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<br>(a) What is s its s momentum?
<br>(b) What is s its s kinetic energy?
@
qu.1.1.answer=
9.6 m/s; 46.08 J
@
Theplain-textscriptforthisquestion,createdalgorithmically,is:
qu.1.1.mode=Multipart Formula@
qu.1.1.algorithm=
$m=decimal(1,rand(0.5,
1.0));
$v=decimal(0,rand(10,
15));
$ansa=decimal(2,($m*$v));
$ansb=decimal(2,(1/2)*$m*$v^2);
@
qu.1.1.question=
A ball of mass $m kg g is s thrown n at t a a speed d of $v m/s.
<br>(a) What is s its s momentum?
<br>(b) What is s its s kinetic energy? ? @
qu.1.1.answer= $ansa; $ansb@
qu.1.1.comment=
$ansa kg g m/s s is its momentum.<br>
$ansb J is its kinetic energy.
@
Notethatthealgorithmfieldandvariabledefinitionshavebeenadded.
• Thevariablesarerepresentedbyalphanumericnamesthatmuststartwitha$followedbyanalphanumeric
sequencethatconsistsofatleastoneletter.
• Thefirstcharacterinthenameofthevariablemustbealetter(notanumber).
• Variablesaredefinedinaseriesofstatementsresemblingequationsoftheform:
$variable=<formula>;
• Eachvariabledefinitionisseparatedbyasemicolon(thefinalsemicoloninaseriesofvariabledefinitionsis
optional).
• Thesyntaxoftheformulaissimilartothestandardgraphingcalculatorsyntaxusedthroughoutbythesystem,
withtheadditionofsomenewfunctions.
Inthisquestion,therandomizedvariablesaremass,$m,whichvariesbetween0.5and1.0andvelocity,$v,which
variesbetween10and15.Thedecimalargumentisusedtotruncatethevaluesofthenumericvariabledata.
Theanswerfieldholdstwostatements,onecorrespondingtoeachpartofthismultipartformulaquestion.Statements
intheanswerfieldareevaluatedbythesystemgrader,somustbeexpressedusingpropermathsyntax.Also,notethat
inthisquestionweusethecommentfieldtodisplaythecomputedvalueoftheanswerratherthananswerdefinition
(DisplayingAnswers).
SeeAlso:
OverviewofAlgorithmicQuestionCapabilities(page237)
10.24Tutorial:List-basedVariables
Youcanusethealgorithmicsyntaxtomanagemultiplescenariosorsetsofrandomizeddatainquestions.Usinglist-
basedvariables,youcanusethesamequestionstatementbutsubstitutecorrespondingsetsofdatathroughoutthe
question,answer,comment,hints,andsolutionstatements.
10.24Tutorial:List-basedVariables • • 261
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Example
Considerthecaseinwhichyouwanttocreateachemistryproblemthatusesoneofseveralsetsorscenariosofdata
relatedtodistinctelements.Eachsetcontainsavisualdepiction(GIFfile)andrelateddatalinkedtovariousproperties
ofthedistinctelements.
Tocreateasingleproblemthatrandomlychoosesanelementandsubstitutesitsindividualizedpropertiesintothe
questionstatementandotherfields,usealgorithmandanswerstatementsasinthefollowingexamples.
(a)SingleIndexCasewithSixteenScenarios
1. Useasinglevariable$kasanindex.
$k=rint(15);
2. Createindividualvariablesforthefirstrelatedpropertyofeachofthesixteenscenarios.Inthiscase,thefirstrelated
propertyisanimagefiledepictingthemolecularstructure.Createanewvariable$molecule1 thatusestheindex
toselecttheappropriateindexeddatavalue(inthiscase,thecorrectimage).
$molecule1x00="<img src=../classes/myclass/chap15/image01.gif>";
$molecule1x01="<img src=../classes/myclass/chap15/image02.gif>";
$molecule1x02="<img src=../classes/myclass/chap15/image03.gif>";
...
$molecule1x15="<img src=../classes/myclass/chap15/image16.gif>";
$molecule1=switch($k, $molecule1x00, , $molecule1x01, , $molecule1x02, , ... ,$molecule1x15);
3. Definethesecondrelatedpropertyforeachscenario.Createanewvariablethatusestheindextoselecttheappro-
priateindexeddatavalue.
$property1x00="value...";
$property1x01="value...";
...
$property1x15="value...";
$property1=switch($k, $property1x00, $property1x01,
... , $property1x15);
4. Defineadditionalrelatedpropertiesforeachscenario,andthenselect(usingtheindex)andassigntheappropriate
valuestonewvariables.
