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 AB  

04 03 02 01 00 99 98 97 96 95  
Functions


Zeros


 

 

 

 

 

 

 

X

 

 

 

Asymptotes

                  X

Symmetry

                   

Domain

        X         X

Odd/Even

                   

Range

        X   X     X

Inverse

                   

Limits

            X X    

Linear Equation

              X    

Continuity

  X X              

Calculus AB  

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


Analyze a Function Given as a Table of Values


 

X

 

 

 

X

X

 

 

 
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Tangent Line Equation

  X X X X X X X X X

Differentiation & Evaluation

  X X X   X        

Increasing & Decreasing Functions

X X X X            

Critical Numbers, Maximum & Minimum Points--Relative & Absolute

X   X X X X X X X X

Concavity

  X X X            

Inflection Points

      X   X   X X  

Average Rate of Change

X     X       X    

Critical Numbers, Maximum & Minimum Points, Increasing & Decreasing, Concavity, Inflection Points from the Graph of f'(x)

X X X   X       X X

Critical Numbers, Maximum & Minimum Points, Increasing & Decreasing, Concavity, Inflection Points from a Table of Values of f(x), f'(x), & f"(x)

    X              

Curve Sketching Using Information from a Table of Values Of f(x), f'(x), and f"(x) or from the Graph of f'(x)

    X         X X  

Mean Value Theorem For Derivatives

    X         X    

Implicit Differentiation

X       X   X     X

Linear Approximation

    X X     X     X

Related Rates

  X X     X     X X

Calculus AB  

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

Area & Interpretation


X

X

X

X

X

X

X

X

X

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

  X       X X      

Properties Of Integrals

  X 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 X  

Volumes of Solids Disks & Washers

X X X X X X X X X X

Volumes With Known Cross-Sections

X X     X       X  

Solving Differential Equations: Separation of Variables

  X   X X X X X    

Drawing Slope Field from Differential Equation

X                  

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

X X X   X X   X   X

Rectilinear Motion: Position, Velocity, & Acceleration; Total Distance from the Graph of Velocity

        X   X      

Rectilinear Motion Analysis from a Graph

      X            

Definite Integral As An Accumulator

X X X   X X X   X  

Accumulation of the Derivative with Initial Condition

X X                

Integration by Parts

                  X

Calculus AB  

04 03 02 01 00 99 98 97 96 95  
Calculator


Draw a Graph In a Given Window


 

 

X

 

 

 

X

X

X

X
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Find the Zeros of a Function

    X         X   X

Find The Intersection Points Of Two Graphs

X X   X X          

Evaluate a Definite Integral

X X X   X X X      

Evaluate a Derivative

X X X X   X