### Calculus

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.

AP^{® }IS A REGISTERED TRADEMARK OF THE COLLEGE BOARD®, WHICH WAS NOT INVOLVED IN THE PRODUCTION OF, AND DOES NOT ENDORSE, THIS PRODUCT.

**State:**National

**Grade Level:**9, 10, 11, 12

**Category:**Advanced Placement

**Course Length:**Year