583 lines
30 KiB
XML
583 lines
30 KiB
XML
<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
|
||
<assessmentItem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
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xsi:schemaLocation="http://www.imsglobal.org/xsd/imsqti_v2p1 http://www.imsglobal.org/xsd/qti/qtiv2p1/imsqti_v2p1.xsd"
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xmlns="http://www.imsglobal.org/xsd/imsqti_v2p1"
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xmlns:xi="http://www.w3.org/2001/XInclude"
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xmlns:xlink="http://www.w3.org/1999/xlink"
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xmlns:m="http://www.w3.org/1998/Math/MathML"
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toolVersion="0.5.1"
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toolName="Mathqurate"
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title="Find side, directly or sine rule - with solution"
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timeDependent="false"
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identifier="Example04-feedbackBlock-templateBlock"
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adaptive="true">
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<responseDeclaration identifier="RESPONSE1" cardinality="single" baseType="float"/>
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<responseDeclaration identifier="HINTREQUEST" cardinality="single" baseType="boolean"/>
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||
<responseDeclaration identifier="SOLREQUEST" cardinality="single" baseType="boolean"/>
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||
<outcomeDeclaration baseType="float" cardinality="single" identifier="SCORE"
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normalMaximum="10.0" normalMinimum="0.0">
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<defaultValue>
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<value>0.0</value>
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</defaultValue>
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||
</outcomeDeclaration>
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||
<outcomeDeclaration baseType="identifier" cardinality="multiple" identifier="FEEDBACK"/>
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||
<outcomeDeclaration baseType="identifier" cardinality="single" identifier="EMPTY"/>
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||
<outcomeDeclaration baseType="boolean" cardinality="single" identifier="seenSolution">
|
||
<defaultValue>
|
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<value>false</value>
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||
</defaultValue>
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||
</outcomeDeclaration>
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||
<outcomeDeclaration baseType="boolean" cardinality="single" identifier="seenHint">
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||
<defaultValue>
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<value>false</value>
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||
</defaultValue>
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||
</outcomeDeclaration>
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||
<outcomeDeclaration baseType="identifier" cardinality="single" identifier="ASKHINT">
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||
<defaultValue>
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<value>askhint</value>
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||
</defaultValue>
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||
</outcomeDeclaration>
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||
<outcomeDeclaration baseType="identifier" cardinality="single" identifier="ASKSOLUTION">
|
||
<defaultValue>
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<value>asksolution</value>
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</defaultValue>
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||
</outcomeDeclaration>
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||
<outcomeDeclaration identifier="oMult" cardinality="single" baseType="float">
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||
<defaultValue>
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||
<value>1.0</value>
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</defaultValue>
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||
</outcomeDeclaration>
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<outcomeDeclaration identifier="oPower" cardinality="single" baseType="float"/>
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<!--The template variables for the calculation are declared, among them iA, an integer variable; it will be used in MathML,
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so the mathVariable attribute is true.-->
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<templateDeclaration identifier="iA" cardinality="single" baseType="integer"
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paramVariable="false" mathVariable="true">
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<defaultValue>
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<value>90</value>
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</defaultValue>
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</templateDeclaration>
