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PreTeXt Sample Book: Abstract Algebra (SAMPLE ONLY)

Exercises 5.7 Multiple 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?

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.
Hint 1.
What did you see last time you went driving?
Hint 2.
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.
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