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GuidelinesforUsingMapleCodeforMaple-gradedQuestions
• AMaple-gradedquestionmustusevalidMaplecodetoevaluatetheanswer.Completeeachlineofcodewith
asemicolon.
• ThelastlineofyourquestioncodemustevaluatetoaBooleanvalue(trueorfalse)orafloating-pointnumber
between0.0and1.1forpartialgrading.Inmanycases,itisrecommendedthatyouusetheMapleevalbcom-
mand.
• Usethelongformnameforallpackagefunctions,forexample,VectorCalculus[ArcLength].
Foranexamplethatusespartialgrading,seeApplyingPartialGradingtoMaple-gradedQuestions(page100).
ProvidingFeedbacktoStudents
• Todisplaythecorrectanswerasfeedbackforastudentresponse,youmustenterthecorrectanswerinthe
EnterMaplecodethatevaluatestothecorrectanswerfield.
• Foropen-endedquestions,suchas"Giveandexampleofanincreasingfunctionontheinterval[0,10]",itis
recommendedthatyouincludeacommentforagradedresponse.Otherwise,nocommentisdisplayedas
feedbacktothestudentiftheresponseisincorrect.CommentsareenteredintheQuestionName&Typescreen.
Maple-gradedQuestionTypeHelpPages
TheAlgorithmDesigner(page81)
Maple-gradedQuestionsintheQuestionEditor(page99)
DisplayingaMaplePlot(page221)
MapleSyntaxQuestionExampleScript(page313)
MathQuestionTypesComparisonTable(page153)
MathematicalFunctions&Operations(page224)
PlottingaStudentResponse(page209)
Tutorial:Maple-basedAlgorithmicQuestionAuthoring(page263)
UsingaMapleRepository(page91)
UsingMapleCodetoPreventCheatinginMapleSyntaxQuestions(page207)
UsingtheCommentFieldinaMapleQuestion(page313)
Maple-gradedFormula
QuestionMode:Maple
QuestionEditorquestiontype:Maple-graded
Questionfile(.qu)syntax:
qu.x.y.mode=Maple@
type=formula@
InMaple-gradedFormulaquestiontypes,studentscanenteramathformula,thatis,anexpressionconstructedof
numbers,variablenames,andthestandardarithmeticexpressionsandfunctions.
Note:IntheQuestionEditor,ontheMaple-gradedquestionscreen,theSelectthetypeofexpressionyouwanttoacceptfield
liststheMaple-gradedFormulaoptionassimplyFormula.
9.2MathQuestionTypes • • 161
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Guidelines
• ThestudentshouldnotuseMaplecommandsintheresponse.Foranexplanation,seeSyntaxandStudent
Responsesbelow.
• Theinstructormustwritecodesuchthatthestudentdoesnothavetouseatrailingsemicolonintheresponse.
Forexample,evalb($RESPONSE=factor(x^2-1));asasinglelineofcodeallowsthestudenttorespondwith(x+1)(x-
1)omittingthetrailingsemicolon.Thisisespeciallyimportant,asquestionscreatedusingtheMaple-gradedFormula
questionsubtypearenotobviousMaplequestionsfromthestudent'sperspective.Anon-Maplestudentusercananswer
aMaple-gradedFormulaquestiontypewithoutknowingMaplesyntax.
Syntax
MapleT.A.verifiesthestudentresponseusingabasicsyntaxchecker.
• IftheanswerisenteredinTextmode,theformulasyntaxcheckerassessestheresponse,changesexpressions
toMaplesyntax,forexample,2xbecomes2*x,andreportserrorsiftheexpressionisnotaformula.Itthen
generatesaMaplestatement.
• IftheansweriscreatedusingtheEquationEditor,aMathMLexpressionisparsed,thesyntaxcheckerisrun
toensuretheanswerisoftypeformula,andthenaMaplestatementisgenerated.
