Writing an AP Calc Assessment
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
Average value investigations using graphical interpretations: students were asked to find the average value of function on a closed interval when presented with a piecewise linear graph
Average value investigations in context: several questions on our quz required students to find an average value after reading text, apply correct units, then interpret their answer in context
Finding displacement from a velocity graph or information in context about acceleration and velocity of an object (race cars)
Determining net accumulation from a given context (penguin populations on an island)
Determining total distance from a velocity graph
Determining final amounts from a given initial condition in both analytic and contextual formats
Investigating the relationship between “rate in” and “rate out” when searching for function extrema or deciding when function values are increasing or decreasing.
Our distractors for multiple choice items considered common errors: forgetting to include a given initial condition or neglecting to make all regions positive when finding total area.
Writing our scoring rubric before reading any student responses helped us clarify what a complete solution should contain. Points on free response items were awarded for correct labels, correct integrands, considering the initial condition, correct final answers, correct interpretations, and successfully comparing rates in with rates out.
Prior to the quiz, plenty of discussion centered on the format and correct linkage when writing average value statements: incorrect placement of division by (b - a) creates linkage errors and students were penalized for this algebraic error (just as AP Exam readers are instructed to do!).
Interpreting displacement was a challenge for many students. Simply stating that something “traveled 18 meters from t = 0 to t = 10” or “she went 18 meters” was not sufficient to communicate net distance or displacement. Consult the CED for examples of correct conclusions and hold your students accountable.