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

​

Questions to Include

• Determine whether (x-k) is a factor of a polynomial

• Find and interpret the remainder when dividing a polynomial by (x-k)

• Find all solutions of a polynomial, including real and complex

• Given one part of a conjugate pair, find the rest of the zeros

• Given the zeros and the y-intercept or a point of a polynomial, write the equation in standard form

​

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.

​

Reflections

Consider giving them a table with one zero for a polynomial with all real, rational zeros and a graph with one real root to find the rest of the non-real zeros.  This way, you’ll know if they can find the zeros algebraically by dividing.  The high-level task is a good example of a higher-order thinking question, but make the constant value “c” or “k” and have them find that.  They’ll use the same skills from the high-level task, but it will be less time intensive for the quiz.