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 a value of c that satisfies the MVT

• Analysis of f’ graph to determine relative extrema, points of inflection, intervals of increasing/decreasing, and intervals of concave up/down on f(x)

• Justifying an absolute extrema with the Candidates Test

• Justifying a relative extrema with the second derivative test (tabular data works great for this!)

• Given info about the sign of the first and second derivative of f, choose a possible graph of f(x)

• Optimization problem (we kept it pretty basic with a fencing question)

• Finding the critical points of an implicit function

• Determining if the EVT, IVT, and MVT can be applied for a given function (represented analytically or graphically)

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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

We used two old FRQ questions from previous AP tests (with slight modifications) for our free response questions (2018 AB5 and 2017 AB3 parts b and d). The parts that students struggled with most were those requiring L’hospital’s rule and evaluating the given function in the Candidates Test (unit circle knowledge required!)

Students have improved a lot throughout this unit in their justifications. Even when arithmetic errors were made, many correct justifications were given for absolute extrema, relative extrema, points of inflection, etc.