<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>1.3.1.1.Collecting terms</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>Simplify, if possible. If not possible enter the original expression.<br></p>

<ol class="HELM_parts">

<li><p>\({@exp1@}=\) [[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</p></li>

<li><p>\({@exp2@}=\) [[input:ans2]] [[validation:ans2]] [[feedback:prt2]]</p></li>

<li><p> \({@exp3@}=\) [[input:ans3]] [[validation:ans3]] [[feedback:prt3]]</p></li>

<li><p> \({@exp4@}=\) [[input:ans4]] [[validation:ans4]] [[feedback:prt4]]</p></li>

<li><p> \({@exp5@}=\) [[input:ans5]] [[validation:ans5]] [[feedback:prt5]]</p></li>

</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>
<ol class="HELM_parts">
    <li>
      <p>All the terms are multiples of \(x\) so this expression can be simplified to:</p>
      <p>\({@exp1@} =({@a1+a2+a3@}) \cdot x = {@ta1@}.\)</p>
    </li>
  
    <li>
      <p>All the terms are multiples of \(q\) so this expression can be simplified to:</p>
      <p>\({@exp2@} =({@b1-b2+b3@}) \cdot q = {@ta2@}.\)</p>
    </li>
  
    <li>
      <p>All the terms are multiples of \(x^2\) so this expression can be simplified to:</p>
      <p>\({@exp3@} = ({@c1+c2@}) \cdot x^2 = {@ta3@}.\)</p>
    </li>
  
    <li>
      <p>All the terms are multiples of \(v^2\) so this expression can be simplified to</p>
      <p>\({@exp4@} = ({@-d1+d2@}) \cdot v^2 = {@ta4@}.\)</p>
    </li>
  
    <li>
        <p>Neither of the terms are similar so this expression cannot be simplified.</p>
    </li>
</ol>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2021072200</text>
    </stackversion>
    <questionvariables>
      <text>simp:false
a1: ev(rand(6)+3, simp);
a2: ev(a1-1,simp);
a3: ev(a1+1, simp);
exp1: a1*x+a2*x+a3*x
ta1: factor(exp1);

b1: ev(rand(4)+2,simp);
b2: ev(b1-1,simp);
b3: ev(b1+10,simp);
exp2: b1*q-b2*q+b3*q;
ta2: factor(exp2);

c1: ev(rand(7)+3,simp);
c2: ev(c1+4,simp);
exp3: c1*x^2+c2*x^2
ta3: factor(exp3);

d1: ev(rand(8)+11,simp);
d2: ev(d1-9,simp);
exp4: -d1*v^2+d2*v^2
ta4: factor(exp4);

e1: ev(rand(5)+3,simp);
e2: ev(e1-1, simp);
exp5: e1*p+e2*q
ta5: factor(exp5);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\[{@exp1@} = {@ta1@}, \quad {@exp2@} = {@ta2@}, \quad {@exp3@} ={@ta3@} \]
\[ {@exp4@} = {@ta4@}, \quad {@exp5@}={@ta5@}\]</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>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
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      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta1</tans>
      <boxsize>6</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
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    </input>
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      <name>ans2</name>
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      <options/>
    </input>
    <input>
      <name>ans3</name>
      <type>algebraic</type>
      <tans>ta3</tans>
      <boxsize>6</boxsize>
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      <options/>
    </input>
    <input>
      <name>ans4</name>
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      <tans>ta4</tans>
      <boxsize>6</boxsize>
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      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
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      <options/>
    </input>
    <input>
      <name>ans5</name>
      <type>algebraic</type>
      <tans>ta5</tans>
      <boxsize>6</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
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      <requirelowestterms>0</requirelowestterms>
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      <options/>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
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        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>EqualComAss</answertest>
        <sans>ans1</sans>
        <tans>ta1</tans>
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        <falsefeedback format="html">
          <text><![CDATA[<p>All three terms are multiples of \(x\) and and can be collected together.</p>]]></text>
        </falsefeedback>
      </node>
    </prt>
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      <name>prt2</name>
      <value>1.0000000</value>
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        <falsefeedback format="html">
          <text><![CDATA[<p>All three terms are multiples of \(q\) and and can be collected together.</p>]]></text>
        </falsefeedback>
      </node>
    </prt>
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        <answertest>EqualComAss</answertest>
        <sans>ans3</sans>
        <tans>ta3</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt3-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
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        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt3-1-F</falseanswernote>
        <falsefeedback format="html">
          <text><![CDATA[<p>All three terms are multiples of \(x^2\) and and can be collected together.</p>]]></text>
        </falsefeedback>
      </node>
    </prt>
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        <falsefeedback format="html">
          <text><![CDATA[<p>All three terms are multiples of \(v^2\) and and can be collected together.</p>]]></text>
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        <answertest>AlgEquiv</answertest>
        <sans>ans5</sans>
        <tans>ta5</tans>
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          <text><![CDATA[<p>Cannot be simplified.<br></p>]]></text>
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      <description/>
      <testinput>
        <name>ans1</name>
        <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>
      <testinput>
        <name>ans5</name>
        <value>ta5</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>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>
      <expected>
        <name>prt4</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt4-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt5</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt5-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ta4</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ta3</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>ta1</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>ta2</value>
      </testinput>
      <testinput>
        <name>ans5</name>
        <value>ta3</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt2-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt3-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt4</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt4-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt5</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt5-1-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>exp1</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>exp2</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>exp3</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>exp4 </value>
      </testinput>
      <testinput>
        <name>ans5</name>
        <value>exp5</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt2-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt3-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt4</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt4-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt5</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt5-1-T</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