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<templateDeclaration identifier="iB" cardinality="single" baseType="integer"
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paramVariable="false" mathVariable="true">
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<defaultValue>
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<value>65</value>
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</defaultValue>
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</templateDeclaration>
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<templateDeclaration identifier="ia" cardinality="single" baseType="integer"
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paramVariable="false" mathVariable="true"/>
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<templateDeclaration identifier="sinA" cardinality="single" baseType="float"
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paramVariable="false" mathVariable="true"/>
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<templateDeclaration identifier="sinB" cardinality="single" baseType="float"
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paramVariable="false" mathVariable="true"/>
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<templateDeclaration identifier="fAns" cardinality="single" baseType="float"
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paramVariable="false" mathVariable="true"/>
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<templateDeclaration identifier="fPiOver180" cardinality="single" baseType="float"
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paramVariable="false" mathVariable="true"/>
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<!--This template variable holds a string which describes the triangle.-->
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<templateDeclaration identifier="sType" cardinality="single" baseType="string"
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paramVariable="false" mathVariable="false"/>
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<!--These template variables control the display of the templateInline and templateBlock elements.-->
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<templateDeclaration baseType="identifier" cardinality="single" identifier="tSol"/>
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<templateDeclaration baseType="identifier" cardinality="single" identifier="tSoli"/>
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<templateProcessing>
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<!-- now do the randomisation and mathematical calculations -->
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<!-- The value of iA is selected randomly from a list of possible values of which several are 90 -->
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<setTemplateValue identifier="iA">
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<random>
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<multiple>
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<baseValue baseType="integer">45</baseValue>
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<baseValue baseType="integer">60</baseValue>
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<baseValue baseType="integer">75</baseValue>
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<baseValue baseType="integer">90</baseValue>
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<baseValue baseType="integer">90</baseValue>
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<baseValue baseType="integer">90</baseValue>
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</multiple>
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</random>
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</setTemplateValue>
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<setTemplateValue identifier="iB">
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<randomInteger min="50" max="85" step="5"/>
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</setTemplateValue>
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<templateConstraint>
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<not>
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<equal toleranceMode="exact">
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<variable identifier="iA"/>
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<variable identifier="iB"/>
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</equal>
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</not>
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</templateConstraint>
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<setTemplateValue identifier="ia">
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<randomInteger min="5" max="50"/>
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</setTemplateValue>
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<setTemplateValue identifier="fPiOver180">
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<divide>
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<mathConstant name="pi"/>
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<baseValue baseType="integer">180</baseValue>
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</divide>
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</setTemplateValue>
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<setTemplateValue identifier="sinA">
