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 triangle and a trig ratio for one of the angles, find other trig ratios

• Use trig ratios to find missing angles in a right triangle

• Find the radian measure given a degree

• Find the degree measure for a given radian

• Evaluate sine, cosine, tangent, secant, cosecant, and cotangent for values on the unit circle

• Determine which angles, in degrees and radians, satisfy given trig ratios

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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

We want the students to view this unit holistically, so be sure to have them make connections between right triangle trig, the unit circle values, degrees and radians, and the six trigonometric ratios.  Consider making the quiz Calculator Inactive so they must use their knowledge of the concepts to answer the “evaluate” questions.  Add a few higher-order thinking questions so they can explain their reasoning, but include skill-based questions as well so that you can see what they know.  They typically struggle with secant, cosecant, tangent, and cotangent due to the use of fractions and radicals.  Make sure to include negative angles and angles larger than 360 so they have to use coterminal angles to evaluate the expressions.