## AP Calculus BC

This is a collection of worksheets I use in my BC Calculus classes. They are all to be done in class, where I can offer help and clarification. They are not intended to stand entirely on their own.

Most importantly, I want students to think mathematically about the concepts behind calculus, and I want them to talk to each other about their understanding of the ideas, and about problems they are having. To encourage this, much of the learning of new material in class is done by means of the worksheets in this collection. In some cases, such as the Intro to Concavity, a worksheet simply introduces a concept, and its purpose is to make students see the issue, the need for a new approach, or the basic concept behind the method. In other cases, such as for the introductory study of limits, a sequence of worksheets includes many different situations, notations, and a variety of problems. In either case, the worksheets guide students through a sequence of problems and questions. After students complete worksheets, clarifications and extensions are considered in class. Frequently, we return to the textbook for more practice on each topic.

Some of my colleagues at IMSA use these worksheets—some have even created their own versions, and all of them have gone through multiple edits over the years based on comments, questions, and suggestions from my colleagues and my students. I’d like to thank my colleagues Dr. Don Porzio, Dr. Micah Fogel, Dr. Janice Krouse, and Mr. George Milauskas for their valuable feedback.

We currently use Calculus, Single Variable, 5th edition, Hughes-Hallett, Gleason, McCallum, et al. ISBN 978-0470-08915-6, John Wiley & Sons

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Browse the *AP Calculus BC* Collections:

A Simple Introduction to Rates

A few quick worksheets to introduce graphically the idea of rates of change – from position to velocity and from velocity to position. Teacher’s notes are included.

Limits

A collection of 6 worksheets that introduces basic types of limits and continuity.

More on Derivatives

Measuring Speed, an introduction to concavity, and the derivative of *b ^{x}*.

Integrals

Riemann sums, trapezoidal sums, and properties of integrals.

Series

Note: Before worksheet Series 1, we explore the graphs and the derivatives at x = 0 of the functions ƒ(x) = sinx, g(x) = x, and h(x) = x – x3/6. Then we create the fourth-degree polynomial to fit ƒ(x) = cosx by setting the appropriate derivatives equal at x = 0.

Differential Equations

We introduce slope fields, Euler’s Method, and solutions by separation of variables. Then we strengthen these ideas when looking at models.