Unit 6 Test

Unit 6 - Day 9

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
  • Find the value of a parameter k that makes a system dependent or inconsistent

  • Writing a system of equations to model a scenario

  • Solving a system of nonlinear equations using substitution (we like ones where they substitute an entire expression instead of just x or y--much like they ask on the SAT!)

  • At most one complete Gaussian elimination problem (these take students a lot of time)

  • Asking students to analyze a step in a Gaussian elimination problem

  • Analyzing a dependent system in context

  • Partial fraction decomposition

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

The biggest feedback we got from our students about this test is that it took too long! Many students felt rushed and were not able to demonstrate their best work. Students felt comfortable using either substitution and elimination to solve linear systems but struggled more with questions requiring an understanding of graphs (Which of the following systems has exactly 2 solutions?) and interpreting dependent systems in context (students were given two florist orders that ended up being equivalent equations and had to realize that the price of a single rose and carnation could not be found).