Exercises 5.19 Fill-In Exercises

<exercises xml:id="fill-in-exercises">
  <title>Fill-In Exercises</title>

  <introduction>
    <p>
      This section has <term>fill-in-the-blank</term> ( <init>FITB</init> )
      exercises using newer syntax, and the subject of active development.
    </p>
  </introduction>

  <exercise label="fillin-numbers-many-tests">
    <title>Fill-In, New Markup Numbers</title>

    <statement>
      <p>
        I love <m>\pi</m>. What number am I thinking of, accurate to two
        decimal places?
      </p>

      <p>
        <fillin width="5" answer="3.14"/>
      </p>
    </statement>
    <evaluation>
      <evaluate>
        <test correct="yes">
          <numcmp use-answer="yes"/>
          <feedback>
            <p>
              The decimal approximation of <m>\pi</m> is
              <m>3.1415926535\ldots</m>, but to two decimal places we write
              <m>3.14</m>.
            </p>
          </feedback>
        </test>
        <!-- Example B -->
        <test>
          <numcmp use-answer="yes" tolerance="0.1"/>
          <feedback>
            <p>
              Your answer is within 0.1 of the value I wanted.
            </p>
          </feedback>
        </test>
        <!-- Example C -->
        <test>
          <numcmp value="42"/>
          <feedback>
            <p>
              That is a reasonable guess, but no.
            </p>
          </feedback>
        </test>
        <!-- Example D -->
        <test>
          <numcmp min="3" max="4"/>
          <feedback>
            <p>
              You chose a value between 3 and 4.
            </p>
          </feedback>
        </test>
        <!-- Example E -->
        <test>
          <numcmp value="3" tolerance="0.5"/>
          <feedback>
            <p>
              You chose a value that rounds to 3.
            </p>
          </feedback>
        </test>
      </evaluate>
    </evaluation>
  </exercise>

  <exercise label="fillin-strings-">
    <title>Fill-In, New Markup Strings</title>

    <statement>
      <p>
        The word I'm thinking about is hinted at by the image.
      </p>

      <p>
        <image source="cartoon-magic.jpg" width="50%"/>
      </p>

      <p>
        What word am I thinking about? <fillin width="5" answer="magic"/>
        (Interactive feedback explores a variety of options: Try what happens
        if you mix the case, or type in a number, or include more than the
        word, or try <q>pizzazz</q>.")
      </p>
    </statement>
    <evaluation>
      <evaluate>
        <!-- Example A -->
        <test correct="yes">
          <strcmp use-answer="yes"/>
        </test>
        <!-- Example B -->
        <test>
          <strcmp use-answer="yes" case="insensitive"/>
          <feedback>
            <p>
              Some of the characters used the wrong case.
            </p>
          </feedback>
        </test>
        <!-- Example C -->
        <test>
          <strcmp>
            [0-9]+
          </strcmp>

          <feedback>
            <p>
              You typed a word made out of digits.
            </p>
          </feedback>
        </test>
        <!-- Example D -->
        <test>
          <strcmp use-answer="yes" strip="no"/>
          <feedback>
            <p>
              Your answer includes the correct word but has extra text.
            </p>
          </feedback>
        </test>
        <!-- Example E -->
        <test>
          <strcmp strip="no" case="insensitive">
            z.+z
          </strcmp>

          <feedback>
            <p>
              Your answer includes text surrounded by z's.
            </p>
          </feedback>
        </test>
      </evaluate>
    </evaluation>

    <hint>
      <p>
        Do you really need a hint? Carefully reread the question.
      </p>
    </hint>
  </exercise>

  <exercise label="ex-demo-jscmp-primes">
    <title>Fill-In, Javascript test of numbers</title>

    <statement>
      <p>
        What is an example of a prime number less than 20?
        <fillin width="5" answer="13"/>
      </p>
    </statement>
    <evaluation>
      <evaluate>
        <test correct="yes">
          <jscmp>
            <!-- test if number is in a list -->
            [2, 3, 5, 7, 11, 13, 17, 19].includes(Number(ans))
          </jscmp>