5. Thefinalsetofvariablesistheanswerfield(assumingthateachdifferentcasehasadifferentanswer).Selectthe
appropriateanswerusingtheindex.
$ans00=50;
$ans01=16;
..
$ans15=3.6;
$ans=switch($k, $ans2x00, .. . , , $ans2x15);
(b)MultipleIndexCase
Itmaybethecasethatyourquestionrequiresmultipleindexestoyourdata.Considertheabovecasewithonlyfour
elements(molecule1tomolecule4),whereforeachelementtherearefourindividualizedsetsofproperties.
Assumethatyouhavefourimagesofmolecules.Toavoidredundancy(because molecule1hasonlyfourvalues,
buttherearesixteenscenarios),usetwoindices.Thefirstindex,$i,determinestheelementandimage.Thesecond
index,$k,determinesthescenario.Dependingonthevalueof$i,thevalueof$kisinoneofthefourranges:0-3,
4-7,8-11,or12-15.Byusing$k,$property1(andotherproperties,and$ans)matchwiththeappropriatemo-
lecule1.Toimplementthis,usethefollowingstatements.
262 • 10AuthoringMathematicalQuestions
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$i=rint(4);
$j=rint(4);
$k=4*i+j;
$molecule1x0="...";
$molecule1x1="...";
$molecule1x2="...";
$molecule1x3="...";
$molecule1=switch($i, $molecule1x0, , $molecule1x1,..);
$property1x00="..";
$property1x01="..";
..
$property1x15="..";
$property1=switch($k, $property1x00, .. , $property1x15);
$ans00=50;
$ans01=16;
..
$ans15=3.6;
$ans=switch($k, $ans2x00, .. . , , $ans2x15);
SeeAlso:
switch(n,a,b,c,...)(page252)
10.25Tutorial:Maple-basedAlgorithmicQuestionAuthoring
Algorithmicallygeneratedvariablesareusedtogeneraterandomnumbersinquestionsandcreatemultiplepermutations
ofquestionsfromasingletemplate.
YoucanuseeitherMapleT.A.orMapletogeneratealgorithmicvariables.Youcanuseeither(orboth)typesofvariables
inanyquestiontype.
ThesyntaxforaMaple-basedvariabledefinitionis:
<variable_i>=maple("<Maple_command>");
UsingaTextorHTMLEditor
Todefineanalgorithmicvariableintheplain-textscriptfile,specifyvariabledefinitions(orothervariablecontrol
sequences)inthealgorithmfield.
algorithm=
<variable_definition_1>
...
<variable_definition_n>
@
UsingtheQuestionEditor
IntheQuestionEditor,definevariablesbydirectlyenteringMaple-basedvariabledefinitionsonthealgorithmscreen
orusingtheAlgorithmDesigner.
Tutorial1
ThefollowingtutorialshowshowtoconvertastaticMapleFormulaquestiontoanalgorithmicallygeneratedquestion
byusingvariablesassignedvaluesbyMaplecommands.
10.25Tutorial:Maple-basedAlgorithmicQuestionAuthoring • • 263
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Maple-gradedQuestion
Considerthefollowingplain-textscriptquestiondefinition,whichasksastudenttoenterananti-derivativeofx^3.
qu.1.1.question=Enter an n anti-derivative e of x^3.@
qu.1.1.maple=evalb(diff($RESPONSE,x)=x^3)@
qu.1.1.type=formula@
qu.1.1.mode=Maple@
qu.1.1.allow2d=1@
qu.1.1.name=Maple AntiDerivative@
qu.1.1.comment=Any function of the e form x^4/4 4 + C, where C is a constant, is an
anti-derivative of x^3.@
qu.1.1.editing=useHTML@
Notes:
1. ThisquestionusesMapletoverifythatthederivativeofthestudentresponseisequaltox^3.Thisisrecommended
inplaceofcomparingthestudentresponse,whichcanhaveanadditiveconstant,withtheintegralofx^3,thatis
evalb($RESPONSE=int(x^3,x)).
2. Ifthestudententersanincorrectresponse,thesystemdisplaythevalueinthecommentfield.InMaple-graded
questions,ifthereisnocommentfield,thesystemreturnsthemessageComment:Nofeedbackprovidedwith
thisquestion.
