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

• Converting points from polar to rectangular and vice versa

• Converting equations from polar to rectangular and vice versa

• Given a polar curve with no axis labels, determine a possible equation

• Describe the length and location of the petals from a polar rose equation

• Describe the difference between polar and Cartesian coordinates

• Graphing polar equations

• Determine the shape of a graph from its equation

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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

Students fared well on this assessment. Most students were able to graph the polar curves without a calculator by making use of the patterns they had found, plotting points, and using symmetry. We challenged students by offering a choice of four deeper thinking questions where they had to explain why the patterns they observed work. For example, we asked students why dented limacons never touch the pole and why graphs with cosine would have polar axis symmetry. We also asked students to explain why the first petal of a sine rose would be at  θ=π/2n. Responses showed various levels of understanding. Some students really impressed us with their explanations!