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>
<!-- to appear as problem with potentially multiple correct -->
<!-- answers (even though there is only one), use           -->
<!--                                                        -->
<!--     <choices multiple-correct="yes">                   -->
<!--                                                        -->
      <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-feedback-math">
      <title>Multiple-Choice, Math in Feedback</title>
      <statement>
        <p>
          What is the coefficient on <m>x^4y^4</m> in <m>(2x+5xy^2)^4</m>?
        </p>
      </statement>
      <choices>
      <choice>
      <statement>
        <p>
          <m>6</m>
        </p>
      </statement>
      <feedback>
        <p>
          Have you accounted for the <m>2</m> and <m>5</m> that are in the original binomial?
        </p>
      </feedback>
      </choice>
      <choice>
      <statement>
        <p>
          <m>60</m>
        </p>
      </statement>
      <feedback>
        <p>
          What should the exponents on <m>2</m> and <m>5</m> be when you expand <m>(2x+5xy^2)^4</m>?
        </p>
      </feedback>
      </choice>
      <choice>
      <statement>
        <p>
          <m>100</m>
        </p>
      </statement>
      <feedback>
        <p>
          Have you included something of the form
          <m>\binom{n}{k}</m> in your computations?
        </p>
      </feedback>
      </choice>
      <choice correct="yes">
      <statement>
        <p>
          <m>600</m>
        </p>
      </statement>
      <feedback>
        <p>
          Correct!
          Using the binomial theorem,
          we get a term containing the monomial <m>x^4y^4</m> by taking two of the first term,
          and two of the second term in the expansion of <m>(2x+5xy^2)^4</m>,
          and so this term is equal to
          <me>
            \binom{4}{2} (2x)^2 (5xy^2)^2 = 6 \cdot 2^2 5^2 x^4 y^4 = 600 x^4 y^4
          </me>.
        </p>
      </feedback>
      </choice>
      </choices>
    </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-forced-checkbox">
      <title>Multiple-Choice, Randomized, One Answer but with Checkboxes</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" multiple-correct="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>
          Yellow
        </p>
      </statement>
      <feedback>
        <p>
          Yellow means slow down.
        </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>
    <exercise xml:id="multiple-choice-in-columns" label="multiple-choice-columns">
      <title>Multiple-Choice, Not Randomized, One Answer</title>
      <idx>stop signs</idx>
      <statement>
        <p>
          What color is a stop sign?
        </p>
        <p>
          Note: we are experimenting with choices in columns (2025-05-17).
          Three columns here.
        </p>
      </statement>
<!-- to appear as problem with potentially multiple correct -->
<!-- answers (even though there is only one), use           -->
<!--                                                        -->
<!--     <choices multiple-correct="yes">                   -->
<!--                                                        -->
      <choices cols="3">
      <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>
      <choice>
      <statement>
        <p>
          Purple
        </p>
      </statement>
      <feedback>
        <p>
          Hmmmmmmm.
        </p>
      </feedback>
      </choice>
      <choice>
      <statement>
        <p>
          Pink
        </p>
      </statement>
      <feedback>
        <p>
          I have never seen a pink road sign!
        </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>
  </exercises>