StudentResponses
Youdonotneedtoexplicitlycheckthatthestudentresponseisaformula.Forexample,youdonotneedtocheck
whetherfactor(expr)isacommandthatcalculatestheexpressionforthestudent.However,astudentresponse
likefactor(x^2-1)wouldbeinterpretedasimplicitmultiplicationandconvertedtof*a*c*t*o*r*(x^2-1).
Assuch,thestudentresponsewillbemarkedaswrong.
YoumayneedtowriteMaplecodeforresponsesthatareinterpretedasformulasbyMapleT.A.,butareMaplecom-
mands.Forexample,ifyouaskforthevalueofsin(Pi/4),youmustusecodetoensurethatthestudentdoesnot
simplyentersin(Pi/4),whichtheMapleT.A.syntaxcheckeracceptsandpassestoMaple.Thecorrectresponse
is,forexample,sqrt(2)/2,whichisalsoaMapleT.A.formulaandaMaplecommand.
Variables
ThevariableeshouldnotbeassignedasaglobalvariableinMaplecode.Itcanbeused,however,asalocalvariable.
SeeAlso:
Maple-gradedQuestionsintheQuestionEditor(page99)
Maple-gradedQuestionType-Overview(page159)
MapleSyntax
QuestionMode:Maple
QuestionEditorquestiontype:Maple-graded
Questionfile(.qu)syntax:
qu.x.y.mode=Maple@
type=maple@
MapleSyntaxisasubtypeoftheMaple-gradedquestiontype.
Inthissubtype,thestudentisrequiredto:
• RespondusingMaplecommandsandexpressions
162 • 9QuestionTypes
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• EntersyntacticallycorrectMapleexpressions
InaMapleSyntaxquestion,youmustspecifywhethertheresponseareaisatext-entryareaorasymbolic-entryarea.
ExampleUses
TheMapleSyntaxsubtypeisparticularlyusefulwhentheansweristobeexpressedasa:
• Definiteintegral,int(f(x),x=a..b)
• Derivative,diff(f(x),x)
• Limit,limit(f(x), x=0)
• Differentialequation,forexample,diff(y(x,t),t,t)=c^2*diff(y(x,t),x,x)
• Set,forexample, {1,4,9}
• Matrix,forexample,
SomeexamplequestionsinvolvingmatricesarecreatedinTutorial:MapleSyntaxQuestionswithMatrices(page124).
MapleSyntaxwithTextEntryResponseOption
qu.x.y.mode=Maple@
type=maple@
allow2d=0
Guidelines
StudentUseofUnevaluatedFormsofMapleCommands
SomeMaplecommandstakeunevaluatedforms.Forexample,Diffistheinertformofdiff.InMapleT.A.,students
aredirectedtoanswerquestionsusingtheunevaluatedformsofMaplecommands.Yourcodeshouldacceptthese
forms.
SemicolonUsage
Theinstructorshouldspecifytothestudent(inthequestiontext)whetheratrailingsemicolonisrequired,oralternatively,
writecodesuchthatthepresenceorabsenceofatrailingsemicolonhasnobearingontheevaluationoftheresponse.
Forexample,evalb($RESPONSE=factor(x^2-1);asonelineofquestioncodedoesnotallowastudentresponse
withasemicolon,suchas(x-1)*(x+1);Theresponseismarkedasincorrect.
Ifthequestioncodecontainstwolines,completedwithsemicolons,suchas
A:= $RESPONSE;
evalb(A=factor(x^2-1);
thestudentcananswerwithorwithoutasemicolonandtheresponseismarkedascorrect.
Syntax
MapleT.A.doesnotcheckthesyntaxofthestudentresponse.
• IftheanswerisenteredinTextmode,itissentdirectlytoMapleforparsing.Thestudentisexpectedtoenter
syntacticallycorrectMapleexpressions.Shortcutssuchas2xaremarkedincorrect.
Astheauthor,youcanverifywhetherthestudentisusingaMaplecommandtocalculatetheanswer.Formoreinform-
ation,seeUsingMapleCodetoPreventCheatinginMapleSyntaxQuestions(page207).
