It Will Also Be an Approved Advanced Placement Course Preparing Students for the Calculus

AP Calculus 2017-2018 Mr. Suydam Room 224 [email protected]

This class is designed to follow the requirements of the University of Missouri-St.Louis’s Calculus I course (MATH 1800). This course provides an introduction to differential and integral calculus. Topics include limits, derivatives, related rates, Newton’s Method, the Mean- Value Theorem, Max-Min problems, the integral, the Fundamental Theorem of Integral Calculus, areas, volumes, and average values. It will also be an approved Advanced Placement course preparing students for the Calculus AB test.

Assignments Participation – Homework will be assigned at the end of every section covered. It will not be turned in. A small quiz will be administered to check for accuracy. These quizzes will be open notes, but not open book. Steps must be shown. Questions from previous sections are fair game for these quizzes. Summative – Each chapter will have a test at the end covering the entire unit. Some units may have a midtest worth half as many points as a test. Retakes are not available for dual credit classes. Questions from the test or midtest will model those found on the quizzes. Final (20% of the semester grade) – The final will be cumulative over the entire semester. Questions will model those found on the tests. The second semester final is under the purview of the University of Missouri-St.Louis.

Materials Pencil Paper Binder or notebook Folder to keep homework or tests Chromebook with charger Textbook – Rogawski’s Calculus for AP 2nd edition Calculator (allowed at certain times but not necessary) (Type of calculator needs to be pre- approved.)

Make-Up Work Schedule make-up tests and quizzes as soon as possible.

Rules Respect others 1) Continuous and discontinuous functions, Intermediate value Theorem (September 22 – October 4)

2) Limits, definition, limit theorems, limits of trigonometric Functions. (October 3 – October 18)

3) Differentiation, basic theorems and formulas, derivatives of trigonometric functions, chain rule and implicit differentiation, slopes of tangent lines (October 19 –November 13)

4) Related rate problems, linear approximations and differentials (November 14 – December 15)

5) Extreme value theorem, mean value theorem, theory of maxima and minima and concavity, with examples (January 3 – January 25)

6) Limits at infinity and asymptotes, graphing functions using methods of calculus (January 26 – February 2)

7) Optimization problems and Newton’s method of approximation (February 5 – February 14)

8) Anti-derivatives and Riemann sums. Definition of the Riemann integral and Fundamental Theorem of Calculus (February 15 – March 9)

9) Evaluating definite and indefinite integrals, method of substitution (March 12 – April 12)

10) Applications of the method of Riemann sums to finding areas between curves, finding volumes of solids including solids of revolution, work done by a force, average values of functions (April 13 – May 7)

What the student will learn in the course:  Understand the theory of limits, continuity, differentiation  Become proficient in using the techniques of differentiation  Obtain the ability to apply differentiation to solve related rates and optimization problems  Understand the concept of a Riemann integral and the use of the Fundamental Theorem of Calculus to calculate Riemann integrals  Use of the method of Riemann sums to find areas, volumes and other geometric and physical quantities  Develop a proper writing style for solutions of mathematical problems