Unit 7 Test (Topics 7.1-7.8)

Unit 7 - Day 11

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
  • Multiple representations (graphical, numerical, analytical, verbal) of function values and behavior

  • Context questions requiring students to interpret differential equations using correct units

  • Sketching slope fields or solutions curves on a given slope field

  • Tangent line applications for a given differential equation

  • Differential equations leading to exponential growth or decay solutions

  • Differential equations requiring separation of variables

  • Opportunities to solve for the constant of integration

  • Differential equations which produce two possible solutions of which one fulfills an initial condition

  • Calculator accessible questions in either the MC or FRQ sections

Grading Tips

Remember, we recommend preparing a scoring rubric for all free response items before you begin grading assessments. Know what information is necessary for a complete and correct response and award points when a student presents that information. Grade for what they know, not what they don’t.


The Unit 7 Test was structured a little differently than our usual assessment. We chose to have students begin with the calculator-allowed free response section. Half the period was budgeted for this section which included one full-length FRQ (exponential growth application), drawing a slope field from a given differential equation, and then another FRQ (sketching a solution curve on a slope field, writing a tangent-line equation from the given differential equation, and then finally solving the differential equation using separation of variables with an initial condition). Students then put away their calculators for the non-calculator section consisting of twelve multiple-choice items.

One of the more interesting MC questions involved error analysis: students were shown an incorrect solution to a separation of variables problem and asked to find the first mistake. This was, of course, a common mistake made by our students!