Writing a Precalculus Assessment

• Include questions in multiple representations (graphical, analytical, tabular, verbal)

• Write questions that reflect learning targets and require conceptual understanding

• Include multiple choice and short answer or free response questions

• Determine scoring rubric before administering the assessment (see below)

• Offer opportunities to practice with and without calculators throughout the year

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Questions to Include

• Determine if a relation models exponential growth or decay by analyzing a scenario, an equation, a table, or a graph

• Write an exponential function from a scenario

• Graph exponential functions and identify horizontal asymptotes and key points

• Find the amount in an account at the end of a specified term with compound interest formulas

• Use “e” to model continuous exponential growth (interest compounded continuously)

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Grading Tips

Look for more than just correct answers. Give students feedback on their justifications, communication, and mathematical thinking. We recommend that you prepare a rubric for the free response and short answer 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

Have students explain how they know something is exponential to assess them on the use of precise language. Give them the horizontal asymptote and y-intercept and have them write an equation.  Make sure the quiz assesses a mix of skills the students can do with a calculator/Desmos and their knowledge of the concepts.  They often see a percent and automatically think it’s exponential, so challenge them with different scenarios like the questions from the Check Your Understandings that require extra thought.