9.2MathQuestionTypes • • 163
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MapleSyntaxwithSymbolicEntryResponseOption
qu.x.y.mode=Maple@
type=maple@
allow2d=2
ForatutorialoncreatingaMapleSyntaxquestionwithSymbolicmoderesponse,seeTutorial:MapleSyntaxQuestions
withMatrices(page124).
Syntax
MapleT.A.parsesthestudentresponseenteredinSymbolmodetoconverttheenteredexpressionintoMaplesyntax,
whichissenttoMaple.
Notethat,sinceatranslationofthesymbolicentryintoaMapleInputexpressiontakesplace,thetechniqueofusing
“$RESPONSE”tocheckwhetherstudentsenteredaspecificcommandmaynotbeappropriate.Thistechniqueisonly
recommendedforMapleSyntaxquestionswiththeTextentryresponseoption.
Variables
ThevariableeshouldnotbeassignedasaglobalvariableinMaplecode.Itcanbeused,however,asalocalvariable.
SeeAlso:
Maple-gradedQuestionsintheQuestionEditor(page99)
Matrix
QuestionMode:Matrix
Questionfile(.qu)syntax:
qu.mode.x.y=matrix@
TheMatrixquestiontypegeneratesannbymmatrixoftextfields,eachofwhichacceptsanumberorformula.
MatrixquestionsmustbecreatedinLaTeXorinaplaintext.qufile.Youmustspecifyauniquematrixasthecorrect
solution.
Note:ItisrecommendedthatyouusetheMapleSyntaxquestiontypeforquestionsthatwillhaveamatrixresponse.
MapleSyntaxquestionsprovidemoreflexibilitythantheMatrixquestionsinquestionauthoringandgrading.With
theMapleSyntaxquestiontype:
• Ratherthanshowingthestudentwithaspecificsizeofmatrixwithablankforeachentry,thestudentcanselectthe
appropriatesizeofthematrixintheiranswer(forinstance,usingaPalette).
• BysendingtheentirematrixtoMapleforgrading,youcanevaluatepropertiesofthematrix(suchaswhetheritis
invertibleorsymmetric).
• Partialgradingispossible.
SeeAlso:
MatrixQuestionsinLaTeX(page297)
MultiFormula
QuestionMode:multiformula
QuestionEditorquestiontype:Mathematicalformula
164 • 9QuestionTypes
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Questionfile(.qu)syntax:
qu.x.y.mode=multi formula@
Inthemultiformulaquestiontype,thecorrectstudentresponseisanunorderedlistofformulas.Usethisforany
unorderedlistofformulasornumbers.Foranorderedlistofformulas,usetheFormulalistquestiontype(seeFormula
List(page158)).
Youcanusethefullrangeoffunctionsintheformulas,thatis,alltrigonometricfunctions,log,ln,abs,andsqrt.
Important:Youmustusesemicolonstoseparatetheitemsinthecorrectanswer(forexample,1;12;12).Ifyouusecommasin
thecorrectanswer,thesystemtreatsthequestionasanorderedlist,andrequiresthatthestudentgivetheirresponseintheorder
inwhichyouenteredthecorrectanswer.
Inatest,theinputfieldfortheresponseappearsasshowninFigure9.5.
Figure9.5:InputFieldforaMultiFormulaQuestion
SeeAlso:
Formula(page156)
FormulaList(page158)
MathematicalFormulaQuestionsintheQuestionEditor(page102)
MultiFormulaQuestionsinLaTeX(page296)
MultipartFormula
QuestionMode:multipartformula
Questionfile(.qu)syntax:
qu.x.y.mode=multipart formula@
Themultipartformulaquestiontypebehavesasamultipartquestioninwhicheachpartisaformulaquestion.It
displaysmultipletextfieldsformultiplestudentresponses.
Note:Amultipartformulaquestiondisplaysmultipleindividualtextfields,whileamultiformulaquestionrequiresastudent
toentermultipleformulasinonetextfieldasitscorrectanswer.