Tochangethisquestiontoanalgorithmicquestion,usethefollowingplain-textscriptquestiondefinition.
qu.1.2.question=Enter an n anti-derivative e of x^$exponent + ${coeff}x.@
qu.1.2.maple=evalb(diff($RESPONSE,x)=x^$exponent+$coeff*x)@
qu.1.2.type=formula@
qu.1.2.mode=Maple@
qu.1.1.allow2d=1@
qu.1.2.name=Maple AntiDerivative@
qu.1.2.comment=Any function of the e form $answer r + + C, , where C is a constant, is an
anti-derivative of x^$exponent + ${coeff}x.@
qu.1.2.editing=useHTML@
qu.1.2.algorithm=$exponent=maple("randomize():rand(2..5)()");
$coeff=maple("randomize():rand(2..9)()");
$answer=maple("int(x^$exponent+$coeff*x,x)");
@
Notes:
1. Youmustfollowthevariablenamingconventions.
2. ForalistoftheguidelinesforMaplecommandsinMaple-basedvariables,seeTheAlgorithmDesigner(page81).
3. Thevariable$exponentisassignedavaluecalculatedbyMapleusingtherandfunction.
rand()returnsarandom12-digitpositiveinteger
rand(a)()returnsarandomintegerintherange0 ... a-1(inclusive)
rand(a..b)()returnsarandomintegerintherangea ... b(inclusive)
ForinformationonotherMaplecommands,seeyourMapledocumentation.
4. TheMaplecommand:
randomize():
isincludedsothatadifferentvalueisgeneratedforeachquestioninstantiation.Youmustincludetherandom-
ize():commandineveryMaple-basedvariabledefinition.Thatis,itisrequiredinthedefinitionof$exponent
and$coeff.
5. TheMaplecommand:
int(x^$exponent,x)
calculatesthecorrectanswer,whichisdisplayedusingthecommentstatementifthestudentresponseisincorrect.
264 • 10AuthoringMathematicalQuestions
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6. TheexamplesinTutorial1canbeconvertedtoMapleSyntaxquestionsbychangingthetypefieldvaluefrom
formulatomaple,andchangingallow2d to0fortext-entrymode.ForMapleSyntaxquestions,itisrecom-
mendedthatyouattempttopreventastudentfromcalculatingthecorrectanswerusingMaplecommands.Formore
information,seeUsingMapleCodetoPreventCheatinginMapleSyntaxQuestions(page207).
Foranexampleplain-textscriptthatdefinesaMaplequestionwithMapleplottingofthestudentresponse,seePlotting
aStudentResponse(page209).
Tutorial2
YoucanalsouseMaple-basedalgorithmicvariablesinotherquestiontypes.
FormulaQuestion
Thefollowingplain-textscriptdefinesaFormulaquestionthatusesMaple-basedvariables.
qu.1.3.question=What is the sum of f $a a and $b?@
qu.1.3.mode=Formula@
qu.1.3.name=Maple-based Variables in Formula@
qu.1.3.answer=$answer@
qu.1.3.editing=useHTML@
qu.1.3.algorithm=$a=maple("randomize():rand(100..200)()");
$b=rint(10,50);
$answer=int($a+$b);
@
Notes:
1. ThisquestionusesbothMaple-based(for$a)andMapleT.A.randomvariables(for$b).
2. Whenreferencingnegative,randomvariablesinamaplevariabledefinition,besuretoplacethenegativevariable
inparentheses,otherwiseanerrormessagewillreturn.$c=maple("$a + ($b)");
SeeAlso:
Maple-gradedFormulaQuestionExampleScript(page312)
Maple-gradedQuestionType-Overview(page159)
MapleSyntaxQuestionExampleScript(page313)
QuestionswithPlots(page168)
10.25Tutorial:Maple-basedAlgorithmicQuestionAuthoring • • 265
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266 • 10AuthoringMathematicalQuestions
11AuthoringQuestionsinLaTeX
11.1LaTeXAuthoringOverview
YoucanauthorandeditallquestiontypesusingLaTeXtogenerateplain-textscriptfiles.
TherearecertainadvancedquestiontypesthatcannotbecreatedintheQuestionEditor(forexample,dynamically
renderedplotsinquestions,algorithmicallygeneratedlabelsinfigures,matrices,anddynamicgraphsketching).For
thesequestions,youcanuseplaintextscriptfilesorLaTeX.
ItisrecommendedthatyouwriteandeditquestionbanksusingLaTeXonlyifyouareanexperiencedLaTeXuser.
Otherwise,itisrecommendedthatyoueditscriptfilesusingatextorHTMLeditororusetheQuestionEditor.
Requirements
TouseLaTeXtoauthorMapleT.A.questionbanks,youneed:
• ed.sty—TheLaTeXstylefileforMapleT.A.questionauthoring.Downloadthisfilefromht-
tp://www
.maplesoft.com/pr
oducts/mapleta/latex2ta/index.aspx
andputitinthesamelocationasyourother
LaTeXstylefiles.