          <feedback>
            <p>
              Any number from the list <m>\{2, 3, 5, 7, 11, 13, 17, 19\}</m>
              is a prime number less than 20.
            </p>
          </feedback>
        </test>
        <test>
          <jscmp>
            <!-- find why it fails to be in list -->
            
                      function(){
                      const val=Number(ans);
                      if (val &lt;= 0) { return "You need to give a positive integer." }
                      if (val &gt;= 20) { return "The integer must be less than 20." }
                      for (let i=2; i&lt;=3; i++) {
                          if (val % i == 0) { return `Your answer is composite; for example, it is divisible by ${i}.` }
                      }
                      return false;
                      }()
          </jscmp>
        </test>
      </evaluate>
    </evaluation>
  </exercise>

  <exercise label="fillin-jscmp-palindrome">
    <title>Fill-In, Javascript test of strings</title>

    <statement>
      <p>
        What is an example of a palindrome? <fillin width="5" answer="radar"/>
      </p>
    </statement>
    <evaluation>
      <evaluate>
        <test correct="yes">
          <jscmp>
            <!-- test if string is palindrome -->
            function(){
                          const r1 = new RegExp("^\\w+$");
                          var result=r1.test(ans);
                          if (result) {
                          let revAns = ans.split("").reverse().join("");
                          result = (ans === revAns);
                          }
                          return result;
                      }()
          </jscmp>

          <feedback>
            <p>
              Any word that is the same forward and backward is a palindrome.
            </p>
          </feedback>
        </test>
        <test>
          <strcmp strip="no">
            \w+\s\w+
          </strcmp>

          <feedback>
            <p>
              Your response needs to be a single word.
            </p>
          </feedback>
        </test>
      </evaluate>
    </evaluation>
  </exercise>

  <exercise label="fillin-random-simple">
    <title>Fill-In, Simple Randomization with Numbers</title>

    <statement>
      <p>
        What is the square of <m>x=<eval obj="myNum"/></m>? <m>x^2=</m>
        <fillin width="5" mode="number" ansobj="mySquare"/>
      </p>
    </statement>
    <setup seed="1234">
      <setupScript>
        v.myNum=RNG.randDiscrete(2, 12, 1);
              v.mySquare=v.myNum**2;
      </setupScript>
    </setup>
    <evaluation>
      <evaluate>
        <test correct="yes">
          <numcmp use-answer="yes"/>
        </test>
        <test>
          <numcmp object="myNum"/>
          <feedback>
            <p>
              You responded with the original number. Now square it.
            </p>
          </feedback>
        </test>
      </evaluate>
    </evaluation>
  </exercise>

  <exercise label="fillin-math-solve-equation">
    <title>Fill-In, Dynamic Math with Simple Numerical Answer</title>

    <statement>
      <p>
        Solve the equation
        <md>
          <eval obj="theFunction"/>
          =0
        </md>
        to get the value of <m>x</m>.
      </p>

      <p>
        <m>x = </m> <fillin width="5" mode="math" ansobj="theAnswer"/>
      </p>
    </statement>

    <solution>
      <p>
        We want to isolate the <m>x</m> in the equation
        <m><eval obj="theFunction"/>=0</m>. Because addition of
        <m><eval obj="b"/></m> is the last operation, we apply the inverse by
        adding <m><eval obj="negB"/></m> to both sides. The new, but
        equivalent equation is now
        <m><eval obj="m"/>x = <eval obj="negB"/></m>. Dividing both sides of
        the equation by <m><eval obj="m"/></m>, we obtain the solution
        <m>x=<eval obj="theAnswer"/></m>.
      </p>
    </solution>
    <setup seed="12345">
      <de-object name="m" context="number">
        <de-random distribution="discrete" nonzero="yes" min="-4" max="5" by="1"/>
      </de-object>
      <de-object name="b" context="number">
        <de-random distribution="discrete" min="-10" max="10"/>
      </de-object>
      <de-object name="negB" context="number">
        <de-number reduce="yes">
          -b
        </de-number>
      </de-object>
      <de-object name="theFunction" context="formula">
        <de-expression mode="formula" reduce="yes">
          m*x+b
        </de-expression>
      </de-object>
      <de-object name="theAnswer" context="formula">
        <de-expression mode="formula" reduce="yes">
          -b/m
        </de-expression>
      </de-object>
    </setup>
    <evaluation>
      <evaluate>
        <test correct="yes">
          <mathcmp use-answer="yes"/>
        </test>
        <test>
          <de-expression mode="formula">
            {{b}}/{{m}}
          </de-expression>

