Writing an AP Calc Assessment 

• Include multiple choice and free response items

• Write questions that reflect learning targets and success criteria

• Determine scoring rubrics for FRQs before administering the assessment

• Require multiple forms of communication: numerical, graphical, analytic, and verbal

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Questions to Include

• Using either (or both) form of the definition of derivative to find a general formula for f’(x) 

• Items asking students to discuss the connection between continuity and differentiability

• Questions to identify, compare, and evaluate function value, average rate of change, definition of a derivative, and derivative notation. 

• Analysis of piecewise functions and differentiability at important domain values

• Writing and interpreting tangent lines given a function and a point on the graph 

• Interpreting a tangent line in context

• Drawing the graph of f’(x) given a graph of the differentiable function f(x)

• Drawing a possible graph for f(x) given a graph of f’(x)

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Grading Tips

Students are still learning about our philosophy for grading quizzes and tests: one multiple choice item is always worth fewer points than one extended response item (On Unit tests, we do try to equalize the overall value of the two sections because we attempt to mirror the structure of the AP test).  Generally, extended response items have multiple entry points for students (success on part b is not entirely dependent on success in part a, for example).  As the year progresses, our expectations for appropriate notation, justification, and organization increase. Insights that received credit in Unit 2 (derivative notation) may not be eligible for credit in Unit 6.

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Our rubrics rarely reward students solely for algebraic or computational skills. However, we are generous with credit for incremental steps in calculus-based solutions and strive to encourage students to show calculus knowledge whenever appropriate!

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Reflections

The majority of the concepts on this quiz were familiar to students and they performed well.  Consider providing a question that will challenge even the high achievers --- this can be rewarding and surprising. For example, our quiz included an item that seemed to invite application of the IVT to a derivative function. Careful students discovered, however, that continuity wasn’t guaranteed and the IVT could not be applied.