PreTeXt Sample Book: Abstract Algebra (SAMPLE ONLY)

<exercises xml:id="matching-exercises">
  <title>Matching Exercises</title>

  <exercise xml:id="matching-one" label="matching-dates">
    <title>Matching Problem, Dates</title>
    <idx>matching US dates</idx>
    <statement>
      <p>
        Match each event in United States history with the year it happened.
      </p>
    </statement>
    <feedback>
      <p>
        Review
        <url href="https://www.britannica.com/list/25-decade-defining-events-in-us-history" visual="www.britannica.com/list/25-decade-defining-events-in-us-history">Encyclopedia Brittania, 25 Decade-Defining Events in U.S. History</url>
        url.
      </p>
    </feedback>
    <cardsort>
    <match>
    <premise order="4">Monroe Doctrine</premise>
    <response>1823</response>
    </match>
    <match>
    <premise order="3">Haymarket Riot</premise>
    <response>1886</response>
    </match>
    <match>
    <premise order="1">Louisiana Purchase</premise>
    <response>1803</response>
    </match>
    <match>
    <premise order="2">Battle of Gettysburg</premise>
    <response>1863</response>
    </match>
    </cardsort>
  </exercise>
  <exercise label="matching-derivatives">
    <title>Matching Problem, Derivatives</title>
    <idx>matching derivatives</idx>
    <statement>
      <p>
        Match each function with its derivative.
      </p>
    </statement>
    <feedback>
      <p>
        Did you compute the derivative of each function in the premises (left column)?
      </p>
    </feedback>
    <cardsort>
    <match>
    <premise order="1"><m>x^3-6x^2+5</m></premise>
    <response><m>3x^2-12x</m></response>
    </match>
    <match>
    <premise order="3"><m>x^{-3}</m></premise>
    <response><m>-3x^{-4}</m></response>
    </match>
    <match>
    <premise order="2"><m>(x+1)^2</m></premise>
    <response><m>2x+2</m></response>
    </match>
    </cardsort>
  </exercise>
  <exercise label="matching-bases">
    <title>Matching Problem, Linear Algebra</title>
    <idx>matching bases and subspaces</idx>
    <statement>
      <p>
        Match each subspace with a basis for that subspace.
        (You may assume that each set is really a basis for at least one of the subspaces.)
      </p>
    </statement>
    <feedback>
      <p>
        Each putative basis is a subset of exactly one of the three subspaces.
        So for each subspace,
        two of the three sets can be ruled out by simply testing that the vectors of the basis are members of the subspace,
        via the membership criteria.
      </p>
    </feedback>
    <cardsort>
    <match>
    <premise order="1"><m>\left\{\langle x,y,z\rangle\mid - y + z = 0\right\}</m></premise>
    <response><m>\left\{\langle -4, 3, 3\rangle, \langle 3, -2, -2 \rangle\right\}</m></response>
    </match>
    <match>
    <premise order="3"><m>\left\{\langle x,y,z\rangle\mid -3x - 5y + z = 0\right\}</m></premise>
    <response><m>\left\{\langle -4, 3, 3\rangle, \langle 5, -4, -5 \rangle\right\}</m></response>
    </match>
    <match>
    <premise order="2"><m>\left\{\langle x,y,z\rangle\mid -2x - 5y + 2z = 0\right\}</m></premise>
    <response><m>\left\{\langle 3, -2, -2 \rangle, \langle 5, -4, -5 \rangle\right\}</m></response>
    </match>
    </cardsort>
    <hint>
      <p>
        For openers, a basis for a subspace must be a
        <em>subset</em> of the subspace.
      </p>
    </hint>
  </exercise>
  <exercise label="matching-function-types">
    <title>Matching Problem, Function Types</title>
    <idx>matching function types</idx>
    <statement>
      <p>
        Sort the following functions into their correct categories.
      </p>
    </statement>
    <feedback>
      <p>
        Review
        <url href="https://activecalculus.org/prelude/sec-changing-linear.html" visual="A precalculus textbook that could help">Active Prelude to Calculus</url>
        url.
      </p>
    </feedback>
    <cardsort>
    <match>
    <response>Linear</response>
    <premise order="4"><m>y=5x+3</m></premise>
    <premise order="5"><m>\pi x - 6y = \sqrt{2}</m></premise>
    <premise order="6"><m>y=\frac{-1}{2}x+e</m></premise>
    </match>
    <match>
    <response>Quadratic</response>
    </match>
    <match>
    <premise order="7"><m>y=x^3-x</m></premise>
    </match>
    <match>
    <response>Exponential</response>
    <premise order="1"><m>y=2^x</m></premise>
    </match>
    <match>
    <response>Power</response>
    <premise order="2"><m>y=x^3</m></premise>
    <premise order="3"><m>y=\sqrt{x}</m></premise>
    </match>
    </cardsort>
  </exercise>
  <exercise label="matching-playing-cards">
    <title>Matching Problem, Playing Cards</title>
    <idx><h>matching</h><h>playing cards</h></idx>
    <statement>
      <p>
        Associate each playing card with every applicable property.
      </p>
    </statement>
    <feedback>
      <p>
        This one should not be very hard.
      </p>
    </feedback>
    <matching>
    <premise ref="jack heart">Jack of Hearts</premise>
    <premise ref="ace spade">Ace of Spades</premise>
    <premise ref="queen spade">Queen of Spades</premise>
    <premise ref="king club">King of Clubs</premise>
    <premise ref="queen diamond">Queen of Diamonds</premise>

    <response xml:id="ace" order="8">Ace</response>
    <response xml:id="king" order="7">King</response>
    <response xml:id="queen" order="6">Queen</response>
    <response xml:id="jack" order="5">Jack</response>
    <response xml:id="heart" order="4">Heart</response>
    <response xml:id="diamond" order="3">Diamond</response>
    <response xml:id="club" order="2">Club</response>
    <response xml:id="spade" order="1">Spade</response>
    </matching>
  </exercise>
  <exercise label="matching-music-history">
    <title>Matching Problem, Popular Music History</title>
    <idx>matching music history</idx>
    <statement>
      <p>
        Drag each performer onto every applicable category.
      </p>
    </statement>
    <feedback>
      <p>
        Paul McCartney, Ringo Starr, Eric Clapton, Elton John.
        Jethro Tull is the name of a band, not a performer,
        and its best-known member would be the flautist Ian Anderson.
      </p>
    </feedback>
    <matching>
    <premise ref="beatle">Paul</premise>
    <premise ref="beatle drum">Ringo</premise>
    <premise ref="guitar yardbirds">Eric</premise>
    <premise ref="piano">Elton</premise>
    <premise>Jethro</premise>

    <response xml:id="beatle">Beatle</response>
    <response xml:id="yardbirds">Yardbirds</response>
    <response xml:id="guitar">Guitarist</response>
    <response xml:id="drum">Drummer</response>
    <response xml:id="flute">Flautist</response>
    <response xml:id="harp">Harpist</response>
    <response xml:id="piano">Pianist</response>
    <response xml:id="math"><em>Some</em> "Math": <m>\sin(x^2)</m></response>
    </matching>
  </exercise>
</exercises>