          <feedback>
            Check for a sign error while isolating
            <m>
              x
            </m>
            .
          </feedback>
        </test>
      </evaluate>
    </evaluation>
  </exercise>

  <exercise label="fillin-math-find-derivatives">
    <title>Fill-In, Dynamic Math with Formulas as Answers</title>

    <statement>
      <p>
        Consider the function <m>f(x)=<eval obj="formula"/></m>. Find
        <m>f'(x)</m> and <m>f''(x)</m>.
      </p>

      <p>
        <m>f'(x) = </m>
        <fillin mode="math" width="15" ansobj="correctD1" name="firstD"/> and
        <m>f''(x)=</m>
        <fillin mode="math" width="15" ansobj="correctD2" name="secondD"/>
      </p>
    </statement>

    <solution>
      <p>
        The derivative of a constant is zero, so
        <m>\frac{d}{dx}[<eval obj="b"/>]=0</m>. The term
        <m>x^{<eval obj="n"/>}</m> is a power, so the power rule gives us
        <m>\frac{d}{dx}[x^{<eval obj="n"/>}]=<eval obj="n"/>x^{<eval obj="nm1"/>}</m>.
        Putting this together, we find <m>f'(x)=<eval obj="correctD1"/></m>.
        Applying the power rule a second time, we find
        <m>f''(x)=<eval obj="correctD2"/></m>.
      </p>
    </solution>
    <setup seed="1234">
      <de-object name="a" context="number">
        <de-random distribution="discrete" min="-4" max="5" by="1" nonzero="yes"/>
      </de-object>
      <de-object name="n" context="number">
        <de-random distribution="discrete" min="2" max="5"/>
      </de-object>
      <de-object name="nm1" context="number">
        <de-number reduce="yes">
          n-1
        </de-number>
      </de-object>
      <de-object name="nm2" context="number">
        <de-number reduce="yes">
          n-2
        </de-number>
      </de-object>
      <de-object name="b" context="number">
        <de-random distribution="discrete" min="-10" max="10" nonzero="yes"/>
      </de-object>
      <de-object name="formula" context="formula">
        <de-expression mode="formula">
          a*x^n+b
        </de-expression>
      </de-object>
      <de-object name="correctD1" context="formula">
        <de-expression mode="derivative" reduce="yes">
          <formula>
            <eval obj="formula"/>
          </formula>
          <variable name="x"/>
        </de-expression>
      </de-object>
      <de-object name="correctD2" context="formula">
        <de-expression mode="derivative" reduce="yes">
          <formula>
            <eval obj="correctD1"/>
          </formula>
          <variable name="x"/>
        </de-expression>
      </de-object>
    </setup>
    <evaluation>
      <evaluate submit="firstD">
        <test correct="yes">
          <mathcmp use-answer="yes"/>
        </test>
        <test>
          <mathcmp obj="correctD2"/>
          <feedback>
            <p>
              You confused which derivative is which.
            </p>
          </feedback>
        </test>
      </evaluate>
      <evaluate submit="secondD">
        <test correct="yes">
          <mathcmp use-answer="yes"/>
        </test>
        <test>
          <eval obj="correctD1"/>
          <feedback>
            <p>
              You confused which derivative is which.
            </p>
          </feedback>
        </test>
      </evaluate>
    </evaluation>
  </exercise>

  <exercise label="fillin-math-decompose-function">
    <title>Fill-In, Dynamic Math with Interdependent Formula Checking</title>

    <statement>
      <p>
        Consider the function
        <md>
          h(x)=
          <eval obj="composition"/>
        </md>.
        Find two nontrivial functions <m>f(x)</m> and <m>g(x)</m> so that
        <m>h(x) = f(g(x))</m>.
      </p>

      <p>
        <m>f(x) = </m>
        <fillin mode="math" width="15" ansobj="outerFormula" name="fGiven"/>
        and <m>g(x)=</m>
        <fillin mode="math" width="15" ansobj="innerFormula" name="gGiven"/>
      </p>
    </statement>

