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PreTeXt Sample Book: Abstract Algebra (SAMPLE ONLY)

Thomas W. Judson, Isaac Newton (Editor)

Exercises 5.9 Multiple Choice Exercises

When this <exercises> division is hosted on Runestone Academy, it will be enabled for group work. See group selection and submission features are at the end of the division. See [cross-reference to target(s) "worksheet-groupwork" missing or not unique] for more detail. (2024-07-24: experimental.)
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1. Multiple-Choice, Not Randomized, One Answer.

    What color is a stop sign?
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  • 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?
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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.)
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  • 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?
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3. Multiple-Choice, Randomized, One Answer.

    What color is a stop sign? [Static versions retain the order as authored.]
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  • 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?
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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.]
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  • 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?
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5. Mathematical Multiple-Choice, Not Randomized, Multiple Answers.

    Which of the following is an antiderivative of 2sin⁡(x)cos⁡(x)?
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  • sin2⁡(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”.
  • sin2⁡(x)
  • The derivative given in the statement of the problem looks exactly like an application of the chain rule to sin2⁡(x).
  • −cos2⁡(x)
  • Take a derivative on −cos2⁡(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?
  • −2cos⁡(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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