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)

• Graph logarithmic functions and identify horizontal asymptotes and key points

• Use properties of logarithms to expand or condense expressions

• Solve logarithmic and exponential equations, including half-life and double-life problems

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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

If giving this assessment online, think of different questions to ask that can’t be solved with Desmos or a calculator.  For example, have students identify the extraneous solution when solving a logarithmic equation, write explanations comparing amounts with different growth formulas, or create their own logarithmic or exponential function when given specific properties.  Include a mix of easy, medium, and challenging questions.  Be sure to incorporate e and the natural log in the mix of questions.