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)

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Questions to Include

• Confirming a given function is (or is not ) the general or particular solution to a given differential
  equation

• Constructing a slope field from a given differential equation

• Identifying the appropriate differential equation for a given slope field

• Given a slope field, sketching a particular solution through an ordered pair

• Given a slope field, sketching several possible general solutions

• Interpreting a differential equation in context

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Grading Tips

Calculators were allowed on this assessment as some of the differential equations contained complex exponential functions. 

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Four multiple-choice questions were used to assess vocabulary (is proportional to, particular solution) and slope field concepts (choose the correct differential equation for the slope field show here, describe the general characteristics of a slope field for a given differential equation).  These questions contributed about one-third of the total points. 

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About one-third of the points were earned by constructing slope fields or drawing general and particular solutions. Students must not draw beyond the given slope field grid. Points may be deducted on the AP Test if student graphs extend beyond the given parameters. 

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Remaining points were earned through interpretation of differential equations in context, writing a general solution or confirming a given equation was in fact a particular (or general) solution to a given differential equation.  

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Reflections

This was a gratifying assessment for most students. Confidence in their calculus abilities was restored for most and we were encouraged by their high level of understanding of differential equations. The biggest hurdles were the process of “confirming” one derivative form was equivalent to another form and remembering the meaning of the phrase “is proportional to.”  This will inform our instruction going forward and both will be topics we revisit during our review for the AP Test.