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<mathOperator name="sin">
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<product>
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<variable identifier="iA"/>
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<variable identifier="fPiOver180"/>
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</product>
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</mathOperator>
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</setTemplateValue>
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<setTemplateValue identifier="sinB">
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<mathOperator name="sin">
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<product>
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||
<variable identifier="iB"/>
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<variable identifier="fPiOver180"/>
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</product>
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</mathOperator>
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</setTemplateValue>
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<setTemplateValue identifier="sinA">
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<roundTo roundingMode="significantFigures" figures="5">
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<variable identifier="sinA"/>
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</roundTo>
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</setTemplateValue>
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<setTemplateValue identifier="sinB">
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<roundTo roundingMode="significantFigures" figures="5">
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<variable identifier="sinB"/>
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</roundTo>
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</setTemplateValue>
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<setTemplateValue identifier="fAns">
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<divide>
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<product>
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<variable identifier="ia"/>
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<variable identifier="sinB"/>
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</product>
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<variable identifier="sinA"/>
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</divide>
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</setTemplateValue>
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<setTemplateValue identifier="fAns">
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<roundTo roundingMode="significantFigures" figures="3">
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<variable identifier="fAns"/>
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</roundTo>
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</setTemplateValue>
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<!-- set up alternative content depending on the value of variable iA -->
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<templateCondition>
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<templateIf>
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<equal toleranceMode="exact">
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<!--If iA is 90, sType contains “right angled”, tSol contains the identifier, SolRightAngle, of the
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templateBlock for the right angle case, and tSoli contains the identifier, SolRightAnglei, of the
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templateInline for the right angle case-->
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<variable identifier="iA"/>
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<baseValue baseType="integer">90</baseValue>
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</equal>
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<setTemplateValue identifier="sType">
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<baseValue baseType="string">right angle</baseValue>
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</setTemplateValue>
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<setTemplateValue identifier="tSol">
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<baseValue baseType="identifier">SolRightAngle</baseValue>
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</setTemplateValue>
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<setTemplateValue identifier="tSoli">
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<baseValue baseType="identifier">SolRightAnglei</baseValue>
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</setTemplateValue>
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</templateIf>
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<templateElse>
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<!--If iA is not 90, sType contains "scalene", tSol contains the identifier, SolScalene, of the templateBlock
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for the scalene case, and tSoli contains the identifier, SolScalenei, of the templateInline for the scalene
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case-->
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<setTemplateValue identifier="sType">
