The College Board offers two exams in calculus -- Calculus AB and Calculus BC -- that are designed to be paired with courses that introduce the concepts of calculus and provide the opportunity to use its methods and applications. The Calculus BC course is described as an extension of the AB course, and both courses are designed to use technology.
Prerequisite Knowledge and Concepts
The Calculus AB course leaves some room for review of the prerequisite concepts, while the BC course assumes knowledge of all concepts prior to beginning study. Prerequisite skills are drawn from algebra, geometry, trigonometry, analytical geometry and elementary functions. Understanding of functions should include properties, algebra and graphs. Additionally, students should know the language of functions and values of trigonometric functions and their multiples.
Goals for Both AP Calculus Exams
In addition to knowledge of functions, students should learn derivatives and rate of change. Topics in integrals and the relationship between the derivative and the definite integral are also covered on both AP exams. Additionally, students should be able to communicate mathematics in both written and oral form, model a physical situation with a function, differential equation or integral, and use technology to solve, test and interpret results. Finally, students should be able to determine the reasonableness of solutions.
Topics on the Calculus AB Exam
Major topics under the category of functions, graphs and limits include limits of functions, asymptotic and unbounded behavior and continuity as property of functions. Study of derivatives includes the concept of the derivative, derivative at a point, derivative as a function, second derivatives and the application and computation of derivatives. Topics in the study of integrals include interpretations and properties of definite integrals, applications of integrals, the fundamental theorem of calculus, techniques and applications of antidifferentiation and numerical approximations of definite integrals.
Topics on the Calculus BC Exam
The AP Calculus BC exam covers all of the same topics as the AB exam. An additional concept under the category of functions, graphs and limits is parametric, polar and vector functions. The study of the application of derivatives adds Euler's method in differential equations and L'Hospital's Rule in the study of integrals. Additionally, the study of integrals and antidifferentiation includes added and more specific applications. Additional topics in the study of polynomial approximations and series include concept of series, series of constants and Taylor series.
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