Syllabus and Course Requirements
Course: AP Calculus AB
Instructor: Ben Stevens
Primary Textbook: Calculus, James Stewart, 5th edition, pub. 2003
Supplemental Textbook: The Essentials of Calculus, Shaw and Taylor, 2015
Course Description: This is a one-year course in calculus designed to be the equivalent of that
taken at a university or college. Students who are successful in this course will be ready for
their second semester of collage calculus. Topics to be covered include Function Analysis,
Limits, Derivatives, Integrals, Applications of Derivatives and Integrals, and the calculus of
inverse functions. Assignments and exams will be focused on success on the AP exam in
May, with particular emphasis on calculator skills and how to respond to the open-ended
questions on the exam.
Each exam will be in AP format, consisting of a multiple-choice section and an openended section. Exams will consist of previous AP exam questions as well as other questions
of a similar level of difficulty. After we finish the coursework we will do a full-scale practice
exam, using an actual AP exam from a previous year, to be done in the same time frame and
graded on the same scale as the AP exam.
Course Objectives and Timeline:
First Quarter
1. Calculate and discuss limits using both algebraic techniques and the technical definition.
2. Have a thorough understanding of a variety of functions, including Polynomial,
Trigonometric, Exponential, Logarithmic, and inverse Trigonometric functions. Analysis on
these families of functions will be done via algebraic techniques, graphing calculators, and
numerical analysis, such as data tables.
3. Understand the Derivative as a limit.
4. Understand the Derivative as a rate of change.
5. Understand the importance of the mean value theorem and the intermediate value theorem.
6. Use the derivative to calculate extreme values, related rates, and perform function analysis.
7. Be able to apply the theory of inverse functions to differentiation, and calculate derivatives of
inverse functions.
8. Use first and second derivative to perform analysis of the graph of a function, including
finding extrema, increasing and decreasing intervals, concavity, and inflection points. Both
the use of intervals and the second derivative test will be required to justify answers.
Second Quarter:
9. Be able to quickly differentiate a variety of functions, including polynomial, trigonometric,
exponential, logarithmic, and inverse trigonometric functions.
10. Be able to apply Newton’s Method of finding roots of functions.
11. Be fluent in their use of graphing calculators to supplement the evidence from analysis, to
solve equations, and to perform non-trivial calculations. Limitations of calculator use and
“hidden behavior” of functions will be emphasized.
12. Understand the Integral as a Riemann sum.
13. Understand the Integral as a signed area function.
Third Quarter:
14. Understand the relationship between the derivative and the integral as shown by the
Fundamental Theorem of Calculus.
15. Be able to integrate a variety of functions by applying known derivatives.
16. Be able to evaluate an integral by using substitution of variables, including a change of
limits in definite integrals.
17. Use the Integral to calculate areas, surface areas, arc lengths, and volumes of appropriately
defined regions.
18. Use the Integral of a rate of change to calculate a total quantity.
Fourth Quarter:
19. Be able to calculate definite integrals to the appropriate accuracy by using a graphing
calculator, and know when such a technique is appropriate.
20. Be able to solve first order separable differential equations by integrating.
21. Be able to apply their knowledge of calculus to a variety of applications in physics, the
natural sciences, and finance.
22. Extended review and practice exams.
Instructional Activities and Procedures: Each day will begin with time to ask questions about
and discuss the previous assignments. Students must take responsibility for asking all the
questions they need to ask in order to understand the material. The new material will be
introduced, with examples and discussion as appropriate, followed by supervised practice.
Students are encouraged to collaborate with one another on difficult problems, and are required
to participate in classroom discussions. There will be occasional group problem-solving activities
to supplement textbook assignments. These activities will emphasize the use of calculators to
experiment or otherwise gain insight into the solution of problems via the use of graphs, data
tables, and the numerical integration and differentiation capabilities of the calculators.
Student Requirements: Each student is required to:
1. Bring a three-ring binder with a supply of paper, pencils, and textbook each day the class
meets
2. A TI-83 OR HIGHER CALCULATOR IS ABSOLUTELY ESSENTIAL, AND MUST
BE BROUGHT TO CLASS EACH DAY.
3. Complete all assignments on time and in a well-organized and legible manner.
4. Successfully complete all tests and quizzes, and final exams.
5. Assume responsibility for learning. Students must ask questions as necessary.
6. Contribute to a class atmosphere of curiosity and cooperation. Aggressive or rude
behavior, tardiness, or arriving unprepared for class violates this requirement.
Evaluation: Quarter grades will be based on a combination of tests, homework, and class work.
Tests will be 33% of the grade, homework 33%, and class work 33%. The semester grade
will be 45% first quarter, 45% second quarter and 10% semester exams.
Homework: Homework assignments will be made on most days, with time allowed in class to
begin and to make sure the students understand the material sufficiently well to finish on
their own. It is the student’s responsibility to ask about any assignments missed due to an
excused absence, and to make them up in a reasonable amount of time, for full credit.