BC is a full-year course in the calculus of functions of a single variable. It includes all topics covered in Calculus AB plus additional topics. Both courses represent college-level mathematics for which most colleges grant advanced placement and credit. The content of Calculus BC is designed to qualify the student for placement and credit in a course that is one course beyond that granted for Calculus AB.

Course Goals

Students should be able to:

  • Work with functions represented in a variety of 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 they should 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 change and should 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 should 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.

The topic outline for Calculus BC includes all Calculus AB topics. Additional topics are marked with a plus sign (+) or an asterisk (*). The topics covered in the course include:

  1. Functions, Graphs, and Limits
    • Analysis of Graphs
    • Limits of Functions (incl. one-sided limits)
    • Asymptotic and Unbounded Behavior
    • Continuity as a Property of Functions
    • *Parametric, Polar, and Vector Functions
  2. Derivatives
    • Concept of the Derivative
    • Derivative at a Point
    • Derivative as a Function
    • Second Derivatives
    • Applications of Derivatives
    • Computation of Derivatives
  3. 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
  4. *Polynomial Approximations and Series
    • *Concept of Series
    • *Series of constants
    • *Taylor Series

For more detail on the course topics covered in Calculus BC, see the Course and Exam Description.

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