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✏️ Editing: sample_questions_wrong.xml

<?xml version="1.0" encoding="UTF-8"?>
<quiz>

  <question type="category">
    <category>
        <text>$course$/Default for Scratch/input_samples</text>
    </category>
  </question>

<question type="stack">
    <name>
      <text>Algebraic input</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Type in {@ta@}.<br></p><p>[[input:ans1]]</p><div>[[validation:ans1]]</div>]]></text>
      <text></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text>ta:a*b</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote>
      <text></text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text>Correct answer, well done.</text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text>Your answer is partially correct.</text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text>Incorrect answer.</text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>2</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords>solve</forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>ta</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
  </question>

<question type="stack">
    <name>
      <text>Algebraic input (answer box sizes test)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>This question just tests answer boxes of multiple sizes.</p><p>[[input:ans1]] [[validation:ans1]]</p><p>[[input:ans2]] [[validation:ans2]]</p><p>[[input:ans3]] [[validation:ans3]]</p><p>[[input:ans4]] [[validation:ans4]]</p><p>[[input:ans5]] [[validation:ans5]]</p><p>[[input:ans7]] [[validation:ans7]]</p><p>[[input:ans10]] [[validation:ans10]]</p><p>[[input:ans15]] [[validation:ans15]]</p><p>[[input:ans20]] [[validation:ans20]]</p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text></text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote>
      <text></text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text>Correct answer, well done.</text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text>Your answer is partially correct.</text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text>Incorrect answer.</text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>2</tans>
      <boxsize>1</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint>2</syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <input>
      <name>ans10</name>
      <type>algebraic</type>
      <tans>2</tans>
      <boxsize>10</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint>2222222222</syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <input>
      <name>ans15</name>
      <type>algebraic</type>
      <tans>2</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint>222222222222222</syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <input>
      <name>ans2</name>
      <type>algebraic</type>
      <tans>2</tans>
      <boxsize>2</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint>22</syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <input>
      <name>ans20</name>
      <type>algebraic</type>
      <tans>2</tans>
      <boxsize>20</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint>12345123451234512345</syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <input>
      <name>ans3</name>
      <type>algebraic</type>
      <tans>2</tans>
      <boxsize>3</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint>222</syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <input>
      <name>ans4</name>
      <type>algebraic</type>
      <tans>2</tans>
      <boxsize>4</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint>2222</syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <input>
      <name>ans5</name>
      <type>algebraic</type>
      <tans>2</tans>
      <boxsize>5</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint>22222</syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <input>
      <name>ans7</name>
      <type>algebraic</type>
      <tans>2</tans>
      <boxsize>5</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint>2222222</syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>2</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>This just takes account of the first answer box!</p>]]></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>This just takes account of the first answer box!<br></p>]]></text>
        </falsefeedback>
      </node>
    </prt>
  </question>

<question type="stack">
    <name>
      <text>Checkbox</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Differentiate {@p@} with respect to $x$.</p><p>[[input:ans1]]</p><div>[[validation:ans1]]</div>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text><![CDATA[/* Create a list of potential answers. */
p:sin(2*x);
ta:[[diff(p,x),true],[p,false],[int(p,x),false],[cos(2*x)+c,false]];
/* The actual correct answer.    */
tac:diff(p,x)
/* Add in a "None of these" to the end of the list.  The Maxima value is the atom null. */
tao:[null, false, "None of these"];
ta:append(ta,[tao]);]]></text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote>
      <text></text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text>Correct answer, well done.</text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text>Your answer is partially correct.</text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text>Incorrect answer.</text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>checkbox</type>
      <tans>ta</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>2</showvalidation>
      <options></options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>Diff</answertest>
        <sans>first(ans1)</sans>
        <tans>diff(p,x)</tans>
        <testoptions>x</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
  </question>

<question type="stack">
    <name>
      <text>Dropdown (shuffle)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Differentiate {@p@} with respect to $x$.</p><p>[[input:ans1]]</p><div>[[validation:ans1]]</div>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text><![CDATA[/* Create a list of potential answers. */
p:sin(2*x);
ta:[[diff(p,x),true],[p,false],[int(p,x),false],[cos(2*x)+c,false]];
/* The actual correct answer.    */
tac:diff(p,x)
/* Randomly shuffle the list "ta". */
ta:random_permutation(ta);
/* Add in a "None of these" to the end of the list.  The Maxima value is the atom null. */
tao:[null, false, "None of these"];
ta:append(ta,[tao]);]]></text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote>
      <text>{@ta@}</text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text>Correct answer, well done.</text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text>Your answer is partially correct.</text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text>Incorrect answer.</text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>dropdown</type>
      <tans>ta</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>2</showvalidation>
      <options></options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>Diff</answertest>
        <sans>first(ans1)</sans>
        <tans>diff(p,x)</tans>
        <testoptions>x</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
  </question>

