**Algebra II**exam, but I've received enough requests that I've decided to post some of the open-ended questions.

### August 2016, Algebra II Part 2

**25.***The volume of air in a person’s lungs, as the person breathes in and out, can be modeled by a sine
graph. A scientist is studying the differences in this volume for people at rest compared to people
told to take a deep breath. When examining the graphs, should the scientist focus on the
amplitude, period, or midline? Explain your choice.*

The scientist should focus on the amplitude because the height of the graph corresponds to the Volume of air in the lungs.

**26.** *Explain how (3 ^{1/5})^{2} can be written as the equivalent radical expression "fifth root of 9".
*

Look at the illustration below:

The question says "explain" so you MUST include an explanation for full credit. You can't just write an equation.

The exponents can be be switched so you have 3 square to the one-fifth power. Three squared is 9. The one-fifth power is the same as taking the fifth root of the number. So (3^{1/5})^{2} is the same as the fifth root of 9.

**27.** *Simplify xi(i - 7i) ^{2}, where i is the imaginary unit.
*

Subtract i - 7i to get -6i. Square (-6i) to get 36i^{2}. Replace i^{2} with -1, so you have xi(-36). Rewrite as -36xi.

Illustrated below.

to be continued.

Any questions?

Comments, corrections welcome.

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