Writing an AP Calc Assessment 

• Include multiple choice and free response items

• Include calculator and non-calculator items

• Write questions that reflect learning targets and success criteria

• Determine scoring rubrics for FRQs before administering the assessment

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Questions to Include

• Using either (or both) form of the definition of derivative to find a general formula for f’(x) 

• Discussing the connection between continuity and differentiability

• Identifying, comparing, and evaluating function value, average rate of change, definition of a derivative, and derivative notation. 

• Analyzing piecewise functions and differentiability at important domain values

• Writing and interpreting equations for tangent lines

• Drawing the graph of f’(x) given a graph of the differentiable function f(x) or drawing a possible graph for f(x) given a graph of f’(x)

• Using the basic rules for derivatives and evaluating derivatives at a point

• Applying appropriate methods for finding derivatives 

• Finding derivatives with independent variables other than x

• Interpreting the graph of f’(x)

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Grading Tips

Remember, we recommend preparing a scoring rubric for all free response items before you begin grading assessments. Know what information is necessary for a complete and correct response and award points when a student presents that information. Grade for what they know, not what they don’t.

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Our unit tests consist of two sections: multiple choice questions and free response questions. We strive to create assessments with the sections approximately equal in overall value to mirror the approach of the AP Calculus Exam in the spring.  The FRQs are the place to assess the communication skills of your students: our students know we will emphasize theorems, definitions and justifications here.  

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Determine before grading if you will accept limit statements without proper notation. We invoked an “inoculation” rule where students were penalized only once for omitting “limit as h approaches 0.” When grading quotient rule responses, maybe the numerator and denominator earn points separately. 

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Reflections

Most students had resolved the quotient rule for this test, but too many used it instead of simplifying complex rational functions, when possible. Surprisingly, students easily justified continuity and non-differentiability, but struggled to remember unit circle values and basic log and exponential identities! So, along with the definition of derivative, the unit circle and logs will be revisited on unit tests all year.