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)
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
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.
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”)