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

• Given a set of conditions, determine whether Law of Sines or Law of Cosines is more appropriate

• Describe the key features of the polar graph given an equation

• Find the magnitude and direction of a vector

• Identify similarities between vectors and polar coordinates and parametric equations

• Solve a triangle using Law of Sines and Law of Cosines

• Convert ordered pairs and equations from rectangular to Cartesian and vice versa

• Produce or identify equivalent polar points

• Eliminate the parameter to convert parametric equations into Cartesian equations

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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

Our students found success on this test, even when they are asked to think about the concepts in a new way. Some students still struggled with converting polar and Cartesian points and finding component form of vectors mainly due to sign errors or lack of knowledge about unit circle values. The ambiguous case for the Law of Sines continues to be a challenge for students, though students fared better on this question than on the checkpoint.