AP Calculus courses are primarily concerned with developing students’ understanding of calculus concepts and providing experience with its methods and applications. The curriculum emphasizes a multi-representational approach, with concepts, results, and problems expressed graphically, numerically, analytically, and verbally. Establishing connections among these various representations is a fundamental priority of the coursework.
Calculus BC is an extension of Calculus AB rather than an enhancement; common topics require a similar depth of understanding, and both courses are intended to be challenging and demanding.
The focus of the courses is on broad concepts and widely applicable methods rather than the mere manipulation or memorization of an extensive taxonomy of functions, curves, theorems, or problem types. Although facility with manipulation and computational competence are important outcomes, they do not constitute the core of the curriculum. Students and teachers use technology regularly to reinforce the relationships among multiple representations of functions, confirm written work, implement experimentation, and assist in interpreting results. Through the use of unifying themes—including derivatives, integrals, limits, approximation, and applications and modeling—the course becomes a cohesive whole developed using the functions listed in the prerequisites.