Derivatives and Integrals An Annotated Discourse

    <section xml:id="section-interactive-exercises" label="section-interactive-exercises">
      <title>Interactive Exercises</title>
      <introduction>
        <p>
          Interactive components, <em>just</em>
          for testing, no commentary.
        </p>
      </introduction>
      <exercises>
        <title>True/False</title>
        <introduction>
          <p>
            A True/False question.
          </p>
        </introduction>
        <exercise label="vector-space-dimension">
          <title>True/False</title>
          <idx>vector space</idx>
          <statement correct="no">
            <p>
              Every vector space has finite dimension.
            </p>
          </statement>
          <feedback>
            <p>
              The vector space of all polynomials with finite degree has a basis,
              <m>B = \{1,x,x^2,x^3,\dots\}</m>, which is infinte.
            </p>
          </feedback>
          <hint>
            <p>
              <m>P_n</m>, the vector space of polynomials with degree at most <m>n</m>,
              has dimension <m>n+1</m> by <xref ref="theorem-FTC"/>. [Cross-reference is just a demo,
              content is not relevant.] What happens if we relax the defintion and remove the parameter <m>n</m>?
            </p>
          </hint>
        </exercise>
      </exercises>
      <exercises>
        <title>Multiple-Choice</title>
        <introduction>
          <p>
            Multiple-Choice problem
          </p>
        </introduction>
        <exercise 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>
      </exercises>
      <exercises>
        <title>Parsons Problem, Math Proof</title>
        <introduction>
          <p>
            With some MathJax.
          </p>
        </introduction>
        <exercise label="number-theory-proof" adaptive="yes">
          <title>Parsons Problem, Mathematical Proof</title>
          <idx>even numbers</idx>
          <statement>
            <p>
              Create a proof of the theorem: If <m>n</m> is an even number,
              then <m>n\equiv 0\mod 2</m>.
            </p>
          </statement>
          <blocks>
          <block order="2">
          <p>
            Suppose <m>n</m> is even.
          </p>
          </block>
          <block order="3">
          <choice>
          <p>
            Then <m>n</m> is a prime number.
          </p>
          </choice>
          <choice correct="yes">
          <p>
            Then there exists an <m>m</m> so that <m>n = 2m</m>.
          </p>
          </choice>
          <choice>
          <p>
            Then there exists an <m>m</m> so that <m>n = 2m + 1</m>.
          </p>
          </choice>
          </block>
          <block order="1" correct="no">
          <p>
            Click the heels of your ruby slippers together three times.
          </p>
          </block>
          <block order="5">
          <p>
            So we have the displayed equation:
            <me>
              n = 2m + 0
            </me>.
          </p>
          <p>
            This is a superfluous second paragraph in this block.
          </p>
          </block>
          <block order="4">
          <p>
            Thus <m>n\equiv 0\mod 2</m>.
          </p>
          </block>
          </blocks>
          <hint>
            <p>
              Dorothy will not be much help with this proof.
            </p>
          </hint>
        </exercise>
      </exercises>
      <exercises>
        <title>Parsons Problem, Code</title>
        <introduction>
          <p>
            Programming Parsons problem, requiring indentation.
          </p>
        </introduction>
        <exercise label="prime-number-program-indent-yes" language="python" adaptive="yes" indentation="hide">
          <title>Parsons Problem, Programming</title>
          <idx>prime numbers</idx>
          <idx>Sieve of Eratosthenes</idx>
          <statement>
            <p>
              The Sieve of Eratosthenes computes prime numbers by starting with a finite list of the integers bigger than 1.
              The first member of the list is a prime and is saved/recorded.
              Then all multiples of that prime
              (which not a prime, excepting the prime itself!)
              are removed from the list.
              Now the first number remaining in the list is the next prime number.
              And the process repeats.
            </p>
            <p>
              The code blocks below can be rearranged to form one of the many possible programs to implement this algorithm to compute a list of all the primes less than <m>250</m>. [Ed. this version of this problem requires the reader to provide the necessary indentation.]
