Quiz (Sections 8.3-8.4)

Unit 8 - Day 13

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
  • Classifying the type of discontinuity from a graph

  • Identifying removable and infinite discontinuities given an equation of a rational function

  • Justifying a function’s continuity at a point

  • Determining the value of a parameter that would make a piecewise function continuous

  • Justifying the existence of a particular output using the Intermediate Value Theorem

  • Determining the number of solutions to an equation of the form f(x)=a given values of a continuous function f(x) in a table

  • Using the definition of continuity to determine the value of a limit or y-value

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

We did not allow calculators on this assessment because we wanted students to demonstrate understanding of holes and vertical asymptotes without looking at a graph. Most students were able to do this successfully as the quadratics in the numerator and denominator were easy to factor. Overall students fared well, but some missed key information about a function’s continuity in the problem stem, which affected the conclusions they were able to make. Removing discontinuities by defining or redefining a point on the graph continues to be challenging.