<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>1.5.2.12 Transposition</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise <br></p>
<p>Transpose, and then fully simplify, the given formulae to make the given variable the subject.</p>
<br>
<ol class="HELM_parts">
<li>\({@eqn1@}\) for \(x\),  [[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</li>
<li>\({@eqn2@}\) for \(x\),  [[input:ans2]] [[validation:ans2]] [[feedback:prt2]]</li>
<li>\({@eqn3@}\) for \(y\),  [[input:ans3]] [[validation:ans3]] [[feedback:prt3]]</li>
<li>\({@eqn4@}\) for \(x\),  [[input:ans4]] [[validation:ans4]] [[feedback:prt4]]</li>
</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<ol class="HELM_parts">
<li>Adding {@a2@} to both sides of the equation gives: \[{@y+a2=a1*x@}\] We can then divide both sides of the equation by {@a1@} and simplify: \[{@x=y/a1+a2/a1@}\]</li>
<li>Subtracting {@a4*y@} from both sides of the equation gives: \[{@a1*x=a3-a4*y@}\] We can then divide both sides by {@a1@} giving: \[{@ta2@}\]</li>
<li>Subtracting{@a5*x@} from both sides of the equality gives: \[{@a1*y=a3-a5*x@}\] Then dividing both sides of the equation by {@a1@} gives: \[{@ta3@}\]</li>
<li>Adding {@a1*x@} to both sides of the equation gives: \[{@13-a2*y=a1*x@}\] Then dividing both sides of the equation by {@a1@} gives \[{@ta4@}\]</li>
</ol>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2021072200</text>
    </stackversion>
    <questionvariables>
      <text>a1:rand([2,3,4]);
a2:rand([6,7,8]);
a3:a1+1
a4:a2+1
a5:a2+2

eqn1: y=a1*x-a2;
eqn2: a4*y+a1*x=a3;
eqn3: a5*x+a1*y=a3;
eqn4: 13-a1*x-a2*y=0;

ta1: x=1/a1*y+a2/a1;
ta2: x=a3/a1-a4/a1*y;
ta3: y=a3/a1-a5/a1*x
ta4: x=13/a1-a2/a1*y</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\[{@eqn1@}, \rightarrow  {@ta1@}\]
\[{@eqn2@}, \rightarrow {@ta2@}\]
\[{@eqn3@}, \rightarrow {@ta3@}\]
\[{@eqn4@}, \rightarrow {@ta4@}\]</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>none</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta1</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>1</checkanswertype>
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      <showvalidation>3</showvalidation>
      <options/>
    </input>
    <input>
      <name>ans2</name>
      <type>algebraic</type>
      <tans>ta2</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>3</showvalidation>
      <options/>
    </input>
    <input>
      <name>ans3</name>
      <type>algebraic</type>
      <tans>ta3</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
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      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>3</showvalidation>
      <options/>
    </input>
    <input>
      <name>ans4</name>
      <type>algebraic</type>
      <tans>ta4</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
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      <syntaxattribute>0</syntaxattribute>
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          <text>This is algebraically equivalent to the given formula but you have either not made x the subject or you have not fully simplified.</text>
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        <name>1</name>
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        <answertest>AlgEquiv</answertest>
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        <sans>ans3</sans>
        <tans>ta3</tans>
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        <name>1</name>
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        <answertest>AlgEquiv</answertest>
        <sans>ans3</sans>
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    <qtest>
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      <description/>
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        <value>ta1</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ta2</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>ta3</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>ta4</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
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        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt3-1-T</expectedanswernote>
      </expected>
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        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
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    </qtest>
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      <description/>
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        <name>ans1</name>
        <value>eqn1</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>eqn2</value>
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      <testinput>
        <name>ans3</name>
        <value>eqn3</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>eqn4</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-2-T</expectedanswernote>
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      <expected>
        <name>prt2</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt2-2-T</expectedanswernote>
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      <expected>
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        <expectedanswernote>prt3-2-T</expectedanswernote>
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        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt4-2-T</expectedanswernote>
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    </qtest>
    <qtest>
      <testcase>3</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>3*y+3</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>3*y+3</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>3*y+3</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>3*y+3</value>
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        <expectedanswernote>NULL</expectedanswernote>
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        <expectedanswernote>NULL</expectedanswernote>
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      <expected>
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      <expected>
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  </question>
</quiz>