<question type="stack">
    <name>
      <text>Equiv input test</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Solve {@p@}.<br></p><p>[[input:ans1]]</p><div>[[validation:ans1]]</div>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>sangwinc<br></p>]]></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text>v:x
p:3*v+7=4
ta:[p,x=(4-7)/3,x=-1]</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote>
      <text></text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text>Correct answer, well done.</text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text>Your answer is partially correct.</text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text>Incorrect answer.</text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>equiv</type>
      <tans>ta</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>5</insertstars>
      <syntaxhint>firstline</syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>last(ans1)</sans>
        <tans>last(ta)</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
  </question>

<question type="stack">
    <name>
      <text>Matrix</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Type in {@M@}<br></p><p>[[input:ans1]]</p><div>[[validation:ans1]]</div>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text>M:matrix([1,2],[3,4])</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote>
      <text></text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text>Correct answer, well done.</text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text>Your answer is partially correct.</text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text>Incorrect answer.</text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>matrix</type>
      <tans>M</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>M</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
  </question>

<question type="stack">
    <name>
      <text>Notes</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Show your working in this box! $x$.<br></p><p>[[input:ans1]]</p><div>[[validation:ans1]]</div>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text></text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote>
      <text></text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text>Correct answer, well done.</text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text>Your answer is partially correct.</text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text>Incorrect answer.</text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>notes</type>
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      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
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      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
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      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
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      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
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        <testoptions></testoptions>
        <quiet>0</quiet>
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        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
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        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
  </question>

<question type="stack">
    <name>
      <text>Radio</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Differentiate {@p@} with respect to $x$.</p><p>[[input:ans1]]</p><div>[[validation:ans1]]</div>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text><![CDATA[/* Create a list of potential answers. */
p:sin(2*x);
ta:[[diff(p,x),true],[p,false],[int(p,x),false],[cos(2*x)+c,false]];
/* The actual correct answer.    */
tac:diff(p,x)
/* Add in a "None of these" to the end of the list.  The Maxima value is the atom null. */
tao:[null, false, "None of these"];
ta:append(ta,[tao]);]]></text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote>
      <text></text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text>Correct answer, well done.</text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text>Your answer is partially correct.</text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text>Incorrect answer.</text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>radio</type>
      <tans>ta</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
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      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
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    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>Diff</answertest>
        <sans>first(ans1)</sans>
        <tans>diff(p,x)</tans>
        <testoptions>x</testoptions>
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        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
  </question>

<question type="stack">
    <name>
      <text>Single char</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Type in $x$<br></p><p>[[input:ans1]]</p><div>[[validation:ans1]]</div>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text></text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote>
      <text></text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text>Correct answer, well done.</text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text>Your answer is partially correct.</text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text>Incorrect answer.</text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>singlechar</type>
      <tans>x</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
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      <forbidfloat>1</forbidfloat>
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      <mustverify>1</mustverify>
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    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>x</tans>
        <testoptions></testoptions>
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        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
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        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
  </question>

<question type="category">
    <category>
        <text>$course$/Default for Scratch</text>

</category>
  </question>

<question type="stack">
    <name>
      <text>test_1_integration</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Find \[ \int {@p@} d{@v@}\] [[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>We can either do this question by inspection (i.e. spot the answer) or in a more formal manner by using the substitution \[ u = ({@v@}-{@a@}).\] Then, since $\frac{d}{d{@v@}}u=1$ we have \[ \int {@p@} d{@v@} = \int u^{@n@} du = \frac{u^{@n+1@}}{@n+1@}+c = {@ta@}+c.\]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text>n:rand(5)+3;
a:rand(5)+3;
v:rand([x,t]);
p:(v-a)^n;
ta:(v-a)^(n+1)/(n+1);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
    </specificfeedback>
    <questionnote>
      <text>$\int {@p@} d{@v@} = {@ta@}$</text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<p><span class="correct">Correct answer, well done.</span></p>]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<p><span class="partially">Your answer is partially correct.</span></p>]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<p><span class="incorrect">Incorrect answer.</span></p>]]></text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta+c</tans>
      <boxsize>20</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords>int</forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
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    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>Int</answertest>
        <sans>ans1</sans>
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        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>1-0-T </trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>1-0-F </falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>1</deployedseed>
    <deployedseed>1001758021</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <testinput>
        <name>ans1</name>
        <value>ta+c</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>1-0-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <testinput>
        <name>ans1</name>
        <value>ta</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>1-0-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <testinput>
        <name>ans1</name>
        <value>n*(v-a)^(n-1)</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>1-0-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>4</testcase>
      <testinput>
        <name>ans1</name>
        <value>(v-a)^(n+1)</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>1-0-F</expectedanswernote>
      </expected>
    </qtest>
  </question>