MultipartformulaquestionsmustbeauthoredinLaTeXorscriptfiles.
Toidentifymultiplecorrectanswers,separateeachwithasemicoloninyouranswerfielddefinitionstatement.(Include
atrailingsemicolonforthelastanswerinthelist.)
Inatest,theinputfieldfortheresponseappearsasshowninFigure9.6.
9.2MathQuestionTypes • • 165
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Question
SeeAlso:
Formula(page156)
MultiFormula(page164)
Numeric
QuestionMode:Numeric
QuestionEditorquestiontype:Numeric
Questionfile(.qu)syntax:
qu.x.y.mode=numeric@
Thenumericquestiontypeaccepts:
• Purenumbers(withoutphysicalunits)indecimalformorscientificnotation
• Numberswithunits
Details:
• Youcannotuseequationsoralgebraicformulasinthecorrectanswer.
• Equivalentnumericexpressionsandunitsarerecognized.Thesystemrecognizesdefaultunitequivalents.You
canalsocreateaquestionbank-specifictableofequivalentunits.
• Studentsarepromptedtoenterresponsesinscientificornumericformat,withorwithoutphysicalunits.
• Youspecifytheinclusionofunitsinthecorrectanswerusingtheanswer.unitsquestionfield.Ifyoudo
notassignavaluetotheanswer.unitsstatement,thecorrectanswerisdimensionless.
• UsingtheoptionalshowUnitsfield,youcontrolwhetherthesystemdisplaysthequestionwiththeUnits
textfield.
166 • 9QuestionTypes
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• Youcancontroltheprecisionandtolerance(ormarginoferror)requiredinstudentresponses.Theeasiestway
tosetthesemodesisbyusingtheQuestionEditortoauthornumericquestions.
• Youcanspecifywhetherarithmeticisallowedinstudentresponses.
Important:Whencreatingquestionsthathaveaspecificnumberofsignificantdigitsinthecorrectanswer,itisrecom-
mendedthatyouusethesigfunctiontocreatealgorithmicvariables.Byusingthesevariablesinthequestionstatement,
feedback,hints,andsolution,youensurethatvaluesaredisplayedwiththecorrectnumberofsignificantdigits.
• SingleormultiplenumericquestionscanbeincludedalongwithotherresponseobjectswithinaQuestionDe-
signerquestion.
Example
qu.1.1.mode=numeric@
qu.1.1.question=
<question_text>
@
qu.1.1.answer.num=<numeric part of the answer, for r example, , 3>@
qu.1.1.answer.units=<units part of the answer, for r example, , m/s>@
qu.1.1.showUnits=<true or r false; ; whether r to o display the e question n with a Units text field>@
qu.1.1.grading=<grading mode; see below>@
qu.1.1.units=<(optional) reference to external table of f units; ; see below>@
qu.1.1.digit=<# sig g digits s (positive integer);
required for r exact_sigd and d toler_sigd d grading
modes>@
qu.1.1.err=<error/tolerance; required for toler_sigd and toler_abs grading modes>@
qu.1.1.perc=<percentage error/tolerance; ; required d for toler_perc grading mode>@
GradingModes
Usingthegradingmode,youcancontroltheprecisionormarginoferrorinthestudentresponsesgradedcorrect.
Precision
exact_sigd
Thenumericvalueofthestudentresponsemustmatchanswer.num.
Thenumberofsignificantdigitsinthestudentresponsemustmatchdigit.
Forexample,ifanswer.num = = 2.5andthedigit = = 3,only2.50iscorrect.Inparticular,
2.5isincorrect.
exact_value
Thenumericvalueofthestudentresponsemustmatchanswer.num.
Forexample,ifanswer.num = 2.5,2.50and2.5arecorrect,but2.500001isincorrect.
MarginofError
toler_perc
Thenumericvalueofthestudentresponsemustbewithinperc %ofanswer.num.
