AP Calculus AB

Electronic copy of 1st Day of School Packet: Click HERE to download a copy of the Welcome Letter, Supply List and Course Syllabus.

***Non-secure class documents can be found on the documents page. Secure class documents (Lesson handouts, Power Point presentations, solutions, etc) can be found on Google Classroom***

Text:

  • Finney, Demana, Waits, and Kennedy. Calculus: Graphical, Numerical, Algebraic,4th ed. New Jersey: Prentice Hall, 2011.

  • Briggs, Cochran, and Gillet. Calculus: Early Transcendentals, 2nd ed. Boston: Pearson, 2015

Course Objectives: Students should be able to:

  • to satisfactorily pass the AP EXAM.

  • work with functions represented in a variety of ways: graphically, numerically, analytically, or verbally. They should understand the connections among these representations.

  • understand the meaning of the derivative in terms of a rate of change and local linear approximation.

  • use derivatives to solve a variety of problems.

  • understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of a rate of change.

  • use integrals to solve a variety of problems.

  • understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.

  • communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems.

  • model a written description of a physical situation with a function, a differential equation, or an integral.

  • use technology to help solve problems, experiment, interpret results, and verify 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.

Topics Covered:

  • Functions, Graphs, and Limits

    • Analysis of Graphs

    • Limits of Functions (including one-sided limits)

    • Asymptotic and unbounded behavior

    • Continuity as a property of functions

  • Derivatives

    • Concept of a derivative

    • Derivative at a point

    • Derivative of a function

    • Second Derivatives

    • Application of Derivatives

    • Computation of Derivatives

  • Integrals

    • Interpretations and properties of definite integrals

    • Application of integrals

    • Fundamental Theorem of Calculus

    • Techniques of antidifferentiation

    • Application of antidifferentiation

    • Numerical approximation to definite integrals