When this <exercises> division is hosted on Runestone Academy, it will be enabled for group work. See group selection and submission features at the end of the division. (2023-07-03: experimental.)

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.

Hint1.

What did you see last time you went driving?

Hint2.

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?

3.Multiple-Choice, Randomized, One Answer.

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.

Hint1.

What did you see last time you went driving?

Hint2.

Maybe go out for a drive?

4.Multiple-Choice, Randomized, Multiple Answers.

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.