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<?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:xp:3*v+7=4ta:[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><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><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><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>true</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: 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><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><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>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: 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></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><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>x</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: 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></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></input><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><tans>ta</tans><testoptions>v</testoptions><quiet>0</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></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: 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></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><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>tas1</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>1</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>rp</tans><boxsize>5</boxsize><strictsyntax>1</strictsyntax><insertstars>1</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>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: 15 --><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: 18 --><question type="stack"><name><text>test_5_cubic_spline</text></name><questiontext format="html"><text><![CDATA[<p>Consider the real function</p><p>\[ f(x) :=\left\{ \begin{array}{ll} {@f0@} & \mbox{for } x\leq {@x0@}, \\ p(x) & \mbox{for } {@x0@} < x < {@x1@}, \\ {@f1@} & \mbox{for } {@x1@}\leq x.\end{array} \right. \]</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: 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]] [[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: 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>n1:2n2:n1+3v:xp:expand((v-n1)*(v-n2))simp:falseta:[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>