AP Calculus BC is a full-year course designed to develop a student’s understanding of the concepts of calculus and to provide experience with its methods and applications. Calculus BC includes all the AB material at the same conceptual level plus additional material to round out a year of college calculus. These additional topics include parametric, polar, and vector functions and infinite sequences and series. The course follows the AP Calculus syllabus as described by the College Board, and all students take the advanced placement exam at the end of the second semester. Essential Questions 1. How is calculus different from the mathematics a student has studied previously? 2. How are the ideas of the area under a curve and the tangent to a curve related to each other? 3. How is it that the concept of a limit arises throughout the study of calculus? Skills Benchmarks 1. Students should recognize calculus as a valuable tool, with the concept of "limit" at its core. 2. Students should have a clear understanding of functions and should be comfortable working with functions represented in various ways: graphs, charts, analytical, or verbal. 3. Students should understand the meaning of the derivative as a rate of change. 4. Students should understand that a definite integral is a limit of Riemann sums and that it is an accumulation of a rate of change. 5. Students should understand that derivatives and integrals are inverses as stated in the Fundamental theorem. 6. Students should be able to model a written description of a physical situation with a function, differential equation, or an integral. 7. Students should be able to analyze, process, and interpret real-world data with various features of the graphing calculator
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