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

• Finding the common ratio given two terms of a geometric sequence

• Writing explicit formulas for the nth term and nth partial sum of a geometric sequence 

• Interpreting scenarios that represent geometric sequences and finding term values and partial sums in context

• Deciding whether an infinite sum will exist or not and explaining why

• Finding the S   and S     expressions by substituting into the sum formula

• Explaining the importance of the base case, induction hypothesis, and induction step in a proof by induction

• Writing a proof by induction

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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

Overall, our students did well on this assessment. We chose to make this a group quiz to provide some extra scaffolding for proof writing. Students were successful at the algebraic manipulation required in the induction step. The sum formula we had them prove was for a specific arithmetic series. Some groups struggled to interpret the geometric scenario and identify the common ratio when given information about a percent decrease, forgetting to subtract the percent from 100 to find the percentage that remains in each subsequent term.