<question type="stack">
    <name>
      <text>test_2_rectangle</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>A rectangle has length {@sg@}cm greater than its width. If it has an area of ${@abs(ar)@}cm^2$, find the dimensions of the rectangle.</p>
 <p>1. Write down an equation which relates the side lengths to the area of the rectangle. <br />[[input:ans1]] [[validation:ans1]] [[feedback:eq]]</p>
 <p>2. Solve your equation. Enter your answer as a set of numbers. <br /> [[input:ans2]] [[validation:ans2]] [[feedback:sol]]</p>
 <p>3. Hence, find the length of the shorter side. <br />[[input:ans3]] cm [[validation:ans3]] [[feedback:short]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>If $x$cm is the width then $(x+{@sg@})$ is the length. Now the area is ${@abs(ar)@}cm^2$ and so \[ {@x*(x+sg)=-ar@}.\] \[ {@x^2+sg*x+ar@}=0\] \[ {@(x+rp)*(x+rn)=0@} \] So that $x={@-rp@}$ or $x={@-rn@}$. Since lengths are positive quantities $x&gt;0$ and we discard the negative root. Hence the length of the shorter side is $x={@-rn@}$cm.</p>]]></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text>rn:-1*(rand(4)+2);
rp:9+rand(6);
ar:rn*rp;
sg:rn+rp;
ta1:x*(x+sg)=-ar;
ta2:x*(x-sg)=-ar;
tas1:setify(map(rhs,solve(ta1,x)));
tas2:setify(map(rhs,solve(ta2,x)));</text>
    </questionvariables>
    <specificfeedback format="html">
      <text></text>
    </specificfeedback>
    <questionnote>
      <text>{@ta1@}, {@tas1@}.</text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<p><span class="correct">Correct answer, well done.</span></p>]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<p><span class="partially">Your answer is partially correct.</span></p>]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<p><span class="incorrect">Incorrect answer.</span></p>]]></text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta1</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>1</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
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      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <input>
      <name>ans2</name>
      <type>algebraic</type>
      <tans>tas1</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>1</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
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      <allowwords></allowwords>
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      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <input>
      <name>ans3</name>
      <type>algebraic</type>
      <tans>rp</tans>
      <boxsize>5</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>1</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
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      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
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    <prt>
      <name>eq</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>SubstEquiv</answertest>
        <sans>ans1</sans>
        <tans>ta1</tans>
        <testoptions></testoptions>
        <quiet>1</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>eq-0-T </trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>1</falsenextnode>
        <falseanswernote>eq-0-F </falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
      <node>
        <name>1</name>
        <answertest>SubstEquiv</answertest>
        <sans>ans1</sans>
        <tans>ta2</tans>
        <testoptions></testoptions>
        <quiet>1</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>eq-1-T </trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>eq-1-F </falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>short</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans3</sans>
        <tans>-rn</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>short-0-T </trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>short-0-F </falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>sol</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text>v1:first(listofvars(ans1));
 ftm:setify(map(rhs,solve(ans1,v1)));</text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>SubstEquiv</answertest>
        <sans>ans1</sans>
        <tans>ta1</tans>
        <testoptions></testoptions>
        <quiet>1</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>3</truenextnode>
        <trueanswernote>sol-0-T </trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>1</falsenextnode>
        <falseanswernote>sol-0-F </falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
      <node>
        <name>1</name>
        <answertest>SubstEquiv</answertest>
        <sans>ans1</sans>
        <tans>ta2</tans>
        <testoptions></testoptions>
        <quiet>1</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>4</truenextnode>
        <trueanswernote>sol-1-T </trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>2</falsenextnode>
        <falseanswernote>sol-1-F </falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
      <node>
        <name>2</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans2</sans>
        <tans>ftm</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>sol-2-T </trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>You have correctly solved the equation you have entered in part 1. Please try both parts again!</p>]]></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>sol-2-F </falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
      <node>
        <name>3</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans2</sans>
        <tans>tas1</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>sol-3-T </trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>sol-3-F </falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
      <node>
        <name>4</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans2</sans>
        <tans>tas2</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>sol-5-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>-</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>sol-5-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>92</deployedseed>
    <deployedseed>1621764605</deployedseed>
    <deployedseed>79313047</deployedseed>
    <deployedseed>1740562616</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <testinput>
        <name>ans1</name>
        <value>ta1</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ev({-rp,-rn},simp)</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>ev(-rn,simp)</value>
      </testinput>
      <expected>
        <name>eq</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>eq-0-T</expectedanswernote>
      </expected>
      <expected>
        <name>short</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>short-0-T</expectedanswernote>
      </expected>
      <expected>
        <name>sol</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>sol-3-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <testinput>
        <name>ans1</name>
        <value>ta2</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ev({rp,rn},simp)</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>ev(-rn,simp)</value>
      </testinput>
      <expected>
        <name>eq</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>eq-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>short</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>short-0-T</expectedanswernote>
      </expected>
      <expected>
        <name>sol</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>sol-5-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <testinput>
        <name>ans1</name>
        <value>x+sg=-ar</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>{-ar-sg}</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value></value>
      </testinput>
      <expected>
        <name>eq</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>eq-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>short</name>
        <expectedscore></expectedscore>
        <expectedpenalty></expectedpenalty>
        <expectedanswernote>NULL</expectedanswernote>
      </expected>
      <expected>
        <name>sol</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>sol-2-T</expectedanswernote>
      </expected>
    </qtest>
  </question>

