PreTeXt Sample Book: Abstract Algebra (SAMPLE ONLY)

<exercises xml:id="multiple-choice-exercises" groupwork="yes" groupsize="5" label="exercises-groupwork">
  <title>Multiple Choice Exercises</title>
  <introduction>
    <p>
      When this <tag>exercises</tag> 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 <xref ref="worksheet-groupwork" /> for more detail. (2024-07-24: experimental.)
    </p>
  </introduction>
  <exercise xml:id="multiple-choice-one" label="multiple-choice-not-randomized">
    <title>Multiple-Choice, Not Randomized, One Answer</title>
    <idx>stop signs</idx>
    <statement>
      <p>
        What color is a stop sign?
      </p>
    </statement>





    <choices>
    <choice>
    <statement>
      <p>
        Green
      </p>
    </statement>
    <feedback>
      <p>
        Green means
        <q>go!</q>.
      </p>
    </feedback>
    </choice>
    <choice correct="yes">
    <statement>
      <p>
        Red
      </p>
    </statement>
    <feedback>
      <p>
        Red is universally used for prohibited activities or serious warnings.
      </p>
    </feedback>
    </choice>
    <choice>
    <statement>
      <p>
        White
      </p>
    </statement>
    <feedback>
      <p>
        White might be hard to see.
      </p>
    </feedback>
    </choice>
    </choices>
    <hint>
      <p>
        What did you see last time you went driving?
      </p>
    </hint>
    <hint>
      <p>
        Maybe go out for a drive?
      </p>
    </hint>
  </exercise>
  <exercise label="multiple-choice-multiple-answers">
    <title>Multiple-Choice, Not Randomized, Multiple Answers</title>
    <idx>stop signs</idx>
    <statement>
      <p>
        Which colors might be found in a rainbow? (Note that the radio buttons now allow multiple buttons to be selected.)
      </p>
    </statement>
    <choices>
    <choice correct="yes">
    <statement>
      <p>
        Red
      </p>
    </statement>
    <feedback>
      <p>
        Red is a definitely one of the colors.
      </p>
    </feedback>
    </choice>
    <choice correct="yes">
    <statement>
      <p>
        Yellow
      </p>
    </statement>
    <feedback>
      <p>
        Yes, yellow is correct.
      </p>
    </feedback>
    </choice>
    <choice>
    <statement>
      <p>
        Black
      </p>
    </statement>
    <feedback>
      <p>
        Remember the acronym<ellipsis /><acro>ROY G BIV</acro>.
        <q>B</q>
        stands for blue.
      </p>
    </feedback>
    </choice>
    <choice correct="yes">
    <statement>
      <p>
        Green
      </p>
    </statement>
    <feedback>
      <p>
        Yes, green is one of the colors.
      </p>
    </feedback>
    </choice>
    </choices>
    <hint>
      <p>
        Do you know the acronym<ellipsis /><acro>ROY G BIV</acro> for the colors of a rainbow,
        and their order?
      </p>
    </hint>
  </exercise>
  <exercise label="multiple-choice-randomized">
    <title>Multiple-Choice, Randomized, One Answer</title>
    <idx>stop signs</idx>
    <statement>
      <p>
        What color is a stop sign? [Static versions retain the order as authored.]
      </p>
    </statement>
    <choices randomize="yes">
    <choice>
    <statement>
      <p>
        Green
      </p>
    </statement>
    <feedback>
      <p>
        Green means
        <q>go!</q>.
      </p>
    </feedback>
    </choice>
    <choice correct="yes">
    <statement>
      <p>
        Red
      </p>
    </statement>
    <feedback>
      <p>
        Red is universally used for prohibited activities or serious warnings.
      </p>
    </feedback>
    </choice>
    <choice>
    <statement>
      <p>
        White
      </p>
    </statement>
    <feedback>
      <p>
        White might be hard to see.
      </p>
    </feedback>
    </choice>
    </choices>
    <hint>
      <p>
        What did you see last time you went driving?
      </p>
    </hint>
    <hint>
      <p>
        Maybe go out for a drive?
      </p>
    </hint>
  </exercise>
  <exercise label="multiple-choice-randomized-multiple-answers">
    <title>Multiple-Choice, Randomized, Multiple Answers</title>
    <idx>stop signs</idx>
    <statement>
      <p>
        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.]
      </p>
    </statement>
    <choices randomize="yes">
    <choice correct="yes">
    <statement>
      <p>
        Red
      </p>
    </statement>
    <feedback>
      <p>
        Red is a definitely one of the colors.
      </p>
    </feedback>
    </choice>
    <choice correct="yes">
    <statement>
      <p>
        Yellow
      </p>
    </statement>
    <feedback>
      <p>
        Yes, yellow is correct.
      </p>
    </feedback>
    </choice>
    <choice>
    <statement>
      <p>
        Black
      </p>
    </statement>
    <feedback>
      <p>
        Remember the acronym<ellipsis /><acro>ROY G BIV</acro>.
        <q>B</q>
        stands for blue.
      </p>
    </feedback>
    </choice>
    <choice correct="yes">
    <statement>
      <p>
        Green
      </p>
    </statement>
    <feedback>
      <p>
        Yes, green is one of the colors.
      </p>
    </feedback>
    </choice>
    </choices>
    <hint>
      <p>
        Do you know the acronym<ellipsis /><acro>ROY G BIV</acro> for the colors of a rainbow,
        and their order?
      </p>
    </hint>
  </exercise>
  <exercise label="mathematical-multiple-choice-multiple-answers">
    <title>Mathematical Multiple-Choice, Not Randomized, Multiple Answers</title>
    <idx>stop signs</idx>
    <statement>
      <p>
        Which of the following is an antiderivative of <m>2\sin(x)\cos(x)</m>?
      </p>
    </statement>
    <choices>
    <choice correct="yes">
    <statement>
      <p>
        <m>\sin^2(x)+832</m>
      </p>
    </statement>
    <feedback>
      <p>
        Remember that when we write <m>+C</m> on an antiderivative that this is the way we communicate that there are <em>many</em>
        possible derivatives, but they all
        <q>differ by a constant</q>.
      </p>
    </feedback>
    </choice>
    <choice correct="yes">
    <statement>
      <p>
        <m>\sin^2(x)</m>
      </p>
    </statement>
    <feedback>
      <p>
        The derivative given in the statement of the problem looks exactly like an application of the chain rule to <m>\sin^2(x)</m>.
      </p>
    </feedback>
    </choice>
    <choice correct="yes">
    <statement>
      <p>
        <m>-\cos^2(x)</m>
      </p>
    </statement>
    <feedback>
      <p>
        Take a derivative on <m>-\cos^2(x)</m> to see that this answer is correct.
        Extra credit: does this answer
        <q>differ by a constant</q>
        when subtracted from either of the other two correct answers?
      </p>
    </feedback>
    </choice>
    <choice>
    <statement>
      <p>
        <m>-2\cos(x)\sin(x)</m>
      </p>
    </statement>
    <feedback>
      <p>
        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.
      </p>
    </feedback>
    </choice>
    </choices>
    <hint>
      <p>
        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
        <em>a single</em> correct answer.
      </p>
    </hint>
  </exercise>
</exercises>