<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>CR-Int-15-partialfrac-9</text>
    </name>
    <questiontext format="html">
      <text>Write \[ {@p@}\] as partial fractions.

[[input:ap]]. 
[[validation:ap]]
[[feedback:partfrac]]

Find \[ \int {@p@} d{@v@}. \]

[[input:ans1]] [[validation:ans1]]
[[feedback:Result]]</text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[Since the degree of the numerator equal to the degree of the denominator we need to use long division.
\[{@p@} = {@factor(simplify(pp1+pp2+pp3))@} + {@pp4@}.\]
Hence, using partial fractions we have
\[{@p@} = {@q@}.\]

So,
\[\begin{array}{rcl}\displaystyle
 \int {@p@} d{@v@} &\displaystyle =&\displaystyle  \int {@q@} d{@v@} \\
   &\displaystyle =&\displaystyle  {@rdm2@} \int {@ppp1@} d{@v@} + {@rdm4@} \int {@ppp2@} d{@v@} + {@rdm3@} \int \left({@ppp3@}\right) d{@v@} + \int {@pp4@} d{@v@} \\
   &\displaystyle =&\displaystyle  {@rdm2*int(ppp1,v)@} + {@rdm4*int(ppp2,v)@} + {@rdm3*int(ppp3,v)@}+ {@int(pp4,v)@} + c \\
   &\displaystyle =&\displaystyle  {@rdm2*int(ppp1,v)+rdm4*int(ppp2,v)+rdm3*int(ppp3,v)+int(pp4,v)@}+c
 \end{array}\]]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text/>
    </stackversion>
    <questionvariables>
      <text>v:x;
rdm1:rand(5)+1;
rdm2:-1-rand(3);
rdm3:7+rand(15);
rdm4:-4-rand(12);
rdm5:1+rand(2);
rdm6:rdm5+rand(2)+1;
ppp1:1/(v+rdm5);
ppp2:1/(v+rdm6);
ppp3:ppp2^2;
pp1:rdm2*ppp1;
pp2:rdm4*ppp2;
pp3:rdm3*ppp3;
pp4:rdm1;
q:pp1+pp2+pp3+pp4;
p:factor(simplify(q));</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\[\int {@p@} d{@v@} = \int {@q@} d{@v@} = {@int(p,v)@}+c.\]</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/>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>int(p,v)+c</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options/>
    </input>
    <input>
      <name>ap</name>
      <type>algebraic</type>
      <tans>q</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>1</requirelowestterms>
      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options/>
    </input>
    <prt>
      <name>partfrac</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>PartFrac</answertest>
        <sans>ap</sans>
        <tans>q</tans>
        <testoptions>v</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>partfrac-0-T </trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>partfrac-0-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>Result</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>Int</answertest>
        <sans>ans1</sans>
        <tans>int(p,v)+c</tans>
        <testoptions>v</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-0-T </trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>Result-0-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>68623458</deployedseed>
    <deployedseed>477628154</deployedseed>
    <deployedseed>1792142425</deployedseed>
    <deployedseed>1511142662</deployedseed>
    <deployedseed>1377908211</deployedseed>
    <deployedseed>352791638</deployedseed>
    <deployedseed>803529781</deployedseed>
    <deployedseed>1036013166</deployedseed>
    <deployedseed>638017134</deployedseed>
    <deployedseed>781484744</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ev(int(p,v)+c,simp)</value>
      </testinput>
      <testinput>
        <name>ap</name>
        <value>q</value>
      </testinput>
      <expected>
        <name>partfrac</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>partfrac-0-T</expectedanswernote>
      </expected>
      <expected>
        <name>Result</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-0-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ev(int(p,v),simp)</value>
      </testinput>
      <testinput>
        <name>ap</name>
        <value/>
      </testinput>
      <expected>
        <name>partfrac</name>
        <expectedscore/>
        <expectedpenalty/>
        <expectedanswernote>NULL</expectedanswernote>
      </expected>
      <expected>
        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>Result-0-F</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>3</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value/>
      </testinput>
      <testinput>
        <name>ap</name>
        <value>p</value>
      </testinput>
      <expected>
        <name>partfrac</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>partfrac-0-F</expectedanswernote>
      </expected>
      <expected>
        <name>Result</name>
        <expectedscore/>
        <expectedpenalty/>
        <expectedanswernote>NULL</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