            </p>
          </statement>
          <blocks>
          <block order="6">
            <cline>n = 250</cline>
          </block>
          <block order="2">
          <choice correct="yes">
            <cline>primes = []</cline>
            <cline>candidates = list(range(2,n))</cline>
          </choice>
          <choice>
            <cline>candidates = []</cline>
            <cline>primes = list(range(2,n))</cline>
          </choice>
          </block>
          <block order="7" correct="no">
            <cline>primes = candidates + [p]</cline>
          </block>
          <block order="8">
            <cline>while candidates:</cline>
          </block>
          <block order="3">
            <cline>p = candidates[0]</cline>
            <cline>primes.append(p)</cline>
          </block>
          <block order="1">
            <cline>for nonprime in range(p, n, p):</cline>
          </block>
          <block order="5">
            <cline>if nonprime in candidates:</cline>
            <cline>candidates.remove(nonprime)</cline>
          </block>
          <block order="4">
            <cline>print(primes)</cline>
          </block>
          </blocks>
        </exercise>
      </exercises>
      <exercises>
        <title>Matching</title>
        <introduction>
          <p>
            Events and dates.
          </p>
        </introduction>
<!-- https://www.britannica.com/list/25-decade-defining-events-in-us-history -->
        <exercise 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>
      </exercises>
      <exercises>
        <title>Clickable Area</title>
        <introduction>
          <p>
            Words, not code.
          </p>
        </introduction>
        <exercise label="clickable-text">
          <title>Clickable Areas,
          <q>Regular</q>
          Text</title>
          <statement>
            <p>
              Identify (by clicking,
              or by circling) all of the nouns in this quotation by Eleanor Roosevelt.
            </p>
          </statement>
          <areas>
          <p>
            <q>The <area>future</area> belongs to <area correct="no">those</area> who believe in the <area correct="yes">beauty</area> of <area correct="no">their</area> <area>dreams</area>.</q>
          </p>
          </areas>
          <feedback>
            <p>
              The incorrect words are pronouns.
            </p>
          </feedback>
        </exercise>
      </exercises>
      <exercises>
        <title>Old-Style Fillin-In</title>
        <introduction>
          <p>
            Do not use this as a model for new exercises.
            Just for backwards-compatibility.
          </p>
        </introduction>
        <exercise label="fillin-string-integer">
          <title>Fill-In, String and Number Answers</title>
          <statement>
            <p>
              Complete the following line of a Python program so that it will declare an integer variable <c>age</c> with an initial value of <c>5</c>.
            </p>
            <p>
              <var/> <c>age = </c> <var/><c>;</c>
            </p>
          </statement>
          <setup>
            <var>
            <condition string="int">
            <feedback>
              <p>
                A variable of type <c>int</c> is appropriate for whole number ages.
              </p>
            </feedback>
            </condition>
            <condition string=".*">
            <feedback>
              <p>
                Remember that Java uses just the first three letters of the word
                <q>integer</q>
                to define an integral type.
              </p>
            </feedback>
            </condition>
            </var>
            <var>
            <condition number="5">
            <feedback>
              <p>
                An integer variable may be initialized to a value.
              </p>
            </feedback>
            </condition>
            <condition string=".*">
            <feedback>
              <p>
                Use <c>5</c> as the initial value of the variable.
              </p>
            </feedback>
            </condition>
            </var>
          </setup>
        </exercise>
      </exercises>
      <reading-questions>
        <title>A Reading Question</title>
        <exercise label="short-answer-question">
          <title>Short Answer</title>
          <statement>
            <p>
              This should be built with a text-box,
              <em>only</em> on a capable server (Runestone).
              So it can be answered
            </p>
          </statement>
          <response/>
        </exercise>
      </reading-questions>
      <subsection>
        <title>Faux Subsection</title>
        <p>
          We used <tag>exercises</tag> divisions above,
          and need a <tag>subsection</tag> to feed the schema.
        </p>
      </subsection>
    </section>