AP Calculus (BC) is similar to the AP Calculus (AB) course except that it covers approximately 40% more material: effectively two semesters of university–level calculus. It is expected that students pursuing this course would  write the Advanced Placement examination in May. This course is even faster paced than the Calculus AB course and consequently requires an even greater commitment from the student. Only the very strongest students of mathematics should consider enrolling on this extremely demanding course.

Course Goals

• 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.

Topics

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