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

• Writing a function to model a real-world scenario

• Determining domain and range from equations and graphs

• Sketching a graph or writing an equation that have given domains and ranges

• Given a parent function and 2-3 transformations, write the new equation then analyze domain, range, extrema, odd/even, intervals of increasing/decreasing, and average rate of change on a given interval

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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

This set of topics could be assessed in other non-traditional ways. Consider randomly assigning each student a parent function and 3 transformations and then having them complete a full analysis of their function including sketching a graph without a calculator. This could also be made interactive by having students roll a die and the first roll determines the parent function they must work with and the 2nd, 3rd, and 4th roll determine what transformations they must perform. This would be more time consuming to grade but might remove some opportunities for cheating if given virtually, since students are highly unlikely to have the exact same function.