Quiz (Sections 4.5-4.6)
Unit 4 - Day 12
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
Identifying amplitude, period, domain, and range from an equation
Identifying a missing coefficient in an equation given a graph
Explaining the range of sine, cosine, secant, and cosecant
Recognizing equivalent equations using reflections and phase shifts
Identifying vertical asymptotes for secant, cosecant, tangent, and cotangent
Selecting an equation with the largest or smallest period (include sine, cosine, and tangent equations in the answer choices)
Given a value of sine or cosine that is not on the unit circle, have students find the sine or cosine of the negative angle, using the idea of even and odd functions.
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.
We suggest avoiding questions that include many transformations of secant, cosecant, tangent, and cotangent. While students must understand how to evaluate these functions and know their basic properties, they will not be required to graph complex transformations in AP Calculus.
You may wish to forego the traditional format of a quiz for these topics and have students complete a card sort instead, that matches equations with transformed graphs of all six trigonometric functions or perhaps only sine, cosine, and tangent.