Forexample,ifperc = 5andanswer.num = 2.5,anyresponsebetween2.5 * 0.95
and2.5 * 1.05iscorrect.Inparticular,2.38888888iscorrect.
toler_abs
Thenumericvalueofthestudentresponsemustbewithin+/- errofanswer.num.Theerror
canbespecifiedasanumericvalueoralgorithmicvariable.
9.2MathQuestionTypes • • 167
Forexample,iferr = 0.25andanswer.num = 2.5,anyresponsebetween2.25and
2.75(inclusive)iscorrect.Inparticular,2.333333333iscorrect.
PrecisionandMarginofError
toler_sigd
Thenumericvalueofthestudentresponsemustbewithin+/-errinthedigitthsignificant
digitofanswer.num(inclusive)andhavedigitsignificantdigits.Theerrorcanbespecified
asanumericvalueoralgorithmicvariable.
Forexample,iferr = 2,digit = 3,andanswer.num = 2.5,theresponses2.48,
2.49, 2.50, 2.51, and2.52arecorrect.Allotherresponses,forexample,2.499 and
2.5,areincorrect.
Forexample,iferr = 1,digit = 3,andanswer.num = 27.18,theresponses27.1
and27.2arecorrect.Although27.3iswithin0.1of27.18roundedto3significantdigits,it
isincorrectbecauseitisnotwithin0.1of27.18.
UsingaQuestionBank-specificTableofUnits
Touseatableofunits,includethefollowingstatement:
qu.<topic_number>.<question_number>.units=<tablename>@
where<tablename>isatableofunitdefinitionsinthequestionbank.Formoreinformation,seeUsingaTableof
Units(page225).
SeeAlso:
NumericQuestionsintheQuestionEditor(page105)
NumericQuestionsinLaTeX(page288)
FormulawithUnits(page159)
ControllingAnswerFormatinNumericQuestions(page204)
ControllingAnswerTolerance(page205)
QuestionDesigner
QuestionMode:QuestionDesigner
QuestionEditorquestiontype:QuestionDesigner
Questionfile(.qu)syntax:
qu.x.y.mode=Inline@
QuestionDesignerquestionscanincorporatemultiplequestiontypeswithinonequestion,includingnearlyallmath
questiontypes.
ForinformationanddetailsontheQuestionDesignerquestiontype,seeQuestionDesignerQuestions(page188).
QuestionswithPlots
BasicSystemPlots
Youcanintegratebasicfunctionplottingorgraphingcomponentsfromalgorithmicformulasinquestionstatements
orfeedback.YoumustuseLaTeXorplaintextscriptauthoringtocreatethesequestions.
168 • 9QuestionTypes
Formoreinformation,seeGraphPlottingApplet,below.
MaplePlots
UsetheMaplecomputeralgebrasystemtogeneratesophisticatedtwo-andthree-dimensionalplotsinyourquestions
andfeedback.SeePlottingUsingMaple(page221).YoucanaddaMapleplotusinganyauthoringmethod.
GraphPlottingApplet
Thegraphplottingappletisaninteractiveplotthatisaddedtoaquestionfordynamicplotting.Theappletdisplays
axesforthegraphevenwhentheaxeslieoutsideoftheviewablearea.