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<baseValue baseType="string">scalene</baseValue>
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</setTemplateValue>
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<setTemplateValue identifier="tSol">
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<baseValue baseType="identifier">SolScalene</baseValue>
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</setTemplateValue>
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<setTemplateValue identifier="tSoli">
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<baseValue baseType="identifier">SolScalenei</baseValue>
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</setTemplateValue>
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</templateElse>
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</templateCondition>
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</templateProcessing>
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<itemBody>
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<p>In triangle ABC, side a=<printedVariable identifier="ia"/>, angle A=<printedVariable identifier="iA"/>° and angle
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B=<printedVariable identifier="iB"/>°. Find the length of side b.</p>
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<div class="">
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<p>Enter your answer to 3 significant figures.</p>
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<textEntryInteraction responseIdentifier="RESPONSE1" expectedLength="20"/>
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</div>
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<div class="">
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<feedbackInline id="feedbackInline3" showHide="show" outcomeIdentifier="FEEDBACK"
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identifier="Correct"> OK </feedbackInline></div>
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<div class="">
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<feedbackInline id="feedbackInline2" showHide="show" outcomeIdentifier="FEEDBACK"
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identifier="Partial"> Not far off - check your rounding... </feedbackInline></div>
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<div class="">
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<feedbackInline id="feedbackInline2" showHide="show" outcomeIdentifier="FEEDBACK"
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identifier="Incorrect"> Incorrect
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</feedbackInline></div>
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<div class="">
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<feedbackBlock id="feedbackBlock11" identifier="THREETRIES" outcomeIdentifier="FEEDBACK"
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showHide="show">
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<p> You have had three attempts at answering this question, so here is the solution:
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</p>
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</feedbackBlock>
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<!-- this feedbackBlock contains the solution,
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which is different depending on the value of iA -->
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<feedbackBlock identifier="SOLUTION" outcomeIdentifier="FEEDBACK" showHide="show">
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<!--Parts of this sentence appear differently, depending on whether or not iA is 90. The template variables sType,
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tSol and tSoli were set during template processing in the templateCondition shown above-->
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<p>This is a <printedVariable identifier="sType"/> triangle, so
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<templateInline templateIdentifier="tSoli" identifier="SolRightAnglei" showHide="show">
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<span> we can use sin(B) to find b directly</span></templateInline>
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<templateInline templateIdentifier="tSoli" identifier="SolScalenei" showHide="show">
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<span> we apply the Sine Rule</span></templateInline>:
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</p>
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<!--The templateBlock elements contain the MathML for the two different solutions: SolRightAngle for iA=90 and
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SolScalene for other values of iA-->
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<templateBlock templateIdentifier="tSol" identifier="SolRightAngle" showHide="show">
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<semantics>
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||
<mtable>
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||
<mtr>
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<mtd columnalign="right">
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<mrow>
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<mi>sin</mi>
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<mfenced close=")" open="(">
