Algebra test items: Trigonometric Functions

This is my third post on constructing test items based on TIMSS Assessment Framework. My first set of examples is about assessing understanding of zeros of polynomial function and the second post is about graphs of rational functions. Of course there are other frameworks that may be used for constructing test item like the Bloom’s Taxonomy. However, in my experience, Bloom’s is not very useful in mathematics, even its revised version.  The best framework so far for mathematics is that of TIMMS’s which I summarized here.

Here are three examples of trigonometry test questions using the three different cognitive levels:  knowing facts, procedures and concepts, applying, and reasoning.

Knowing

If  cos²(3x-3) = 5 , what is the value of 1-sin² (3x-3) equal to?

a. 0

b. 1

c. 3

d. 4

e. 5

Applying

Given the graphs of f and g, sketch the graph of f+g.

Reasoning

Which of the following functions will have the same set zeroes as function g, given that g(x) = sin kx and f(x) = k?

a. f+g

b. f–g

c. fg

d. g/f

e. gof