AP Calculus AB

Credit Hours: 1.0

Course Length: 2 Semesters

Course Description

The Advanced Placement Calculus AB course is equivalent to the Calculus I college-level course. The rigor and pace of this course is consistent with calculus offerings at many colleges and universities and will prepare students for the Advanced Placement Exam. Upon successful completion of the exam, students may receive college credit and will be well-prepared for additional advanced mathematics coursework.

AP® Calculus AB builds upon prior knowledge in previous mathematics course work. Students will explore topics within the three big ideas covered in the course: (1) limits, (2) derivatives, and (3) integrals. This course allows students to gain conceptual understanding through discussions, group activities and investigations. Students will learn how to use the graphing calculator to help solve problems, experiment, interpret results, and support conclusions. In order to prepare for the exam, students will complete weekly AP® practice quizzes and unit exams that will conform to the constraints of the AP® exam.

Course Prerequisites

Students should complete four years of secondary mathematics designed for college-bound students. These courses should explore topics in algebra, geometry, trigonometry, analytic geometry, and elementary functions. Students should be familiar with the properties of these elementary functions, which include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions.

Required Textbook(s) and/or Materials

Students must have access to a graphing calculator (preferably a TI-83/TI-84) and a word processing program (Google Docs or Microsoft Word).

Major Concepts

According to the College Board, students who are enrolled in AP® Calculus AB will be able to:

  • Work with functions represented in multiple ways: graphical, numerical, analytical, or verbal.
  • Understand the meaning of the derivative in terms of a rate of change and local linear approximation and use derivatives to solve problems.
  • Understand the meaning of the definite integral as a limit of Riemann sums and as the net accumulation of change and use integrals to solve problems.
  • Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
  • Communicate mathematics and explain solutions to problems verbally and in writing.
  • Model a written description of a physical situation with a function, a differential equation, or an integral.
  • Use technology to solve problems, experiment, interpret results, and support conclusions.
  • Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
  • Develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.