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 School District U46
 Curriculum
 High School
 AP Calculus
AP Calculus

**Proficiency rubrics for each Reporting Strand can be found by clicking on the underlined links, or by using the Rubric Assembler**
Scope and Sequence and Rubrics
District Course Description
Assessment Dates Problem Solving Rubric
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