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

• Evaluating and interpreting functions (including combinations, compositions, piecewise and inverses) given in context; identifying intervals of increasing/decreasing and other key features such as average rate of change in context

• Writing new equations based on a transformation, a combination, composition, or inverse

• Identifying domain and range graphically and analytically

• Generating examples of relations that are not functions, that are functions, and that are one-to-one functions (preferably in verbal, analytical, and graphical representations!)

• Finding the domain of a combination and composition of functions, as well as the domain and range of an inverse 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 are still getting used to the rigor of a Precalculus test. Although students generally feel comfortable performing the procedure of finding a combination, composition, or inverse, they still struggle to communicate about these ideas. Nevertheless, we have found that students feel less anxiety about the dreaded word problem because they are used to seeing ideas represented in contexts.  Overall, we find ourselves giving shorter tests than we have in years past because the questions tend to pack more of a punch and connect topics from multiple sections.