North Carolina Association of Advanced Placement Mathematics Teachers

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North Carolina Association of
Advanced Placement Mathematics Teachers

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A more current index to Free-Response Questions by topic can be found in the Excel file posted at the site for Howell & Montgomery's Be Prepared for the AP Calculus Exam (Skylight Publishing).
 
Calculus AB           Calculus BC

Prepared by Earl Mitchelle & Patricia Morris

Calculus BC  

04 03 02 01 00 99 98 97 96 95  
Functions and Graphs


Domain and Range


 

 

 

 

X

 

X

 

 

X
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Odd & Even

                   

Intercepts

                   

Calculus BC  

04 03 02 01 00 99 98 97 96 95  
Limits and Continuity


Finite Limits


 

 

 

X

 

 

 

 

 

 
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Limits At Infinity Infinite Limits

        X   X X X  

Definition of Continuity

                   

Calculus BC  

04 03 02 01 00 99 98 97 96 95  
Differential Calculus


Definition of the Derivative


 

 

 

 

 

 

 

 

 

 
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Analyze a Function Given as a Table of Values

      X            

Tangent/Normal Line Equations

  X   X X X   X X  

Derivatives of Composite Functions (Chain Rule)

      X     X      

Increasing & Decreasing Functions

  X X X   X X X    

Critical Numbers

    X X X X X X    

Concavity

  X X X   X       X

Inflection Points

  X       X   X X X

Average Rate of Change & Instantaneous Rate of Change

X   X     X   X X  

Extreme Values

    X X   X X X    

Higher Order Derivatives

              X    

Optimization Problems: Maximum & Minimum Values, Relative & Absolute

    X     X     X X

Curve Sketching using Information from a Table of Values of f(x), f'(x), f''(x), or from a Graph of f'(x)

    X X   X   X    

Mean Value Theorem For Derivatives

          X        

Implicit Differentiation

X       X          

Linear Approximation

      X   X        

Related Rates

  X               X

Calculus BC  

04 03 02 01 00 99 98 97 96 95  
Integral Calculus


Area and/or Interpretation


X

X

X

 

X

X

X

X

 

X
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Riemann Sums Using Left, Right, & Midpoint Evaluation Points

          X        

Properties of Integrals

  X X     X       X

Trapezoidal Rule

      X         X  

Fundamental Theorems

  X X     X X X   X

Mean (Average) Value

X   X X   X X   X  

Volumes of Solids: Disks & Washers

X X X   X X X   X X

Volumes with Known Cross-Sections

  X     X     X    

Rectilinear Motion: Equations for Position, Velocity, & Acceleration; Direction Of Motion; Total Distance

        X          

Rectilinear Motion: Analysis from a Graph

      X X          

Definite Integral as an Accumulator

X X X   X X X   X  

Work*

                X  

Calculus BC  

04 03 02 01 00 99 98 97 96 95  
Calculator


Draw a Graph in a Given Window


 

 

 

 

 

 

X

X

X

X
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Find the Intersection Points of Two Graphs

  X     X     X   X

Evaluate A Definite Integral

  X X   X X X X X  

Evaluate A Derivative

X   X X   X        

Calculus BC  

04 03 02 01 00 99 98 97 96 95  
Methods of Integration


Integration by Parts


 

 

 

 

 

 

 

 

 

 
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Integration by Partial Fractions

                   

Improper Integrals

      X         X  

Calculus BC  

04 03 02 01 00 99 98 97 96 95  
Sequences and Series


Tests for Convergence


 

 

 

 

X

 

X

 

X

 
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Geometric Series

      X            

Alternating Series & Error Approximation

  X     X          

p-Series

                   

Manipulation of Power Series

X X X X     X X X X

Power Series: Radius of Convergence

        X   X      

Power Series: Interval of Convergence

    X X            

Maclaurin Series

  X X       X   X  

Taylor Series

X   X   X X X X   X

Lagrange Error Bound

X         X        

Derivatives of Vector & Parametrically Defined Functions

X X X X X X X X   X

Tangent Lines to Parametrically Defined Curves

X X   X X          

Arc Length, Including Parametrically Defined Curves

              X   X

Velocity & Acceleration Vectors for Motion on a Curve

X   X   X X X X    

Polar Coordinate Graphs

  X                

Area & Polar Curves

  X                

Calculus BC  

04 03 02 01 00 99 98 97 96 95  
Differential Equations


Solving Differential Equations by Separation of Variables


 

X

 

X

X

 

X

X

 

 
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Logistic Differential Equations

X                  

Slope Fields

    X   X   X      

Euler's Method

    X X   X X