Quiz (Sections 8.1-8.2)

Unit 8 - Day 7

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.