    <solution>
      <p>
        Noticing that the expression <m><eval obj="innerFormula"/></m> appears
        inside parentheses with a power, it makes sense to think of that as
        the inner function, defining <m>g(x) = <eval obj="innerFormula"/></m>.
        The outer function describes what happens to that. If we imagined
        replacing the formula <m><eval obj="innerFormula"/></m> with a box and
        then call that box our variable <m>x</m>, we find the outer function
        is given by <m>f(x) = <eval obj="outerFormula"/></m>.
      </p>

      <p>
        This is not the only non-trivial composition. Can you find others?
      </p>
    </solution>
    <setup seed="4321">
      <de-object name="a" context="number">
        <de-random distribution="discrete" min="-4" max="5" by="1" nonzero="yes"/>
      </de-object>
      <de-object name="n" context="number">
        <de-random distribution="discrete" min="2" max="5"/>
      </de-object>
      <de-object name="b" context="number">
        <de-random distribution="discrete" min="-10" max="10" by="1" nonzero="yes"/>
      </de-object>
      <de-object name="c" context="number">
        <de-random distribution="discrete" min="-4" max="5" by="1" nonzero="yes"/>
      </de-object>
      <de-object name="d" context="number">
        <de-random distribution="discrete" min="-10" max="10" by="1" nonzero="yes"/>
      </de-object>
      <de-object name="outerFormula" context="formula">
        <de-expression mode="formula" reduce="yes">
          a*x^n+b
        </de-expression>
      </de-object>
      <de-object name="innerFormula" context="formula">
        <de-expression mode="formula" reduce="yes">
          c*x+d
        </de-expression>
      </de-object>
      <de-object name="identityFunction" context="formula">
        <de-expression mode="formula">
          x
        </de-expression>
      </de-object>
      <de-object name="composition" context="formula" reduce="yes">
        <de-expression mode="substitution">
          <formula>
            <eval obj="outerFormula"/>
          </formula>
          <variable name="x">
            <eval obj="innerFormula"/>
          </variable>
        </de-expression>
      </de-object>
    </setup>
    <evaluation answers-coupled="yes">
      <evaluate name="fGiven">
        <test>
          <eval obj="identityFunction"/>
          <feedback>
            <p>
              <m>f(x)=x</m> is not allowed for nontrivial compositions.
            </p>
          </feedback>
        </test>
        <test>
          <logic op="not">
            <mathcmp>
              <eval obj="composition"/>
              <de-expression context="formula" mode="substitution">
                <formula>
                  <eval obj="fGiven"/>
                </formula>
                <variable name="x">
                  <eval obj="gGiven"/>
                </variable>
              </de-expression>
            </mathcmp>
          </logic>
          <mathcmp>
            <eval obj="composition"/>
            <de-expression context="formula" mode="substitution">
              <formula>
                <eval obj="gGiven"/>
              </formula>
              <variable name="x">
                <eval obj="fGiven"/>
              </variable>
            </de-expression>
          </mathcmp>

          <feedback>
            <p>
              You have composed in the wrong order.
            </p>
          </feedback>
        </test>
      </evaluate>
      <evaluate name="gGiven">
        <test>
          <eval obj="identityFunction"/>
          <feedback>
            <m>
              g(x)=x
            </m>
            is not allowed for nontrivial compositions.
          </feedback>
        </test>
      </evaluate>
      <evaluate all="yes">
        <test correct="yes">
          <mathcmp>
            <eval obj="composition"/>
            <de-expression context="formula" mode="substitution">
              <formula>
                <eval obj="fGiven"/>
              </formula>
              <variable name="x">
                <eval obj="gGiven"/>
              </variable>
            </de-expression>
          </mathcmp>
          <logic op="not">
            <mathcmp>
              <eval obj="fGiven"/>
              <eval obj="identityFunction"/>
            </mathcmp>
          </logic>
          <logic op="not">
            <mathcmp>
              <eval obj="gGiven"/>
              <eval obj="identityFunction"/>
            </mathcmp>
          </logic>
        </test>
      </evaluate>
    </evaluation>
  </exercise>
</exercises>