Unit 4

Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

Day 8

Day 9

Day 10

Day 11

Day 12

Day 13

Day 14

Day 15

Day 16

Day 17

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All Units

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

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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

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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.

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Reflections

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.