AP Calculus AB

  •   What is Calculus?

    Welcome to AP Calculus AB.  AP Calculus AB is a year long course designed to prepare you for the AP Calculus AB Exam in early May.  The course will be taught with a balanced approach using a "Rule of Four:  Numerical Analysis, Graphical Analysis, Analytic/Algebraic Analysis, and Verbal/Written Analysis." 

    Here are the units that we will study:

     1.  Limits and Continuity (3 - 4 weeks)

    Rates of Change

    Limits at a Point

    Limits Involving Infinity

    Discontinuity

    Rates of Change and Tangent Lines

      2.  The Derivative (5 - 6 weeks)

    Derivative of a Function

    Differentiability

    Rules for Differentiation

    Applications of the Derivative

    Derivatives of Trigonometric Functions

    The Chain Rule

    Implicit Differentiation

    Derivatives of Inverse Trigonometric Functions

    Derivatives of Exponential and Logarthmic Functions

    3.  Applications of the Derivative (3 - 4 weeks)

    Extreme Values

    Implications of the Derivative (Theorems about Continous and Differentiable Functions)

    Connecting f' and f" with the graph of f(x).

    Optimization Problems

    Linearization Models

    Related Rates

    4.  The Definite Integral (3 - 4 weeks)

    Approximating Areas

    Accumulation Functions

    Properties of Definite Integrals

    The Fundamental Theorem of Calculus

    5.  Differential Equations and Mathematical Modeling (3 - 4 weeks)

    Slope Fields

    Antiderivatives

    Integration using U-substitution

    Integration by Parts

    Separable Differential Equations

    Logistic Growth

    6.  Applications of Definite Integrals (3 weeks)

    Integral as Net Change

    Area Between Curves

    Calculating Volume

    7.  Review / Test Preparation (3 - 5 weeks)

            Multiple Choice Practice

            Free-Response Practice

    8.  After the Exam (4 - 5 weeks)

    Limits of Sequences & Series, Taylor and MacLaurin Polynomials

    Review/Research Projects

    Advanced Integration Techniques

    College Math Requirements and Expectations

    Review for Local Exam