# PreTeXt Sample Book: Abstract Algebra (SAMPLE ONLY)

## Exercises5.7Multiple Choice Exercises

### 1.Multiple-Choice, Not Randomized, One Answer.

What color is a stop sign?
• Green
• Green means “go!”.
• Red
• Red is universally used for prohibited activities or serious warnings.
• White
• White might be hard to see.
Hint 1.
What did you see last time you went driving?
Hint 2.
Maybe go out for a drive?

### 2.Multiple-Choice, Not Randomized, Multiple Answers.

Which colors might be found in a rainbow? (Note that the radio buttons now allow multiple buttons to be selected.)
• Red
• Red is a definitely one of the colors.
• Yellow
• Yes, yellow is correct.
• Black
• Remember the acronym…ROY G BIV. “B” stands for blue.
• Green
• Yes, green is one of the colors.
Hint.
Do you know the acronym…ROY G BIV for the colors of a rainbow, and their order?

What color is a stop sign? [Static versions retain the order as authored.]
• Green
• Green means “go!”.
• Red
• Red is universally used for prohibited activities or serious warnings.
• White
• White might be hard to see.
Hint 1.
What did you see last time you went driving?
Hint 2.
Maybe go out for a drive?

Which colors might be found in a rainbow? (Note that the radio buttons now allow multiple buttons to be selected.) [Static versions retain the order as authored.]
• Red
• Red is a definitely one of the colors.
• Yellow
• Yes, yellow is correct.
• Black
• Remember the acronym…ROY G BIV. “B” stands for blue.
• Green
• Yes, green is one of the colors.
Hint.
Do you know the acronym…ROY G BIV for the colors of a rainbow, and their order?

### 5.Mathematical Multiple-Choice, Not Randomized, Multiple Answers.

Which of the following is an antiderivative of $$2\sin(x)\cos(x)\text{?}$$
• $$\sin^2(x)+832$$
• Remember that when we write $$+C$$ on an antiderivative that this is the way we communicate that there are many possible derivatives, but they all “differ by a constant”.
• $$\sin^2(x)$$
• The derivative given in the statement of the problem looks exactly like an application of the chain rule to $$\sin^2(x)\text{.}$$
• $$-\cos^2(x)$$
• Take a derivative on $$-\cos^2(x)$$ to see that this answer is correct. Extra credit: does this answer “differ by a constant” when subtracted from either of the other two correct answers?
• $$-2\cos(x)\sin(x)$$
• The antiderivative of a product is not the product of the antiderivatives. Use the product rule to take a derivative and see that this answer is not correct.
Hint.
You can take a derivative on any one of the choices to see if it is correct or not, rather than using techniques of integration to find a single correct answer.