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<mi>B</mi>
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</mfenced>
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</mrow>
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||
</mtd>
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||
<mtd columnalign="center">
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||
<mo>=</mo>
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||
</mtd>
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||
<mtd columnalign="left">
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||
<mfrac>
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||
<mi>b</mi>
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||
<mi>a</mi>
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||
</mfrac>
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||
</mtd>
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||
</mtr>
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||
<mtr>
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||
<mtd columnalign="right">
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||
<mi>b</mi>
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</mtd>
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||
<mtd columnalign="center">
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||
<mo>=</mo>
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||
</mtd>
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||
<mtd columnalign="left">
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||
<mi>a</mi>
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<mrow>
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||
<mi>sin</mi>
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||
<mfenced close=")" open="(">
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||
<mi>B</mi>
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||
</mfenced>
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||
</mrow>
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||
</mtd>
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||
</mtr>
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||
<mtr>
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||
<mtd columnalign="right">
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||
<mi>b</mi>
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||
</mtd>
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||
<mtd columnalign="center">
|
||
<mo>=</mo>
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||
</mtd>
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||
<mtd columnalign="left">
|
||
<mrow>
|
||
<mi>ia</mi>
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||
<mo>×</mo>
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||
<mi>sin</mi>
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||
<mfenced close=")" open="(">
|
||
<mi>iB</mi>
|
||
</mfenced>
|
||
</mrow>
|
||
</mtd>
|
||
</mtr>
|
||
<mtr>
|
||
<mtd columnalign="right"/>
|
||
<mtd columnalign="center">
|
||
<mo>=</mo>
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||
</mtd>
|
||
<mtd columnalign="left">
|
||
<mi>fAns</mi>
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||
</mtd>
|
||
</mtr>
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||
</mtable>
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||
<annotation encoding="SnuggleTeX">\begin{eqnarray*}
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\\sin(B)&=&\frac{b}{a}\\
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b&=&a\sin(B)\\
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||
&=&\qv{ia}\times\sin(\qv{iB})
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||
&=&\qv{fAns} \end{eqnarray*}</annotation>
|
||
</semantics>
|
||
</math>
|
||
</templateBlock>
|
||
<templateBlock templateIdentifier="tSol" identifier="SolScalene" showHide="show">
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||
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
||
<semantics>
|
||
<mtable>
|
||
<mtr>
|
||
<mtd columnalign="right">
|
||
<mfrac>
|
||
<mi>a</mi>
|
||
<mrow>
|
||
<mi>sin</mi>
|
||
<mfenced close=")" open="(">
|
||
<mi>A</mi>
|
||
</mfenced>
|
||
</mrow>
|
||
</mfrac>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mo>=</mo>
|
||
</mtd>
|
||
<mtd columnalign="left">
|
||
<mfrac>
|
||
<mi>b</mi>
|
||
<mrow>
|
||
<mi>sin</mi>
|
||
<mfenced close=")" open="(">
|
||
<mi>B</mi>
|
||
</mfenced>
|
||
</mrow>
|
||
</mfrac>
|
||
</mtd>
|
||
</mtr>
|
||
<mtr>
|
||
<mtd columnalign="right">
|
||
<mfrac>
|
||
<mi>ia</mi>
|
||
<mrow>
|
||
<mi>sin</mi>
|
||
<mfenced close=")" open="(">
|
||
<mi>iA</mi>
|
||
</mfenced>
|
||
</mrow>
|
||
</mfrac>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mo>=</mo>
|
||
</mtd>
|
||
<mtd columnalign="left">
|
||
<mfrac>
|
||
<mi>b</mi>
|
||
<mrow>
|
||
<mi>sin</mi>
|
||
<mfenced close=")" open="(">
|
||
<mi>iB</mi>
|
||
</mfenced>
|
||
</mrow>
|
||
</mfrac>
|
||
</mtd>
|
||
</mtr>
|
||
<mtr>
|
||
<mtd columnalign="right">
|
||
<mi>b</mi>
|
||
</mtd>
|
||
<mtd columnalign="center">
|
||
<mo>=</mo>
|
||
</mtd>
|
||
<mtd columnalign="left">
|
||
<mfrac>
|
||
<mrow>
|
||
<mi>ia</mi>
|
||
<mo>×</mo>
|
||
<mi>sin</mi>
|
||
<mfenced close=")" open="(">
|
||
<mi>iB</mi>
|
||
</mfenced>
|
||
</mrow>
|
||
<mrow>
|
||
<mi>sin</mi>
|
||
<mfenced close=")" open="(">
|
||
<mi>iA</mi>
|
||
</mfenced>
|
||
</mrow>
|
||
</mfrac>
|
||
</mtd>
|
||
</mtr>
|
||
