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

• Classifying the type of discontinuity from a graph

• Identifying removable and infinite discontinuities given an equation of a rational function

• Justifying a function’s continuity at a point

• Determining the value of a parameter that would make a piecewise function continuous

• Justifying the existence of a particular output using the Intermediate Value Theorem

• Determining the number of solutions to an equation of the form f(x)=a given values of a continuous function f(x) in a table

• Using the definition of continuity to determine the value of a limit or y-value

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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 did not allow calculators on this assessment because we wanted students to demonstrate understanding of holes and vertical asymptotes without looking at a graph. Most students were able to do this successfully as the quadratics in the numerator and denominator were easy to factor. Overall students fared well, but some missed key information about a function’s continuity in the problem stem, which affected the conclusions they were able to make. Removing discontinuities by defining or redefining a point on the graph continues to be challenging.