Writing an AP Calc Assessment 

• Include calculator and non-calculator items

• Include multiple choice and free response items

• Write questions that reflect learning targets and success criteria

• Determine scoring rubric for FRQs before administering the assessment (see below)

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Questions to Include

• Determining the concavity of a curve given data in various formats (equation of f(x), graph of f’(x), tabular data), with proper justification

• Determining the relative extrema of a function given data in various formats (equation of f(x), graph of f’(x), tabular data), with at least one question requiring the use of the Second Derivative Test as justification

• Finding absolute extrema given an equation of a function; students must use the Candidates test to justify their answer

• Sketch a possible graph of f(x) given a graph of f’(x)

• Conceptual questions requiring students to identify relative extrema or concavity from equations involves unknown constants a and b
   

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Grading Tips

We recommend that you prepare a rubric for the free response items before you begin grading your quizzes or tests. Know what information is necessary for a complete and correct response and award points when a student presents that information. Many of the “Why did I get marked down?” questions are eliminated when you share the components that earn points. 

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Reflections

• Errors in reasoning are sometimes difficult to identify based on responses to multiple choice items. However, when presented with a chart of values for g(x), g'(x), and g"(x) at selected x-values, it became apparent that students were reluctant to consider the second derivative test when asked to locate relative extrema. In other questions, sign charts were used well, but teachers must reiterate the position of the College Board when awarding points for sign charts on FRQs: sign charts will not be accepted as the sole justification for extrema. Students must provide the necessary calculus to earn full credit.