<mtr>
|
||
<mtd columnalign="right"/>
|
||
<mtd columnalign="center">
|
||
<mo>=</mo>
|
||
</mtd>
|
||
<mtd columnalign="left">
|
||
<mfrac>
|
||
<mrow>
|
||
<mi>ia</mi>
|
||
<mo>×</mo>
|
||
<mi>sinB</mi>
|
||
</mrow>
|
||
<mrow>
|
||
<mi>sinA</mi>
|
||
</mrow>
|
||
</mfrac>
|
||
</mtd>
|
||
</mtr>
|
||
<mtr>
|
||
<mtd columnalign="right"/>
|
||
<mtd columnalign="center">
|
||
<mo>=</mo>
|
||
</mtd>
|
||
<mtd columnalign="left">
|
||
<mi>fAns</mi>
|
||
</mtd>
|
||
</mtr>
|
||
</mtable>
|
||
<annotation encoding="SnuggleTeX">\begin{eqnarray*}
|
||
\frac{a}{\sin(A)}&=&\frac{b}{\sin(B)}\\
|
||
\frac{\qv{ia}}{\sin(\qv{iA})}&=&\frac{b}{\sin(\qv{iB})}
|
||
b&=&\frac{A\times\sin(B)}{\sin(A)}\\
|
||
&=&\frac{\qv{ia}\times\sin(\qv{iB})}{\sin(\qv{iA})}\\
|
||
&=&\qv{fAns} \end{eqnarray*}</annotation>
|
||
</semantics>
|
||
</math>
|
||
</templateBlock>
|
||
|
||
<!--This sentence is the same for all values of iA-->
|
||
|
||
<p>So the expected answer is <printedVariable identifier="fAns"/>.</p>
|
||
</feedbackBlock></div>
|
||
|
||
<!-- Explain why the score is zero (after viewing solution) -->
|
||
|
||
<feedbackBlock identifier="SEEN-SOLUTION" outcomeIdentifier="FEEDBACK" showHide="show">
|
||
<p> Since you have viewed the solution, your score for this question will be 0. </p>
|
||
</feedbackBlock>
|
||
|
||
<!-- show the solution button -->
|
||
|
||
<feedbackBlock identifier="asksolution" outcomeIdentifier="ASKSOLUTION" showHide="show">
|
||
<div>
|
||
<endAttemptInteraction id="endAttemptInteraction2" responseIdentifier="SOLREQUEST" title="Show Solution"/>
|
||
</div>
|
||
</feedbackBlock>
|
||
</itemBody>
|
||
<responseProcessing>
|
||
<setOutcomeValue identifier="FEEDBACK">
|
||
<multiple>
|
||
<variable identifier="EMPTY"/>
|
||
</multiple>
|
||
</setOutcomeValue>
|
||
<responseCondition>
|
||
<responseIf>
|
||
<variable identifier="SOLREQUEST"/>
|
||
<setOutcomeValue identifier="FEEDBACK">
|
||
<multiple>
|
||
<baseValue baseType="identifier">SOLUTION</baseValue>
|
||
</multiple>
|
||
</setOutcomeValue>
|
||
<setOutcomeValue identifier="seenSolution">
|
||
<baseValue baseType="boolean">true</baseValue>
|
||
</setOutcomeValue>
|
||
<setOutcomeValue identifier="completionStatus">
|
||
<baseValue baseType="identifier">completed</baseValue>
|
||
</setOutcomeValue>
|
||
<setOutcomeValue identifier="ASKSOLUTION">
|
||
<baseValue baseType="identifier">null</baseValue>
|
||
</setOutcomeValue>
|
||
</responseIf>
|
||
<responseElse>
|
||
<responseCondition>
|
||
<responseIf>
|
||
<isNull>
|
||
<variable identifier="RESPONSE1"/>
|
||
</isNull>
|
||
<setOutcomeValue identifier="SCORE">
|
||
<baseValue baseType="float">0</baseValue>
|
||
</setOutcomeValue>
|
||
</responseIf>
|
||
<responseElse>
|
||
<responseCondition>
|
||
<responseIf>
|
||
<equalRounded roundingMode="significantFigures" figures="3">
|
||
<variable identifier="fAns"/>
|
||
<variable identifier="RESPONSE1"/>
|
||
</equalRounded>
|
||
<setOutcomeValue identifier="FEEDBACK">
|
||
<multiple>
|
||
<baseValue baseType="identifier">Correct</baseValue>
|
||
</multiple>
|
||
</setOutcomeValue>
|
||
<setOutcomeValue identifier="SCORE">
|
||
<baseValue baseType="float">10.0</baseValue>
|
||
</setOutcomeValue>
|
||
</responseIf>
|
||
<responseElseIf>
|
||
<equalRounded roundingMode="significantFigures" figures="2">
|
||
<variable identifier="RESPONSE1"/>
|
||
<variable identifier="fAns"/>
|
||
</equalRounded>
|
||
<setOutcomeValue identifier="FEEDBACK">
|
||
<multiple>
|
||
<baseValue baseType="identifier">Partial</baseValue>
|
||
</multiple>
|
||
</setOutcomeValue>
|
||
<setOutcomeValue identifier="SCORE">
|
||
<baseValue baseType="float">5.0</baseValue>
|
||
</setOutcomeValue>
|
||
</responseElseIf>
|
||
<responseElse>
|
||
<setOutcomeValue identifier="FEEDBACK">
|
||
<multiple>
|
||
<baseValue baseType="identifier">Incorrect</baseValue>
|
||
</multiple>
|
||
</setOutcomeValue>
|
||
<setOutcomeValue identifier="SCORE">
|
||
<baseValue baseType="float">0.0</baseValue>
|
||
</setOutcomeValue>
|
||
</responseElse>
|
||
</responseCondition>
|
||
<responseCondition>
|
||
<responseIf>
|
||
<gt>
|
||
<variable identifier="numAttempts"/>
|
||
<baseValue baseType="integer">3</baseValue>
|
||
</gt>
|
||
<setOutcomeValue identifier="FEEDBACK">
|
||
<multiple>
|
||
<baseValue baseType="identifier"> THREETRIES </baseValue>
|
||
<baseValue baseType="identifier"> SOLUTION </baseValue>
|
||
</multiple>
|
||
</setOutcomeValue>
|
||
|
||
<!-- completionStatus must be specifically set to completed in adaptive questions -->
|
||
|
||
<setOutcomeValue identifier="completionStatus">
|
||
<baseValue baseType="identifier">completed</baseValue>
|
||
</setOutcomeValue>
|
||
<setOutcomeValue identifier="ASKSOLUTION">
|
||
<baseValue baseType="identifier">null</baseValue>
|
||
</setOutcomeValue>
|
||
</responseIf>
|
||
</responseCondition>
|
||
<responseCondition>
|
||
<responseIf>
|
||
<variable identifier="seenSolution"/>
|
||
<setOutcomeValue identifier="FEEDBACK">
|
||
<multiple>
|
||
<variable identifier="FEEDBACK"/>
|
||
<baseValue baseType="identifier">SEEN-SOLUTION</baseValue>
|
||
</multiple>
|
||
</setOutcomeValue>
|
||
<setOutcomeValue identifier="SCORE">
|
||
<baseValue baseType="float">0.0</baseValue>
|
||
</setOutcomeValue>
|
||
</responseIf>
|
||
</responseCondition>
|
||
</responseElse>
|
||
</responseCondition>
|
||
</responseElse>
|
||
</responseCondition>
|
||
</responseProcessing>
|
||
</assessmentItem>
|