Quiz (Sections 9.4-9.6)

Unit 9 - Day 14

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
  • Finding derivatives using shortcuts (include integer and rational exponents)

  • Justifying whether a piecewise function is differentiable

  • Finding values of parameters so that a piecewise function is differentiable

  • Determining if a function is differentiable from a graph

  • Determining behavior of f from a graph of f’

  • Given a quadratic derivative, find the relative extrema of the original function

  • Given a graph of f, selecting the appropriate graph of f’

  • Given a graph of f’, selecting a possible graph of f

  • Determining whether a function is differentiable over some interval given its equation

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.


Results from this quiz varied greatly. Some students struggled to apply any patterns for finding the derivative of a function, whereas others showed mastery of the analytical skills of finding a derivative but struggled to connect graphs. Determining differentiability from a graph proved easy for students but dealing with piecewise functions and justifying differentiability was much harder. We were impressed with some explanations about the connections between the graphs of f and f’. Despite this being such a difficult concept, students are showing a lot of growth!