Exercises 3.12 Matching Exercises

            <exercises xml:id="matching-exercises" xmlns:pi="http://pretextbook.org/2020/pretext/internal">

            <title>Matching Exercises</title>

            <introduction>

              <p>
                Matching exercises come in two varieties.
                Their differences are most noticeable in interactive versions.
                <dl>

                <li>

                  <title>Cardsort</title>

                  <p>
                    A <tag>cardsort</tag> asks users to match items in a 1-1 or many-1 fashion.
                    The interactive version of these involves dragging <q>card</q>s from the left column (the <tag>premise</tag>s) into containers on the right (the <tag>response</tag>s).
                  </p>

                </li>

                <li>

                  <title>Matching</title>

                  <p>
                    A <tag>matching</tag> interactive asks users to form connections between the <tag>premise</tag>s in the left column and the <tag>response</tag>s on the right.
                    This format supports many-many matches.
                  </p>

                </li>

                </dl>

              </p>

            </introduction>

            <!-- https://www.britannica.com/list/25-decade-defining-events-in-us-history -->

            <exercise xml:id="matching-one" label="matching-dates">

              <title>Cardsort 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>Cardsort 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>Cardsort 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>Cardsort 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.
                  And we have a gratuitous image to test the use of HTML in this component.
                </p>

                <image source="datafiles/golden-gate-bridge.png" width="50%"/>

                </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>

              <exercise xml:id="cardsort-basic" label="cardsort-basic">

                <title>Cardsort Problem, Basic Arithmetic</title>

                <idx>matching US dates</idx>

                <statement>

                  <p>
                    This is a simple exercise to test some grading behavior.
                  </p>

                </statement>

                <cardsort>

                <match>

                <premise order="1">2 + 3</premise>

                <premise order="3">4 + 1</premise>

                <response>5</response>

                </match>

                <match>

                <premise order="2"><m>12 + 2</m></premise>

                <response>14</response>

                </match>

                </cardsort>

              </exercise>

              <exercise label="matching-graph-types">

                <title>Cardsort Problem, Graphs of Functions</title>

                <idx>matching graphs to function types</idx>

                <statement>

                  <p>
                    Each figure below shows the graph of a single function.
                    Match each graph with the type of function it pictures.
                  </p>

                  <sidebyside widths="30% 30% 30%">

                    <figure xml:id="cardsort-graph-one">

                      <caption>Graph One</caption>

                      <image>

                        <shortdescription>
                          a smooth curve that rises, falls, and rises again, crossing the horizontal axis three times
                        </shortdescription>

                        <prefigure label="prefigure-cardsort-cubic" xmlns="https://prefigure.org">
                        <diagram dimensions="(300,300)" margins="5">

                        <definition>
f(x) = (x^3 - 4*x)/2
                        </definition>

                        <coordinates bbox="[-4,-4,4,4]">

                        <grid-axes xlabel="x" ylabel="y"/>

                        <graph at="graph" function="f"/>

                        </coordinates>

                        </diagram>

                        </prefigure>

                      </image>

                    </figure>

                    <figure xml:id="cardsort-graph-two">

                      <caption>Graph Two</caption>

                      <image>

                        <shortdescription>
                          a wave oscillating steadily between one high value and one low value, three full times across the view
                        </shortdescription>

                        <prefigure label="prefigure-cardsort-sine" xmlns="https://prefigure.org">
                        <diagram dimensions="(300,300)" margins="5">

                        <definition>
g(x) = 2*sin(3*pi*(x - 1)/4)
                        </definition>

                        <coordinates bbox="[-4,-4,4,4]">

                        <grid-axes xlabel="x" ylabel="y"/>

                        <graph at="graph" function="g"/>

                        </coordinates>

                        </diagram>

                        </prefigure>

                      </image>

                    </figure>

                    <figure xml:id="cardsort-graph-three">

                      <caption>Graph Three</caption>

                      <image>

                        <shortdescription>
                          three branches split by two dashed vertical lines; the central branch rises to a single peak between them
                        </shortdescription>

                        <prefigure label="prefigure-cardsort-rational" xmlns="https://prefigure.org">
                        <diagram dimensions="(300,300)" margins="5">

                        <definition>
h(x) = 4/(x^2 - 4)
                        </definition>

                        <coordinates bbox="[-4,-4,4,4]">

                        <grid-axes xlabel="x" ylabel="y"/>

                        <line endpoints="((-2,-4),(-2,4))" stroke="red" dash="9 6"/>

                        <line endpoints="((2,-4),(2,4))" stroke="red" dash="9 6"/>

                        <graph at="branch-left" function="h" domain="(-4, -2.2)"/>

                        <graph at="branch-center" function="h" domain="(-1.73, 1.73)"/>

                        <graph at="branch-right" function="h" domain="(2.2, 4)"/>

                        </coordinates>

                        </diagram>

                        </prefigure>

                      </image>

                    </figure>

                  </sidebyside>

                </statement>

                <feedback>

                  <p>
                    A polynomial is defined everywhere, with no breaks and no repetition.
                    A trigonometric function repeats itself at regular intervals.
                    A rational function may have vertical asymptotes where its denominator vanishes<mdash/>and while the central branch of <xref ref="cardsort-graph-three"/> may resemble a downward-opening parabola, a parabola has no asymptotes.
                  </p>

                </feedback>

                <cardsort> <match> <premise order="1">Graph Two</premise> <response>Trigonometric Function</response> </match> <match> <premise order="3">Graph One</premise> <response>Polynomial Function</response> </match> <match> <premise order="2">Graph Three</premise> <response>Rational Function</response> </match> </cardsort>

              </exercise>

              </exercises>