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

• Finding values of c that satisfy the Mean Value Theorem on a closed interval of a given function

• Interpreting the solution to a Mean Value Theorem result

• Identifying intervals of increasing/decreasing and relative extrema from a graph of f’(x)

• Sketching a graph that meets requirements for having critical points, relative and absolute extrema at certain x-values

• Justifying whether the conditions of the Extreme Value Theorem or Mean Value Theorem have been met

• Question requiring the candidates test to identify absolute and relative extrema

• Identifying intervals of increasing/decreasing and relative extra from complex equations using a calculator

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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

• Our students struggled the most with writing good justifications for their answers. A wide variety of reasons were given but only a few would meet College Board requirements. Saying that the derivative crosses the x-axis is NOT a justification for relative extrema that suffices on the AP test. 

• To prepare for this quiz, consider having students make a justification cheat sheet, where a phrase is written in the left-hand column, and its proper justification is written on the right-hand column. Students can fold the paper and quiz themselves. (Ex: Statement: “f(x) has a critical point at x=c” Justification: “f’(c)=0 or undefined”)