<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>PT.6.6 (Is not expanded equation a circle rational)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>By calculating the appropriate quantity decide whether the equation \({@circ@}=0\) represents a circle.</p>
<p>appropriate quantity = [[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>
<p>Thus the equation represents a circle. [[input:ans2]] [[validation:ans2]][[feedback:prt2]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>Note that the equation is not given in expanded form. Therefore we begin by dividing the given equation by {@aa@} to get \({@expand(circ1)@} = 0\). Then quantity we must calculate is \(g^2 + f^2 -c\). For the equation to be that of a circles' we require this quantity to be strictly greater than zero. Here we have \[ g = {@gg/aa@}, f = {@ff/aa@} \mbox{ and } c = {@cc/aa@}. \] Thus, \( g^2 + f^2 - c = {@ta1@}\) and the statement is {@ta2@}</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2020081700</text>
    </stackversion>
    <questionvariables>
      <text><![CDATA[aa: 1+rand(5);
gg: 1+ rand(5);
ff: 1+rand(5);
cc: 1+rand(30);

circ: aa*x^2 + aa*y^2 + 2*gg*x + 2*ff*y + cc;
circ1: x^2 + y^2 +((2*gg)/aa)*x + ((2*ff)/aa)*y +(cc/aa);

ta1: (gg/aa)^2+(ff/aa)^2 -cc/aa;

eqn: (gg/aa)^2+(ff/aa)^2 -cc/aa;

if (eqn > 0) then ta2: true else ta2: false;]]></text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>{@circ@}: \(g^2+f^2 - c = {@ta1@}\), {@ta2@}</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <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>
    <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>5</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>3</showvalidation>
      <options/>
    </input>
    <input>
      <name>ans2</name>
      <type>boolean</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>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options/>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>ta1</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>prt2</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans2</sans>
        <tans>ta2</tans>
        <testoptions/>
        <quiet>1</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt2-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt2-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>878267904</deployedseed>
    <deployedseed>448335939</deployedseed>
    <deployedseed>1808506071</deployedseed>
    <deployedseed>186565008</deployedseed>
    <deployedseed>2098286020</deployedseed>
    <deployedseed>2087526351</deployedseed>
    <deployedseed>786358214</deployedseed>
    <deployedseed>438242610</deployedseed>
    <deployedseed>901989075</deployedseed>
    <deployedseed>919209164</deployedseed>
    <deployedseed>1328890808</deployedseed>
    <deployedseed>660343082</deployedseed>
    <deployedseed>705224657</deployedseed>
    <deployedseed>376867024</deployedseed>
    <deployedseed>1376121384</deployedseed>
    <deployedseed>319355234</deployedseed>
    <deployedseed>1734786524</deployedseed>
    <deployedseed>990840112</deployedseed>
    <deployedseed>2111063905</deployedseed>
    <deployedseed>2062014767</deployedseed>
    <deployedseed>1448214547</deployedseed>
    <deployedseed>1944584564</deployedseed>
    <deployedseed>497251867</deployedseed>
    <deployedseed>85174360</deployedseed>
    <deployedseed>261511482</deployedseed>
    <deployedseed>1305509100</deployedseed>
    <deployedseed>2071336720</deployedseed>
    <deployedseed>1677306321</deployedseed>
    <deployedseed>2095989914</deployedseed>
    <deployedseed>582992443</deployedseed>
    <deployedseed>410504035</deployedseed>
    <deployedseed>1823102914</deployedseed>
    <deployedseed>2058284416</deployedseed>
    <deployedseed>1878016248</deployedseed>
    <deployedseed>793580781</deployedseed>
    <deployedseed>1440028956</deployedseed>
    <deployedseed>377416279</deployedseed>
    <deployedseed>1879934891</deployedseed>
    <deployedseed>714475736</deployedseed>
    <deployedseed>2079164565</deployedseed>
    <deployedseed>1571868743</deployedseed>
    <deployedseed>1188261290</deployedseed>
    <deployedseed>988889845</deployedseed>
    <deployedseed>332691168</deployedseed>
    <deployedseed>1983675502</deployedseed>
    <deployedseed>1034277690</deployedseed>
    <deployedseed>481550403</deployedseed>
    <deployedseed>1391923200</deployedseed>
    <deployedseed>2120079880</deployedseed>
    <deployedseed>1449480424</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ta1</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ta2</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>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ta1-1</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ta2</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>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
