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

• Write the equation of a line tangent to sine or cosine function at a particular point

• Find derivatives using product rule and quotient rule analytically

• Given functions in tables or graphs, find derivatives of their products or quotients

• Given the value of a derivative and three of the components needed to calculate it, find the fourth component

• Finding rate of change using the product rule or quotient rule in context

• Determining the strategy needed to find a derivative of a given function

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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 did very well on this assessment. Errors tended to come from not knowing unit circle values or incorrectly finding the slope on a graph. While some students still found the derivatives of numerator and denominator functions separately, most students applied the product rule and quotient rule appropriately.

 

The most commonly missed question was one where we provided 3 functions and asked students to determine which of the three required the use of the quotient rule. Only one of them required the quotient rule since the others (1/x^2 and (x^2)/4 could be rewritten using negative exponents or with a coefficient.