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Unit 6 - Day 21

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)

Grading Tips

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!

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