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

• Item requiring conceptual application of the chain rule (Ex: If g(x)=f(h(x)), find g’(x))

• A table question where only selected values of f, g, f’, and g’ are given (See Check Your Understanding #4)

• Items requiring procedural knowledge of the chain rule (include trig functions, exponential functions, and polynomials!)

• Item requiring 2 or more chains (See Check Your Understanding #2)

• Scaffolded free response question(s)

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Grading Tips

We recommend that you prepare a rubric for the free response items before you begin grading your quizzes or tests. Know what information is necessary for a complete and correct response and award points when a student presents that information. Many of the “Why did I get marked down?” questions are eliminated when you share the components that earn points.  

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Reflections

• Although this quiz covers only one topic, students must remember all their derivative rules from unit 2, so this quiz actually requires synthesizing many ideas learned so far this year. Encourage students to review their derivative rules regularly using flashcards, online quizzes, or other study strategies.

• When going over quizzes, it is likely that you will find several common chain rule mistakes. Emphasize a growth mindset when discussing these mistakes instead of criticizing students for forgetting things you have likely told them over and over. We like to deem certain mistakes as “important” if they grow our understanding of the mathematics, help ourselves and others learn, and give us opportunities to avoid making the same mistake in the future. One way to do this is through the teaching protocol “My Favorite No.” Check out this video to see it in action.

• Because the chain rule is an important and ubiquitous component of the AP Calculus curriculum, we felt this topic required its own assessment. After multiple days of practice and activities, students have implemented the chain rule on a variety of functions and variables. The 3.1 quiz should reflect these varied applications.

• It should not be a surprise to students if questions about continuity or differentiability appear on this quiz or on any future quiz or test. Teachers should also feel free to include questions that require students to recognize different forms of the definition of derivative. Hopefully, students will continue to review these concepts and definitions if they anticipate seeing them on a quiz or test!