<question type="stack">
    <name>
      <text>test_3_matrix</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Calculate \[ {@A@}.{@B@}\]</p>
<p> [[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>To multiply matrices $A$ and $B$ we need to remember that the $(i,j)$th entry is the scalar product of the $i$th row of $A$ with the $j$th column of $B$.</p>
<p>\[ {@A@}.{@B@} = {@C@} = {@D@}.\]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text><![CDATA[A:ev(rand(matrix([5,5],[5,5]))+matrix([2,2],[2,2]),simp);
B:ev(rand(matrix([5,5],[5,5]))+matrix([2,2],[2,2]),simp);
TA:ev(A.B,simp);
TB:ev(A*B,simp);
BT:transpose(B);
C:zeromatrix (first(matrix_size(A)), second(matrix_size(A)));
S:for a:1 thru first(matrix_size(A)) do for b:1 thru second(matrix_size(A)) do C[ev(a,simp),ev(b,simp)]:apply("+",zip_with("*",A[ev(a,simp)],BT[ev(b,simp)]));
D:ev(C,simp);
C:C;]]></text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
    </specificfeedback>
    <questionnote>
      <text>${@A@}.{@B@}={@TA@}$</text>
    </questionnote>
    <questionsimplify>0</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<p><span class="correct">Correct answer, well done.</span></p>]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<p><span class="partially">Your answer is partially correct.</span></p>]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<p><span class="incorrect">Incorrect answer.</span></p>]]></text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>matrix</type>
      <tans>TA</tans>
      <boxsize>3</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>TA</tans>
        <testoptions></testoptions>
        <quiet>1</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>1-0-T </trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>1</falsenextnode>
        <falseanswernote>1-0-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
      <node>
        <name>1</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>TB</tans>
        <testoptions></testoptions>
        <quiet>1</quiet>
        <truescoremode>=</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>1-1-T </trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>Remember, you don't multiply matrices by multiplying the corresponding entries! A quite different process is needed.</p>]]></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>2</falsenextnode>
        <falseanswernote>1-1-F </falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
      <node>
        <name>2</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>A+B</tans>
        <testoptions></testoptions>
        <quiet>1</quiet>
        <truescoremode>=</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>1-3-T</trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>Please multiply the matrices. It looks like you have added them instead!</p>]]></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>1-3-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>86</deployedseed>
    <deployedseed>219862533</deployedseed>
    <deployedseed>1167893775</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <testinput>
        <name>ans1</name>
        <value>TA</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>1-0-T </expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <testinput>
        <name>ans1</name>
        <value>TB</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>1-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>4</testcase>
      <testinput>
        <name>ans1</name>
        <value>1</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore></expectedscore>
        <expectedpenalty></expectedpenalty>
        <expectedanswernote>NULL</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>5</testcase>
      <testinput>
        <name>ans1</name>
        <value>A</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>1-3-F</expectedanswernote>
      </expected>
    </qtest>
  </question>

