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

• Identifying amplitude, period, domain, and range from an equation

• Identifying a missing coefficient in an equation given a graph

• Explaining the range of sine, cosine, secant, and cosecant 

• Recognizing equivalent equations using reflections and phase shifts

• Identifying vertical asymptotes for secant, cosecant, tangent, and cotangent

• Selecting an equation with the largest or smallest period (include sine, cosine, and tangent equations in the answer choices)

• Given a value of sine or cosine that is not on the unit circle, have students find the sine or cosine of the negative angle, using the idea of even and odd functions. 

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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 suggest avoiding questions that include many transformations of secant, cosecant, tangent, and cotangent. While students must understand how to evaluate these functions and know their basic properties, they will not be required to graph complex transformations in AP Calculus.

You may wish to forego the traditional format of a quiz for these topics and have students complete a card sort instead, that matches equations with transformed graphs of all six trigonometric functions or perhaps only sine, cosine, and tangent.