<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>AlgMap-5.2</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Subsitute \(s\) = \({@s@}\) and \(t\) = \({@t@}\) into the equation: \[\frac{s^2+2t^2}{3-st}.\] <br /> Be sure to leave your answer as a fraction in it's simplest form. <br /> [[input:ans]] [[validation:ans]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>Subsituting \(s\) = \({@s@}\) and \(t\) = \({@t@}\) into the equation: \[\frac{s^2+2t^2}{3-st} = \frac{\left({@s@}\right)^2+2\left({@t@}\right)^2}{3-\left({@s@}\right)\times\left({@t@}\right)} = \frac{{@ev(s^2,simp)@}+{@ev(2*t^2,simp)@}}{3-{@ev(s*t,simp)@}} = \frac{@ev(s^2+2*t^2,simp)@}{@ev(3-s*t,simp)@} = \frac{@num(ta1)@}{@num(ta2)@}\times\frac{@denom(ta2)@}{@denom(ta1)@} = {@ta@}.\]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text/>
    </stackversion>
    <questionvariables>
      <text>simp:true;
a:rand(4)+1;
b:a+rand(4)+1;
c:rand(4)+1;
d:a+rand(4)+1;
s:a/b;
t:c/d;
ta1:(s^2+2*t^2);
ta2:(3-s*t);
ta:ta1/ta2;
simp:false;</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\[ t={@t@}, s={@s@}, \frac{s^2+2t^2}{3-st} = {@ta@}.\]</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>0</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
      <name>ans</name>
      <type>algebraic</type>
      <tans>ta</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options/>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>0</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>EqualComAss</answertest>
        <sans>ans</sans>
        <tans>ta</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>1-0-T </trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>1</falsenextnode>
        <falseanswernote>1-0-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
      <node>
        <name>1</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans</sans>
        <tans>ta</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>1-1-T </trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>Your answer is algebraically equivalent to the correct answer but is not fully simplified. Leave you answer as a single fraction in it's lowest terms. You also mustn't include any operative symbols.</p>]]></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>1-1-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>451140016</deployedseed>
    <deployedseed>1812942129</deployedseed>
    <deployedseed>1068922088</deployedseed>
    <deployedseed>2071430651</deployedseed>
    <deployedseed>104749342</deployedseed>
    <deployedseed>146875856</deployedseed>
    <deployedseed>1916296736</deployedseed>
    <deployedseed>1505666457</deployedseed>
    <deployedseed>1818816456</deployedseed>
    <deployedseed>1321390961</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans</name>
        <value>ta</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>1-0-T</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
