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

• Evaluate various limits from a graph, including in places where the function is continuous

• Evaluate limits from tables

• Interpret limit statements in words

• Evaluate limits using direct substitution

• Evaluate limits of rational functions that involve factoring

• Evaluate limits related to the graphs of y=sin(x)/x and y=|x|/x and its transformations

• Identify when a limit does not exist

• Evaluate limits of piecewise functions

• Determine parameter values so that the limit of a piecewise function exists

​

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

Our students really impressed us on this quiz! Students were able to parse limit notation and describe function behavior using limits. They were able to reason about when a limit does and does not exist, and were especially successful at evaluating limits from graphs. Some students still struggled to evaluate limits at a hole, especially when the output was defined as a different y-value. This was especially true when the function was presented analytically and students had to factor, cancel, and re-substitute in the given x-value.