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Calculus BC Course Perspective
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by Dan Kennedy
Baylor School
Chattanooga, Tennessee
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| | Please note: The official College Board® Course Description is available below in "More."
A Deeper Understanding of Calculus Concepts
Calculus BC is a course in single-variable calculus that includes all the topics of Calculus AB (techniques and applications of the derivative, techniques and applications of the definite integral, and the Fundamental Theorem of Calculus) plus additional topics in differential and integral calculus (including parametric, polar, and vector functions) and series. It is equivalent to at least a year of calculus at most colleges and universities. Algebraic, numerical, and graphical representations are emphasized throughout the course.
So that students might better appreciate the connections among various representations, it is assumed that they will have access to graphing calculators in class and on homework. To that end, and to shift the emphasis from mere computation to a deeper understanding of concepts, graphing calculators are required on portions of the AP Examination.
Prerequisites for the student include two years of algebra and a year of geometry, plus a strong grounding in elementary functions and their graphs, including trigonometry (usually gained in an additional course called precalculus or college algebra). Some schools precede Calculus BC with an accelerated precalculus course that covers some of the early topics in differential calculus, thereby freeing up more time for BC topics in the following year. Attitude prerequisites include a willingness to work both in and out of class, a willingness to collaborate with classmates to foster mutual understanding, and a sincere intent to place out of the first year of college calculus rather than repeat it.
Prerequisites for the teacher include a good understanding of calculus, a willingness to teach and learn from good students, and (if possible) the ability to attend a College Board® AP workshop or Summer Institute to communicate the goals of the course.
Although the goal for students should be to learn calculus rather than to succeed on a single assessment, the desire to do well on the AP Examination can be a strong motivation for students and an exploitable resource for teachers. It is recommended that teachers obtain copies of old AP Examinations (from colleagues or from the College Board), learn how they are graded, and hold students to that level of performance throughout the course.
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