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>

    <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>
      <matches>
      <match order="4">
      <premise>Monroe Doctrine</premise>
      <response>1823</response>
      </match>
      <match order="3">
      <premise>Haymarket Riot</premise>
      <response>1886</response>
      </match>
      <match order="1">
      <premise>Louisiana Purchase</premise>
      <response>1803</response>
      </match>
      <match order="2">
      <premise>Battle of Gettysburg</premise>
      <response>1863</response>
      </match>
      </matches>
    </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>