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