For use with AP® Courses

AP Calculus is a full-year, high school credit course that is intended for the student who has successfully mastered a minimum of four high school level mathematics courses that cover analytical and conceptual algebra (with heavy emphasis on functions), coordinate and plane geometry, and trigonometric functions. It is highly recommended that the student successfully complete pre-calculus as a prerequisite. The course primarily focuses on the skills and methods of analyzing graphical behavior of functions, the definition of a derivative as well as applications of derivatives, integration and their relationships with the graphical function.

Upon successfully completing the course, the student should have mastered the following concepts:

  • Perform operations on functions including composition and inverses.
  • Using calculation and estimation to evaluate limits.
  • Analyze infinite limits and the correlation between their values and the graph's behavior; estimate and understand discontinuity and continuous functions.
  • Compute the derivative of a function using the power rule, product and quotient rule, chain rule and all trigonometric rules.
  • Use the concept of a derivative to interpret a function's rate of change and continuity; construct the equation of a line tangent to a curve; evaluate the intervals for which a function is increasing or decreasing.
  • Interpret the Mean Value Theorem.
  • Evaluate the second derivative and find the points of inflection.
  • Utilize the derivative through application problems involving area under a curve, velocity, acceleration and speed.
  • Evaluate a definite integral using the Fundamental Theorem of Calculus, Riemann Sums, and the rate of change formula.

Some assignments in this course require the use of resources that must be supplied by the user. These outside resources are listed below by assignment.

Suggested Resources for Teachers:

  • Complete Solutions Guide, Volume 1, by Bruce H. Edwards (University of Florida), ISBN-10: 0618149317
  • Complete Solutions Guide, Volume 2, by Bruce H. Edwards (University of Florida), ISBN-10: 0618149325
  • Instructor's Resource Guide, by Ann Rutledge Kraus (The Pennsylvania State University, The Behrend College), ISBN-10: 0618149309


AP* can change your life. Through college-level AP* courses, you enter a universe of knowledge that might otherwise remain unexplored in high school; through AP* Exams, you have the opportunity to earn credit or advanced standing at most of the nation's colleges and universities. —from the AP* Web page at

The AP* program is administered by the College Board to provide college-level courses and college credit for advanced high school students. You can learn more about The College Board and the AP* at its Web site, which includes study suggestions and sample questions for the English Language and Composition exam offered each spring. Find these at:

State: National, California, Florida, Georgia, New York, North Carolina, Oklahoma, Texas, Utah, Washington
Grade Level: 11, 12
Category: Advanced Placement
Course Length: Year