AP Calculus

Students should be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations. Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation, and should be able to use derivatives to solve a variety of problems. Students should understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change, and should be able to use integrals to solve a variety of problems. Students should understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus. Students should be able to communicate mathematics and explain solutions to problems both verbally and in written sentences. Students should be able to model a written description of a physical situation with a function, a differential equation, or an integral. Students should be able to use technology to help solve problems, experiment, interpret results, and support conclusions. Students should be able to determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement. Students should develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.

The AP Calculus AB exam is 3 hours and 15 minutes long. Section I lasts 1 hour and 45 minutes, and has 45 multiple-choice questions. Section II lasts 90 minutes and has 6 free-response questions. Each section is divided into two parts with separate time limits. Section I, Part A is 1 hour with 30 multiple-choice questions. A calculator is not required for this part. Solve each of the following problems. After examining the form of the choices, select the best answer to each question. Section I, Part B is 45 minutes with 15 multiple-choice questions. A graphing calculator is required for this part. Solve each of the following problems. After examining the form of the choices, select the best answer to each question. Section Directions–Section II Part A is 30 minutes with 2 free-response questions. A graphing calculator is required for this part. On this section, you will answer each question in multiple parts, shown on separate pages. You are advised to spend approximately 15 minutes on each question. You may use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Section II, Part B is 60 minutes with 4 free-response questions. A calculator is not required for this part. On this section, you will answer each question in multiple parts, shown on separate screens. You may move back and forth among the parts of the question you are answering, but once you answer the last part of the question and go on to the next one, you cannot go back to any part of the question you finished. You are advised to spend approximately 15 minutes on each question.

Topics covered after the AP Calculus AB exam include, but are not limited to the following topics: Advanced Integration Techniques (U-DV, Tic-Tac-Toe, Trig. Powers, Trig. Substitution, Long Division, Partial Fractions, Improper Integrals); More Applications of the Integral (Arc Length, Center of Mass, Density, Area of Polar Equations, Area of Parametric Function); and Sequences and Series (Geometric, Ratio Test, P-Test, Taylor Series, MacLauren Series)