<question type="stack">
    <name>
      <text>test_5_cubic_spline</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Consider the real function</p>
<p>\[ f(x) :=\left\{ \begin{array}{ll} {@f0@} &amp; \mbox{for } x\leq {@x0@}, \\ p(x) &amp; \mbox{for } {@x0@} &lt; x &lt; {@x1@}, \\ {@f1@} &amp; \mbox{for } {@x1@}\leq x.\end{array} \right. \]</p>
<p>{@plot(pg,[x,(x0-3),(x1+3)],[y,-3,3])@}</p>
<p>Find the cubic polynomial $p(x)$ which makes $f(x)$ continuously differentiable. </p>
<p>$p(x)=$[[input:ans1]]</p>
<div>[[validation:ans1]]</div>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>First we need to find the information which $p(x)$ needs to satisfy.  This is</p>
<p>\[ p({@x0@})={@subst(x=x0,f0)@}.\]</p>
<p>\[ p({@x1@})={@subst(x=x1,f1)@}.\]</p>
<p>\[ p'({@x0@})={@subst(x=x0,diff(f0,x))@}.\]</p>
<p>\[ p'({@x1@})={@subst(x=x1,diff(f1,x))@}.\]</p>
<p>If we define $p(x)$ to be the cubic </p>
<p>\[ p(x) = a_3 x^3 + a_2 x^2 + a_1 x + a_0,\]</p>
<p>We then set up the matrix equation</p>
<p>\[ {@CS@} {@CV@} = {@CT@} \]</p>
<p>Solving this gives the coefficients, from which we get the polynomial.</p>
<p>{@ta@}.</p>]]></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.0000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text><![CDATA[x0 : -1;
f0 : 1;
x1 : 2;
f1 : sin(%pi*x)
/* Note, we should really use inf instead of 1000 here, but Maxima gives up plotting with the options used by STACK */
pg:if x<x0 then f0 else if x<x1 then 1000 else f1;
CS:matrix([1,x0,x0^2,x0^3],[0,1,2*x0,3*x0^2],[1,x1,x1^2,x1^3],[0,1,2*x1,3*x1^2])
CT:transpose(matrix([ev(f0,x=x0),subst(x=x0,diff(f0,x)),ev(f1,x=x1),subst(x=x1,diff(f1,x))]));
CV:transpose(matrix([a0,a1,a2,a3]));
CS2:invert(CS).CT;
ta : matrix([1,x,x^2,x^3]).CS2;]]></text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
    </specificfeedback>
    <questionnote>
      <text>{@ta@}</text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<p>Correct answer, well done.</p>]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<p>Your answer is partially correct.</p>]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<p>Incorrect answer.</p>]]></text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text><![CDATA[anspt : if (x>x0 and x<x1) then ans1 else 1000;]]></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>subst(x=x0,ans1)</sans>
        <tans>subst(x=x0,f0)</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.2500000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Your answer does not satisfy ${@p(x0)=subst(x=x0,f0)@}$.</p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>1</name>
        <answertest>AlgEquiv</answertest>
        <sans>subst(x=x1,ans1)</sans>
        <tans>subst(x=x1,f1)</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.2500000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>2</truenextnode>
        <trueanswernote>prt1-2-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>+</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>2</falsenextnode>
        <falseanswernote>prt1-2-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Your answer does not satisfy ${@p(x1)=subst(x=x1,f1)@}$.</p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>2</name>
        <answertest>AlgEquiv</answertest>
        <sans>subst(x=x0,diff(ans1,x))</sans>
        <tans>subst(x=x0,diff(f0,x))</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.2500000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>3</truenextnode>
        <trueanswernote>prt1-3-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>+</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>3</falsenextnode>
        <falseanswernote>prt1-3-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Your answer does not satisfy $p'({@x0@})={@subst(x=x0,diff(f0,x))@}$.</p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>3</name>
        <answertest>AlgEquiv</answertest>
        <sans>subst(x=x1,diff(ans1,x))</sans>
        <tans>subst(x=x1,diff(f1,x))</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.2500000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>4</truenextnode>
        <trueanswernote>prt1-4-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>+</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>4</falsenextnode>
        <falseanswernote>prt1-4-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Your answer does not satisfy $p'({@x1@})={@subst(x=x1,diff(f1,x))@}$.</p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>4</name>
        <answertest>AlgEquiv</answertest>
        <sans>degree(ans1,x)</sans>
        <tans>3</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>5</truenextnode>
        <trueanswernote>prt1-5-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>5</falsenextnode>
        <falseanswernote>prt1-5-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Your answer is not a cubic!</p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>5</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>ta</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-6-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>+</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-6-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Your answer is plotted below, although part of your graph might appear out of range of the plot!</p>
<p>{@plot([pg,anspt],[x,(x0-3),(x1+3)],[y,-3,3])@}</p>]]></text>
        </falsefeedback>
      </node>
    </prt>
    <qtest>
      <testcase>1</testcase>
      <testinput>
        <name>ans1</name>
        <value>ta</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-6-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <testinput>
        <name>ans1</name>
        <value>x^2</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-6-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <testinput>
        <name>ans1</name>
        <value>(2*%pi/9+2/27)*x^3-x^2/9+(-2*%pi/3-4/9)*x-4*%pi/9+20/27</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.7500000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-6-F</expectedanswernote>
      </expected>
    </qtest>
  </question>

