AP Calculus

AP Calculus

 

AB Scope and Sequence                 BC Scope and Sequence

 

**Proficiency rubrics for each Reporting Strand can be found by clicking on the underlined links,** 

 or by using the Rubric Assembler

 

Limits

  • 1.1  The concept of a limit can be used to understand the behavior of functions.
  • 1.2  Continuity is a key property of functions that is defined using limits.

 

 

 

Derivatives

  • 2.1 The derivative of a functions is defines as the limit of a difference quotient and can be determined using a variety of strategies.
  • 2.2 The Mean Value Theorem connects the behavior of a differentiable function over an interval to the behavior of the derivative of that function at a particular point in the interval. 

 

 

 

Derivative Application

  • 3.1 The derivative has multiple interpretations and applications including those that involve instantaneous rates of change.
  • 3.2 A function’s derivative, which is itself a function can be used to understand the behavior of the function.  

 

 

 

Integrals

  • 4.1 Antidifferentiation is the inverse process of differentiation
  • 4.2 The definite integral of a function over an interval is the limit of a Riemann sum over that interval and can be calculated using a variety of strategies
  • 4.3 The Fundamental Theorem of Calculus, which has two distinct formulations, connects differentiation and integration

 

 

 

Integral Application

  • 5.1 The definite integral of a function over an interval is a mathematical tool with many interpretations and application involving accumulation. 
  • 5.2 Antidifferentiation is an underlying concept involved in solving separable differential equations.  Solving separable differential equations involves determining a function or relation given its rate of change.

 

 

 

Series

  • 6.1  The sum of an infinite number of real numbers may converge
  • 6.2  A function can be represented by an associated power series over the interval of convergence for the power series.

 

 

 

Polar, Parametric and Vectors

  • Use polar, parametric and vectors functions with derivatives and  integrals

 

 

 

AP Synthesis

  • Cumulative Assessment and Application of Standards