AP Calculus

Scope and Sequence and Rubrics

Limits

• 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

Derivatives

• 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

Integrals

• 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 Application

• 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

Series

• 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