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Unit 4 Test

Unit 4 - Day 17

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
  • Evaluating with Right Triangle Trig - find ratios from a right triangle, missing angles when given the sides, missing sides when given the angle and another side, etc.

  • The Unit Circle - evaluate expressions using all six trigonometric ratios for angles on the unit circle; include coterminal angles greater than 2pi and less than -2pi

  • Graph all six trigonometric functions with transformations; identify key feature of each graph, including asymptotes for secant, cosecant, tangent, and cotangent

  • Evaluate expressions with inverse trig

  • When given a ratio, use inverse trig to find the other ratios

  • Trigonometric Modeling: interpret period and amplitude in context

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.


Students will struggle with the domain and range of the inverse trig functions so make sure you ask a mix of simple and challenging questions.  Specifically something like arccos(cos(4π/3)),where the inverse does not undo the original, but the answer is actually (2π/3). Have students identify equations from graphs as well as graph 1-2 periods of a few of the 6 functions.  Consider having a calculator active section and a calculator inactive section so that students must show their knowledge of the unit circle.

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