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

• Quadratics--identify key features of a quadratic from multiple forms (standard, vertex, and intercept form);

• Quadratics--rewrite the equation of a quadratic from one form into another by completing the square

• Polynomials--identify key features of a polynomial (zeros, x-intercepts, y-intercept, multiplicity of zeros, end behavior, etc.)

• Polynomials--sketch a graph of a polynomial given certain features

• Polynomials--find all solutions

• Polynomials--find remainders by dividing or using the Remainder Theorem

• Rationals--identify key features of a rational function (end behavior, vertical asymptotes, holes, intercepts, etc.)

• Rationals--solve simple rational equation

• Rationals--Real-world context

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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

This is a long unit with many parts, so make sure to have a good representation of questions for the test.  Students may get end behavior mixed up for polynomials and rationals, so include at least one of each so they can show they know when a function is approaching infinity or negative infinity or a horizontal asymptote. If giving the test online, consider including questions that won’t be answerable via a quick Desmos graph so the students must show what they learned in the unit.  This can be accomplished by using the same methods as we did with the lessons For example, leave out a missing variable when dividing and have them solve for the missing piece (Day 7), give them a table of values and have them find the remaining solutions (Day 9), or have them solve for complex solutions algebraically (Day 8).