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<quiz>
  <question type="stack">
    <name>
      <text>1.3.1.5. Collecting terms with fractions</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> \( \displaystyle {@exp1@} =\) [[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</p>


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


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

</li><li><p> \( {@exp4@} =\) [[input:ans4]]&nbsp; where \(a\) and \(b\) are constants.&nbsp;<br></p>





<p>[[validation:ans4]] [[feedback:prt4]]<br></p><p><br></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>Both fractions have a common denominator of \({@a2@}\), so the expression can be simplified to:</p>
        <p>\(\displaystyle {@exp1@} = {@ta1@}.\)</p>
    </li>

    <li>
        <p>There are two multiples of \( x^2 \) which are like terms. The expression can be simplified to:</p>
        <p>\( \displaystyle{{@exp2@} = {@ta2@}}.\)</p>
    </li>

    <li>
        <p>The expression {@exp3@} cannot be simplified.</p>
    </li>

    <li>
        <p>Both terms are multiples of \( x^2 \), so they are like terms. The expression can be simplified to:</p>
      <p>\({@exp4@} = {@ta4@}.\)</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(4)+2, simp);
a2: ev(a1+1, simp);
a3: a2;
exp1: (a1/a2)*x^2 + x^2/a3;
ta1:ev(exp1,simp);


b1: 0.5;
b2: rand([3,5]);
b3: 4;
b4: rand([7,9,11,13]);
b5:2;
exp2: b1*x^2 + (b2/b3)*x^2  - b4/b5*x;
ta2: ev(exp2,simp);

c1: ev(rand(4)+3,simp);
c2: ev(c1+4,simp);
c3:c1;
c4:c2;
exp3: c1*x^3 - c2*x + c3*y*x + c4;
ta3: c1*x^3 - c2*x + c3*y*x + c4;

d1: rand([2,3,4]);
exp4: -d1*a*x^2 + b*x^2;
ta4:(b - d1*a)*x^2;</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\[{@exp1@}={@ta1@}, \quad {@exp2@}={@ta2@}\]
\[{@exp3@}= {@ta3@}, \quad {@exp4@}={@ta4@} \]</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>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
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      <options/>
    </input>
    <input>
      <name>ans2</name>
      <type>algebraic</type>
      <tans>ta2</tans>
      <boxsize>15</boxsize>
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    <input>
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          <text><![CDATA[<p></p><div title="Page 2">
			<div>
				<div>
					<div>
						<p>Both fractions have a common denominator of \({@a2@}\), so the expression can be simplified to \({@ta1@}\).</p>
					</div>
				</div>
			</div>
		</div><br><p></p>]]></text>
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          <text><![CDATA[<p>There are two multiples of \( x^2 \) which are like terms. The expression can be simplified to {@ta2@}.</p>]]></text>
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          <text><![CDATA[<p>Cannot be simplified.<br></p>]]></text>
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          <text><![CDATA[<p>Both terms are multiples of \( x^2 \), so they are like terms. The expression can be simplified to \( {@ta4@} \).&nbsp;</p>]]></text>
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    <qtest>
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      <description/>
      <testinput>
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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>
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        <name>ans1</name>
        <value>2*ta1</value>
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        <name>ans2</name>
        <value>ta2+1</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>ta3*2</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>ta4+1</value>
      </testinput>
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        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
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    </qtest>
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      <testcase>3</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>exp1</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>exp2</value>
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        <value>exp3</value>
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        <value>exp4</value>
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      <expected>
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        <expectedscore>0.0000000</expectedscore>
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        <expectedanswernote>prt4-1-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
