AP Calculus


    Scope and Sequence and Rubrics

    District Course Description

    Assessment Dates  Problem Solving Rubric



    • Estimate limits of functions graphically and numerically
    • Determine limits of functions algebraically
    • Apply concepts of continuity (including the intermediate value theorem)
    • Applying the definition of derivative


    • Calculating and estimating derivatives
    • Calculate derivatives using chain rule
    • Applying the Mean Value Theorem

    Derivative Application

    • Solving problems involving rectilinear motion
    • Solve problems involving related rates
    • Solve problems involving optimization
    • Use derivatives to analyze properties of a function
    • Analyze various representations of functions using derivatives


    • Recognize antiderivatives of basic functions
    • Recognize antiderivatives of advanced functions
    • Approximate a definite integral
    • Calculate a definite integral using areas and properties
    • Use the Fundamental Theorem of Calculus to analyze functions
    • Evaluate an improper integral or show that an improper integral diverges, using L’Hopital when appropriate.

    Integral ApplicationIntegral

    • Use and interpret the definite integral to solve problems in various contexts
    • Estimate solutions to differential equations using Euler’s method and slope fields.
    • Apply definite integrals to problems involving motion
    • Apply definite integrals to problems involving area and volume
    • Analyze differential equations and obtain general and specific solutions including logistic functions


    • Determine whether a series converges or diverges
    • Construct & use Taylor polynomials
    • Determine or estimate the sum of a series using error
    • Write a power series representing a given function and determine the radius and interval of convergence of a power series

    Polar, Parametric and Vectors

    • Calculate the derivatives of vectors, parametric, and polar functions
    • Use derivatives to analyze the particle motion using vectors and parametric functions
    • Use the definite integrals to find the distance & position of a particle moving along a curve given by a parametric of a vector values functions
    • Find the area bounded by a polar curve and arc length of a curve defined parametrically

    AP Synthesis

    • Cumulative Assessment of Standards