Unit 3 Test

Unit 3 - Day 11

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
  • Determine if a relation models exponential growth or decay by analyzing a scenario, an equation, a table, or a graph

  • Write an exponential function from a scenario

  • Graph exponential functions and identify horizontal asymptotes and key points

  • Find the amount in an account at the end of a specified term with compound interest formulas

  • Use “e” to model continuous exponential growth (interest compounded continuously)

  • Graph logarithmic functions and identify horizontal asymptotes and key points

  • Use properties of logarithms to expand or condense expressions

  • Solve logarithmic and exponential equations, including half-life and double-life problems

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

If giving this assessment online, think of different questions to ask that can’t be solved with Desmos or a calculator.  For example, have students identify the extraneous solution when solving a logarithmic equation, write explanations comparing amounts with different growth formulas, or create their own logarithmic or exponential function when given specific properties.  Include a mix of easy, medium, and challenging questions.  Be sure to incorporate e and the natural log in the mix of questions.