<?xml version="1.0" encoding="UTF-8"?>
<quiz>
<!-- question: 0 -->
<question type="category">
<category>
<text>$course$/Default for Scratch/input_samples</text>
</category>
</question>
<!-- question: 1 -->
<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>
</questiontext>
<generalfeedback format="html">
<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: 2 -->
<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: 3 -->
<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: 4 -->
<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: 5 -->
<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: 6 -->
<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: 7 -->
<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>
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<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>
<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>0</requirelowestterms>
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<options></options>
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<value>1.0000000</value>
<autosimplify>1</autosimplify>
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<text></text>
</feedbackvariables>
<node>
<name>0</name>
<answertest>AlgEquiv</answertest>
<sans>ans1</sans>
<tans>true</tans>
<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: 8 -->
<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>
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<text>Correct answer, well done.</text>
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<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>
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<variantsselectionseed></variantsselectionseed>
<input>
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<type>radio</type>
<tans>ta</tans>
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<feedbackvariables>
<text></text>
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<node>
<name>0</name>
<answertest>Diff</answertest>
<sans>first(ans1)</sans>
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<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: 9 -->
<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>
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<questionnote>
<text></text>
</questionnote>
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<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>
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<variantsselectionseed></variantsselectionseed>
<input>
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<name>0</name>
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<sans>ans1</sans>
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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: 0 -->
<question type="category">
<category>
<text>$course$/Default for Scratch</text>
</category>
</question>
<!-- question: 13 -->
<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>
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<defaultgrade>1.0000000</defaultgrade>
<penalty>0.1000000</penalty>
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<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>
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<text><![CDATA[<p><span class="correct">Correct answer, well done.</span></p>]]></text>
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<text><![CDATA[<p><span class="partially">Your answer is partially correct.</span></p>]]></text>
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<text><![CDATA[<p><span class="incorrect">Incorrect answer.</span></p>]]></text>
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<text></text>
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<truepenalty></truepenalty>
<truenextnode>-1</truenextnode>
<trueanswernote>1-0-T </trueanswernote>
<truefeedback format="html">
<text></text>
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<falsescoremode>=</falsescoremode>
<falsescore>0.0000000</falsescore>
<falsepenalty></falsepenalty>
<falsenextnode>-1</falsenextnode>
<falseanswernote>1-0-F </falseanswernote>
<falsefeedback format="html">
<text></text>
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<deployedseed>1001758021</deployedseed>
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<name>prt1</name>
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<testcase>2</testcase>
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<value>ta</value>
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<name>prt1</name>
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<testcase>3</testcase>
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<testcase>4</testcase>
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</qtest>
</question>
<!-- question: 14 -->
<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 \(x>0\) and we discard the negative root. Hence the length of the shorter side is \(x={@-rn@}\)cm.</p>]]></text>
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<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>
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<specificfeedback format="html">
<text></text>
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<questionnote>
<text>{@ta1@}, {@tas1@}.</text>
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<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>
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<multiplicationsign>dot</multiplicationsign>
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<truenextnode>-1</truenextnode>
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<text></text>
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<falsescore>0.0000000</falsescore>
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<falsenextnode>1</falsenextnode>
<falseanswernote>eq-0-F </falseanswernote>
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<text></text>
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<node>
<name>1</name>
<answertest>SubstEquiv</answertest>
<sans>ans1</sans>
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<truenextnode>-1</truenextnode>
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<text></text>
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<truenextnode>-1</truenextnode>
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<text></text>
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<falsenextnode>-1</falsenextnode>
<falseanswernote>short-0-F </falseanswernote>
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<text></text>
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<prt>
<name>sol</name>
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<text>v1:first(listofvars(ans1));
ftm:setify(map(rhs,solve(ans1,v1)));</text>
</feedbackvariables>
<node>
<name>0</name>
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<trueanswernote>sol-0-T </trueanswernote>
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<text></text>
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<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>
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<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>
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<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: 15 -->
<question type="stack">
<name>
<text>test_3_matrix</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Calculate \[ {@A@}.{@B@}\]</p>
<p>Â [[input:ans1]]Â [[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: 18 -->
<question type="stack">
<name>
<text>test_5_cubic_spline</text>
</name>
<questiontext format="html">
<text><![CDATA[<p>Consider the real function</p>
<p>\[ f(x) :=\left\{ \begin{array}{ll} {@f0@} & \mbox{for } x\leq {@x0@}, \\ p(x) & \mbox{for } {@x0@} < x < {@x1@}, \\ {@f1@} & \mbox{for }Â {@x1@}\leq x.\end{array} \right. \]</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. Â 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>\[ p(x) = a_3 x^3 +Â a_2 x^2 +Â a_1 x +Â a_0,\]</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: 16 -->
<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]]Â [[validation:ans1]]Â [[feedback:prt1]]</p>
<p>and \(\arg(z^{@n@})=\)[[input:ans2]]Â [[validation:ans2]]Â [[feedback:prt2]]</p>]]></text>
</questiontext>
<generalfeedback format="html">
<text><![CDATA[<p>It makes sense that the index laws should still apply. Â 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>\[ {@q^n@} = {@a^n@} e^{@b*n*%i*%pi@} = {@a^n@} e^{@ev(b*n,simp)*%i*%pi@} =Â {@a^n@} e^{@p*%i*%pi@}.\]</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: 19 -->
<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: 23 -->
<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. 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. 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: 0 -->
<question type="category">
<category>
<text>$course$/Default for Scratch/input_samples</text>
</category>
</question>
<!-- question: 10 -->
<question type="stack">
<name>
<text>Textarea test</text>
</name>
<questiontext format="html">
<text><![CDATA[Dummy maths input: \({@ta@}\).<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]]</p><div>]]></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: 11 -->
<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: 12 -->
<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>