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Quiz (Sections 9.1-9.3)

Unit 9 - Day 8

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
  • Calculating average rate of change from a graph, table, or equation

  • Estimating instantaneous rate of change from a graph or table

  • Calculating instantaneous rate of change using the limit definition

  • Interpreting a negative derivative in context

  • Writing the equation of a tangent line

  • Comparing average and instantaneous rates of change using slopes of secant lines and tangent lines from a graph

  • Given a piecewise linear graph, interpret a limit of a difference quotient as asking for the slope of the graph at a particular x-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.


Overall students did well distinguishing between average and instantaneous rates of change and estimating instantaneous rate of change from a graph or table. Students also demonstrated an understanding of tangent lines as being distinct from derivative equations, as this can be a common misconception for students. Calculating the average or instantaneous rate of change from an equation was still a struggle for some students. Algebra errors abounded.


Proper limit notation was sparse in student responses. Students either did not include the limit at all, or wrote that the limit as h approaches 0 was equal to the difference quotient instead of taking the limit OF the difference quotient. This is something that we will continue to work on throughout the unit.

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