<question type="stack">
    <name>
      <text>text_4_complex-De Moivre's</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Given a complex number $\displaystyle z={@q@}$ <span class="nolink">determine<br /></span></p>
<p>$|z^{@n@}|=$[[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</p>
<p>and $\arg(z^{@n@})=$[[input:ans2]] [[validation:ans2]] [[feedback:prt2]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>It makes sense that the index laws should still apply.  This is called De Moivre's theorem.</p>
<p>\[ {@q^n@} ={@a^n@} e^{@b*n*%i*%pi@}.\]</p>
<p>Recall that</p>
<p>\[ e^{i\theta} = \cos(\theta)+i\sin(\theta).\]</p>
<p>Working with the principle argument $0\leq \theta \leq 2\pi$ gives us</p>
<p>\[ {@q^n@} = {@a^n@} e^{@b*n*%i*%pi@} = {@a^n@} e^{@ev(b*n,simp)*%i*%pi@} = {@a^n@} e^{@p*%i*%pi@}.\]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text>a : ev(2+rand(15),simp);
b : ev((-1)^rand(2)*((1+rand(10)))/(2+rand(15)),simp);
n : ev(3+rand(20),simp);
q : a*%e^(b*%i*%pi);
p : ev(mod(b*n,2),simp);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text></text>
    </specificfeedback>
    <questionnote>
      <text>{@q^n = a^n*(cos(p*%i*%pi)+%i*sin(p*%i*%pi))@}</text>
    </questionnote>
    <questionsimplify>0</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<p>Correct answer, well done.</p>]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<p>Your answer is partially correct.</p>]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<p>Incorrect answer.</p>]]></text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>a^n</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <input>
      <name>ans2</name>
      <type>algebraic</type>
      <tans>p*%pi</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>a^n</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty>0.0000000</truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty>0.0000000</falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>prt2</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>[cos(ans2),sin(ans2)]</sans>
        <tans>[cos(b*%pi*n),sin(b*%pi*n)]</tans>
        <testoptions></testoptions>
        <quiet>1</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt2-1-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt2-1-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
    <qtest>
      <testcase>1</testcase>
      <testinput>
        <name>ans1</name>
        <value>a^n</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value></value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore></expectedscore>
        <expectedpenalty></expectedpenalty>
        <expectedanswernote>NULL</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <testinput>
        <name>ans1</name>
        <value></value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>b*n*%pi</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore></expectedscore>
        <expectedpenalty></expectedpenalty>
        <expectedanswernote>NULL</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <testinput>
        <name>ans1</name>
        <value></value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>p*%pi</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore></expectedscore>
        <expectedpenalty></expectedpenalty>
        <expectedanswernote>NULL</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
    </qtest>
  </question>

