Syllabus

AP Calculus AB Syllabus

Overview

The course begins with a review of the three elementary families of functions and operations with functions. The concept and basic processes of finding limits is introduced and then used to develop algorithms to find the instantaneous rate of change (the derivative) of a function, the accumulation of the dependent variable (the integral), and their applications. Emphasis is placed on using the tools of calculus to solve complex problems in preparation for the AP Calculus AB exam.

Resources

Larson, R.E., Hostetler, R.P., and Edwards, B.H. Calculus with Analytic Geometry . 6 th ed. Boston: Houghton Mifflin, 1998

Hughes-Hallett, D., Gleason, A.M., et al. Calculus . 2 nd ed. New York: John Wylie & Sons. 1998

Foerster, P.A. Calculus Explorations . Emeryville, CA: Key Curriculum Press, 1998.

TI 83/84 or TI 89 graphing calculators.

Course Outline

Function Review 2 Weeks

Functions, their graphs, and operations with functions are briefly reviewed.

Limits 3 Weeks

Concept of a limit, properties of limits, existence of limits and one-sided limits, limits and continuity, intermediate value theorem.

Differentiation 3 Weeks

Slope as rate of change, local linearity of curves, limit approach to slope of tangent at a given point, basic rules of differentiation, the chain rule, implicit differentiation.

Application of Differentiation 4 Weeks

Extrema, MVT for differentiation, first and second derivative tests, curve sketching, optimization, related rates.

Integration 5 Weeks

Rules of antidifferentiation, indefinite integrals, particular solutions, integrals as area under the curve, Riemann sums, fundamental theorem of calculus, integration by substitution, integration by parts, trapezoid rule, Simpson's rule.

Transcendental Functions 3 Weeks

Logarithmic and exponential differentiation and integration, inverse functions, bases other than e , applications.

Differential Equations 2 Weeks

Slope fields, separation of variables, particular solutions.

Application of Integration 4 Weeks

Area between curves, volume by disk method, volume by shell method, solids with known cross sections.

Review 5 Weeks

Emphasize topics in the AP exam. Students write problem solving logs when working on complex problems, identifying salient facts, giving reasons for the techniques attempted, and self-evaluating their results. This information is shared and compared with the strategies of other students and the teacher. Evaluations mirror the AP exam.

Instruction Strategy

Instruction is by guided exploration using the texts and other sources with students working sometimes individually, sometimes in small groups, and sometimes as a class. Demonstration of solutions are presented by either students or the teacher and evaluated by the entire class.

Technology

Most of the students have or are supplied with TI 83/84 calculators. Students who have TI 89 are also supported. Over the course of instruction, they will learn to use a broad variety of calculator functions in problem solving and get an introduction to programming, writing their own programs for solving quadratic equations and using the trapezoid method of numerical integration.

Evaluation

Students are evaluated based upon their performance on tests and quizzes as well as written responses to investigations that use calculus concepts to solve real world problems. The tests are a mix of algorithmic calculation, multiple choice questions, and free response questions. The majority of the multiple choice and free response questions come from released AP exams.

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