• Clickanddragthegraphareatobringupacursorthatdisplaysthecoordinatesofthecurrentpoint
• Shift-clickanddragthegraphareatoshifttheviewablearea
• Ctrl-clickanddragthegraphtore-scaletheimage
qu.1.topic=Plot@
qu.1.1.mode=Multi Formula@
qu.1.1.name=X-intercepts@
qu.1.1.editing=useHTML@
qu.1.1.question=<p class="noindent">What t are e the
<math xmlns="http://www.w3.org/1998/Math/MathML" " display="inline">
<mi class="MathClass-ord">x</mi></math>
-intercepts of the graph shown?</p>
<applet code="applets.grapher.Graph" width="350" height="350"
archive="graphing.jar">
<param name="y1" value="(x-1)(x+3)(x-5)"></param>
<param name="xMin" " value="-6"></param>
<param name="xMax" " value="6"></param>
<param name="yMin" " value="-6"></param>
<param name="yMax" " value="6"></param>
<param name="gridLines" " value="12"></param>
</applet>@
qu.1.1.answer=-3;1;5@
qu.1.2.mode=Multi Formula@
qu.1.2.name=X-intercepts@
qu.1.2.editing=useHTML@
qu.1.2.question=<p class="noindent">What t are e the
<math xmlns="http://www.w3.org/1998/Math/MathML" " display="inline">
<mi class="MathClass-ord">x</mi></math>
-intercepts of the graph shown?</p>
<applet code="applets.grapher.Graph" width="350" height="350"
archive="graphing.jar">
<param name="y1" value="(x-1)(x-3)(x-5)"></param>
<param name="xMin" " value="2"></param>
<param name="xMax" " value="6"></param>
<param name="yMin" " value="-6"></param>
<param name="yMax" " value="6"></param>
<param name="gridLines" " value="12"></param>
</applet>@
qu.1.2.answer=-3;1;5@
SeeAlso:
GraphPlottingAppletinQuestions(page90)
PlottingaStudentResponse(page209)
AuthoringQuestionswithEmbeddedPlotsExampleScript(page316)
GraphPlottinginLaTeXQuestions(page279)
9.2MathQuestionTypes • • 169
RestrictedFormula
QuestionMode:Restrictedformula
QuestionEditorquestiontype:Mathematicalformula
Questionfile(.qu)syntax:
qu.x.y.mode=Restricted formula@
IntheRestrictedformulaquestiontype,thecorrectanswerisaformulathatusesonlybasicoperations(forexample,
arithmeticoperationsandsqrt).Youcanusethisforquestionsthatrequireaformulawithoutphysicalunitsthatdoes
notincludetrigonometricfunctions,log,ln,orabs,andwhichisnotanequation.
WhenauthoringinthesystemQuestionEditor,ifyouincludearestrictedfunctioninthecorrectanswer,thesystem
warnsyouthatthefunctionisnotallowedinrestrictedmode.
Note:Iftheanswerisanumber(thatis,doesnothaveanyvariables),itisrecommendedthatyouspecifyinthequestion
textwhetheranexactansweroranapproximationisrequired.Inthecaseofanapproximation,themarginoferror
mustbespecifiedinyourcorrectanswer.Thiscanbedonebyspecifyingamarginoferrorusingthe?operator.
Forexample,iftheanswerfieldwere
{2.34 ? ? 0.01}
anyresponsebetween2.33and2.35(inclusive)wouldbegradedcorrect.Inotherwords,thenumber
followingthe?operatoristhemarginoferror.Formoreinformationontolerances,seeSettingaMarginof
ErrorinNon-numericQuestions(page206).
SeeAlso:
MathematicalFormulaQuestionsintheQuestionEditor(page102)
Equation(page156)
Formula(page156)
RestrictedFormulaQuestionsinLaTeX(page293)
VectorsofFormulas
QuestionMode:Ntuple
QuestionEditorquestiontype:Mathematicalformula
Questionfile(.qu)syntax:
qu.x.y.mode=Ntuple@
TheNtuplequestiontyperequiresavectorofformulas(asequencedlist)incorrectresponses.Usethisforquestions
withvectorsofformulasornumbers.Youcanusethefullrangeoffunctionsintheformulas,thatis,alltrigonometric
functions,log,ln,abs,andsqrt.
• Thisisanorderedlist.Theentriesmustappearinthesameorderasinthegivencorrectanswer.
• Thecorrectanswergivenshouldhaveparentheses,suchas(3,5)or(2,1,-3),becausethisisindicatedinthein-
structionsundertheanswerbox.However,aresponseisgradedcorrectwithorwithouttheparentheses.
• ThistypeisgradedinthesamemannerastheFormulaListtype.Theonlydifferenceistheinstructionsgiven
tothestudents.
Inatest,theinputfieldfortheresponseappearsasshowninFigure9.7.
170 • 9QuestionTypes
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