<question type="stack">
    <name>
      <text>text_6_odd_even</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>1. Give an example of an odd function by typing an expression which represents it. $f_1(x)=$ [[input:ans1]]. [[validation:ans1]] [[feedback:odd]]</p>
<p>2. Give an example of an even function. $f_2(x)=$ [[input:ans2]]. [[validation:ans2]] [[feedback:even]]</p>
<p>3. Give an example of a function which is odd and even. $f_3(x)=$ [[input:ans3]]. [[validation:ans3]] [[feedback:oddeven]]</p>
<p>4. Is the answer to 3. unique? [[input:ans4]] (Or are there many different possibilities.) [[validation:ans4]] [[feedback:unique]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.3333333</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text></text>
    </questionvariables>
    <specificfeedback format="html">
      <text></text>
    </specificfeedback>
    <questionnote>
      <text></text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<p><span class="correct">Correct answer, well done.</span></p>]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<p><span class="incorrect">Your answer is partially correct.</span></p>]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<p><span class="partially">Incorrect answer.</span></p>]]></text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>x^3</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <input>
      <name>ans2</name>
      <type>algebraic</type>
      <tans>x^4</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <input>
      <name>ans3</name>
      <type>algebraic</type>
      <tans>0</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <input>
      <name>ans4</name>
      <type>boolean</type>
      <tans>true</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <prt>
      <name>even</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text>sa:ans2-subst(x=-x,ans2);</text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>sa</sans>
        <tans>0</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>even-0-T </trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>even-0-F </falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Your answer is not an even function. Look, \[ f(x)-f(-x)={@sa@} \neq 0.\]</p>]]></text>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>odd</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text>sa:subst(x=-x,ans1)+ans1;</text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>sa</sans>
        <tans>0</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>odd-0-T </trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>odd-0-F </falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Your answer is not an odd function. Look, \[ f(x)+f(-x)={@sa@} \neq 0.\]</p>]]></text>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>oddeven</name>
      <value>2.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text>sa1:subst(x=-x,ans3)+ans3;
sa2:ans3-subst(x=-x,ans3);</text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>sa1</sans>
        <tans>0</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>0.5000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>1</truenextnode>
        <trueanswernote>ODD</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>1</falsenextnode>
        <falseanswernote>oddeven-0-F </falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Your answer is not an odd function. Look, \[ f(x)+f(-x)={@sa1@} \neq 0.\]</p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>1</name>
        <answertest>AlgEquiv</answertest>
        <sans>sa2</sans>
        <tans>0</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.5000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>EVEN</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>+</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>oddeven-1-F </falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Your answer is not an even function. Look, \[ f(x)-f(-x)={@sa2@} \neq 0.\]</p>]]></text>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>unique</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans4</sans>
        <tans>true</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>unique-0-T </trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>unique-0-F </falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
    <qtest>
      <testcase>1</testcase>
      <testinput>
        <name>ans1</name>
        <value>x^3</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>cos(x)</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>0</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>true</value>
      </testinput>
      <expected>
        <name>even</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>even-0-T</expectedanswernote>
      </expected>
      <expected>
        <name>odd</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>odd-0-T</expectedanswernote>
      </expected>
      <expected>
        <name>oddeven</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>EVEN</expectedanswernote>
      </expected>
      <expected>
        <name>unique</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>unique-0-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <testinput>
        <name>ans1</name>
        <value>x^2</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>x^3</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>x^3</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>false</value>
      </testinput>
      <expected>
        <name>even</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.3333333</expectedpenalty>
        <expectedanswernote>even-0-F</expectedanswernote>
      </expected>
      <expected>
        <name>odd</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.3333333</expectedpenalty>
        <expectedanswernote>odd-0-F</expectedanswernote>
      </expected>
      <expected>
        <name>oddeven</name>
        <expectedscore>0.5000000</expectedscore>
        <expectedpenalty>0.3333333</expectedpenalty>
        <expectedanswernote>oddeven-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>unique</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.3333333</expectedpenalty>
        <expectedanswernote>unique-0-F</expectedanswernote>
      </expected>
    </qtest>
  </question>

