AP Calculus BC Course Outline

Calculus BC can be provided by those schools who are capable to complete all the prerequisites that are required, before the course. Calculus BC is a full-year course in the calculus of functions of a single variable. It consist of all the topics included in Calculus AB and extra additional topics. Both courses represent college-level mathematics for which most colleges grant AP and credit. Calculus BC content is aimed to design, to qualify a student for placement and credit in a course that is one course wider that granted for Calculus AB.

Course Goals: Students should be able to:

  • Work with functions showed in a variety of ways like: Graphical, numerical, analytical, or verbal. You should be able to understand the connections among these representations.
  • Understand the meaning of the derivative in terms of a rate of change and local linear approximation and you should be able to use derivatives to solve a variety of different problems.
  • Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and you should be able to use integrals to solve a variety of different problems.
  • Understand the relationship between the derivative and the definite integral as expressed in parts of the Fundamental Theorem of Calculus.
  • Integrate as well as communicate mathematics both orally and in well-written sentences and you should be able to explain solutions of questions.
  • Model a written description of a physical situation with a function, a differential equation, or an integral.
  • Technological advancement for problem solving, experiment, interpretation of results and verification of conclusions.
  • Determine the reasonableness of solutions like sign, size, relative accuracy, and units of measurement.
  • Appreciation of calculus as a coherent body of knowledge and as a human accomplishment.

The outline for Calculus BC also includes all Calculus AB topics. Topics that are additional are marked with a plus sign ( + ) or an asterisk ( * ). The topics covered in the course are quoted below:

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

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

Polynomial Approximations and Series

  • Concept of Series
  • Series of constants
  • Taylor Series