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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> <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> <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> 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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> 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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> </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>n1:2 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>