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
Four representations (graphical, numerical, analytical, verbal) of approximations and integrals
Approximations with Riemann sums (left, right, midpoint) or trapezoids
Analysis of approximations (over, under) with justification
Applications of integration as accumulation (with and without an initial condition)
Using the FTC: differentiating and evaluating definite integrals
Translating Riemann sum limits to integral notation
Integration problems requiring multi-step solutions
Questions requiring numerical integration (fnInt or Math:9, for example)
Remember, prepare a scoring rubric for the FRQs before you begin grading. Decide what is necessary for a complete, correct response and award points when a student presents that information. Grade for what they know, not what they don’t.
We have adapted many of the FRQ scoring techniques used at the AP reading. Students are inoculated from repeated neglect of +C and we deduct only one point from their final score. We deduct points for “linkage errors” when students write a run-on equation that eventually becomes false. When combining an initial condition with an integral, correct placement of the initial condition and the dx term is vital. A student who adds the initial condition after the integral without including the differential term will lose a point.
The FTC was prominent and presented in many forms on this assessment. Students evaluated definite integrals using tables and graphs, produced antiderivatives and derivatives, and found net areas under graphs. To test conceptual understanding of integration, we asked students to choose an equivalent integral involving a u-sub (which required changing the limits of integration AND a correction factor!)
Our FRQ items were edits of 2016 AB3 (accumulation and a revisit of max and min concepts) and 2006 AB4 (the rocket problem). Both questions provided adequate challenges for most students!