<question type="stack">
    <name>
      <text>text_7_solve_quadratic</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p></p><p>Solve {@first(ta)@}, by factoring and working line by line. &nbsp;Leave your answer in the form ${@v@}=\cdots \mbox{ or } {@v@}=\cdots$ in fully simplified form.</p><p>[[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>\[ {@stack_disp_arg(ta, true)@} \]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text>n1:2
n2:n1+3
v:x
p:expand((v-n1)*(v-n2))
simp:false
ta:[p=0,(v-n1)*(v-n2)=0,v-n1=0 nounor v-n2=0,v=n1 nounor v=n2]</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote>
      <text>{@ta@}</text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text>Correct answer, well done.</text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text>Your answer is partially correct.</text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text>Incorrect answer.</text>
    </prtincorrect>
    <multiplicationsign>none</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>equiv</type>
      <tans>ta</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>5</insertstars>
      <syntaxhint>firstline</syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options>firstline</options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>0</autosimplify>
      <feedbackvariables>
        <text>foundfac1:ev(sublist(ans1,lambda([ex], equationp(ex) and is(rhs(ex)=0))),simp);
foundfac2:ev(any_listp(lambda([ex], second(ATFacForm(lhs(ex),lhs(ex),x))), foundfac1),simp);</text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>EquivFirst</answertest>
        <sans>ans1</sans>
        <tans>ta</tans>
        <testoptions>x</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
      <node>
        <name>1</name>
        <answertest>EqualComAss</answertest>
        <sans>last(ans1)</sans>
        <tans>last(ta)</tans>
        <testoptions></testoptions>
        <quiet>1</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>2</truenextnode>
        <trueanswernote>prt1-2-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>2</falsenextnode>
        <falseanswernote>prt1-2-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[Your answer is not in the correct form, which is ${@v@}=\cdots \mbox{ or } {@v@}=\cdots$ where numbers are fully simplified.<p><br></p>]]></text>
        </falsefeedback>
      </node>
      <node>
        <name>2</name>
        <answertest>AlgEquiv</answertest>
        <sans>foundfac2</sans>
        <tans>true</tans>
        <testoptions></testoptions>
        <quiet>1</quiet>
        <truescoremode>+</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-3-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-3-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>The question asked you to solve the equation by factoring the equation. &nbsp;The factored form should appear as one line in your working.</p>]]></text>
        </falsefeedback>
      </node>
    </prt>
    <qtest>
      <testcase>1</testcase>
      <testinput>
        <name>ans1</name>
        <value>ta</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-3-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <testinput>
        <name>ans1</name>
        <value>[p=0, (x-n1)*(x-n1) = 0, x=n1 nounor n2]</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore></expectedscore>
        <expectedpenalty></expectedpenalty>
        <expectedanswernote>NULL</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <testinput>
        <name>ans1</name>
        <value> [p=0,x-n1 = 0 nounor x-n2 = 0,x = n1 nounor x = n2]</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-3-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>4</testcase>
      <testinput>
        <name>ans1</name>
        <value>[p=0,(x-(n1+n2)/2)^2-ev((n1+n2)^2/4-n1*n2,simp)=0,(x-(n1+n2)/2)^2=ev((n1+n2)^2/4-n1*n2,simp),(x-(n1+n2)/2)=+-ev(sqrt((n1+n2)^2/4-n1*n2),simp),x=ev((n1+n2)/2+sqrt((n1+n2)^2/4-n1*n2),simp) nounor x=ev((n1+n2)/2-sqrt((n1+n2)^2/4-n1*n2),simp)]  </value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-3-F</expectedanswernote>
      </expected>
    </qtest>
  </question>

<question type="category">
    <category>
        <text>$course$/Default for Scratch/input_samples</text>

</category>
  </question>

<question type="stack">
    <name>
      <text>Textarea test</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[Dummy maths input:&nbsp; ${@ta@}$.<br>[[input:ans1]] [[validation:ans1]]]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text>ta:[x=1,x=2]</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[[[feedback:prt1]]&lt;/p&gt;&lt;div&gt;]]></text>
    </specificfeedback>
    <questionnote>
      <text>vendor/bin/phpunit --group qtype_stack</text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text>Correct answer, well done.</text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text>Your answer is partially correct.</text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text>Incorrect answer.</text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>textarea</type>
      <tans>ta</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>1</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>ta</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
  </question>

<question type="stack">
    <name>
      <text>True/false</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>All generalizations are false: [[input:ans1]] [[validation:ans1]]</p><p><br></p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text></text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote>
      <text></text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text>Correct answer, well done.</text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text>Your answer is partially correct.</text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text>Incorrect answer.</text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>boolean</type>
      <tans>false</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>false</tans>
        <testoptions></testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>0.5000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>Who knows!</p>]]></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.5000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>Who knows!<br></p>]]></text>
        </falsefeedback>
      </node>
    </prt>
  </question>

<question type="stack">
    <name>
      <text>Units</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>What is gravity?</p><p>[[input:ans1]]</p><div>[[validation:ans1]]</div>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text></text>
    </generalfeedback>
    <defaultgrade>1.0000000</defaultgrade>
    <penalty>0.1000000</penalty>
    <hidden>0</hidden>
    <questionvariables>
      <text>ta:9.81*m*s^-2</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote>
      <text></text>
    </questionnote>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text>Correct answer, well done.</text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text>Your answer is partially correct.</text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text>Incorrect answer.</text>
    </prtincorrect>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <matrixparens>[</matrixparens>
    <variantsselectionseed></variantsselectionseed>
    <input>
      <name>ans1</name>
      <type>units</type>
      <tans>ta</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint></syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords></forbidwords>
      <allowwords></allowwords>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options></options>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackvariables>
        <text></text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <answertest>Units</answertest>
        <sans>ans1</sans>
        <tans>ta</tans>
        <testoptions>3</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty></truepenalty>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty></falsepenalty>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text></text>
        </falsefeedback>
      </node>
    </prt>
  </question>

</quiz>

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