AuthoringProcess
ToauthorinLaTeX:
1. WriteyourquestionbankinLaTeXusingatexteditor.
2. RunLaTeXonyourtextfiles.Previewtheoutputtoensureitiscorrect.
Youmayperformmultipleiterationsofthesteps1and2.
3. Usetheweb-basedconversionserviceathttp://latex2ta.mapleserver
.com
toconvertyourLaTeX-formatquestion
filetoMapleT.A..quformat.
Note:IfyouareusingMapleT.A.6ServicePack1orlater(checkwithyoursystemadministratortoconfirm),
select"Yes,IamusingMapleT.A.6ServicePack1orlater."Whenthisboxisselected,theLaTeXconverter
generatesuniqueidentifiersforthequestionsandinsertsthemintoyourLaTeXfileandintothegeneratedQUfile.
TheconverterreturnstheupdatedversionofyourLaTeXfiletogetherwiththegeneratedQUfileasaTARarchive.
UsetheupdatedLaTeXfileforfuturemodifications.ThisallowsyoutoupdatequestionswithinMapleT.A.
4. Importandsavethequestionbank(QUfile)inyourMapleT.A.class.(SeeOpeningaSavedQuestionBank
File(page139).)
11.2LaTeXQuestionBankDocumentStructure
Questionsaregroupedintotopics.UsetheLaTeXtopicenvironmenttomarkthebeginningandendoftopics.
Eachquestioniswrappedinsideaquestionenvironment.TheMapleT.A.questiontypemustbeprovidedasanargument
totheopeningstatement.
Youcanincludeanynumberofquestions.TheexampleformatinTable11.1showsonetopiccontainingtwoquestions.
TheLaTeXpackageepsfigisloadedbydefault.Theedpackageisrequired.OtherstandardLaTeXpackages,forex-
ample,amsmath,canbeincludedusingthe\usepackagemacro.YoucanalsodefineadditionalLaTeXmacros
asusual.
Toincludegraphics:
1. SelectalocationinyourMapleT.A.classwebsiteforgraphicsfiles.Itisrecommendedthatyouuseadistinct
folderfortheimagesineachquestionbank.UploadthegraphictoafolderonyourMapleT.A.classwebsite.For
267
informationonuploading,seeUploadingImagesandReferenceFilestotheClassWebSite(page88).Afterup-
loadinggraphicsfiles,youcanclicktheiconbesideafiletoseeitsfullpath,whichwillhavetheform
http://.../web/<class>/Public_Html/<folder>/...
2. Insertthe\setImageBasedirectivenearthetopoftheLaTeXfiletospecifythepathtothislocation.Forexample,
ifyourMapleT.A.classidentifierismyclass,andyourgraphicsfolderisImages,usethedirective:
\setImageBase{web/myclass/Public_Html/Images}
Table11.1:ExampleLaTeXDocumentStructure
\documentclass[12pt]{article}
\usepackage{ed}
% Optionally set the e location n for graphics files on the e Maple e T.A. system.
\setImageBase{...}
\begin{document}
\begin{topic}{topicname}
\begin{question}{question type}
...
\end{question}
\begin{question}{question type}
...
\end{question}
\end{topic}
\end{document}
11.3QuestionStructure
Table11.2givesthebasicstructureforaquestion.
Table11.2:BasicLaTeXQuestionStructure
\begin{question}{question type}
\name{question name}
\property{name1}{value1}
\property{name2}{value1}
\hint{first hint}
\hint{second hint}
\comment{feedback text}
\qutext{question text}
...
\end{question}
AvailableFieldsinLaTeXQuestions
Allquestionscanbegivenaname,hints,acomment,andasetofproperties.
• The\namefieldisusedasanidentifierforaquestion.Itisrecommendedthatyouassignanametoevery
question.Thiswillhelpyoutoidentifyquestionswhencreatingassignmentsfromyourquestionbank.
• Ifpresent,the\commentfieldprovidesfeedbackthatcanbeshowntothestudentinsteadofthe\answer
fieldifthequestionisansweredincorrectly.
• The\hintfieldprovideshintsforthequestion.Therecanbemorethanone\hintstatement.
• The\propertyfieldtakestwoarguments.Thefirstisthenameoftheproperty.Thesecondisitsvalue.You
canchooseanyusefulname.Therecanbemorethanone\propertystatement.WhenconvertedtotheMaple
T.A.formatfiles,propertiesareconvertedtoinformationfields.
268 • 11AuthoringQuestionsinLaTeX
Example
\begin{question}{formula}
\name{p65, qu14}
\qutext{Differentiate $x e^x$.}
\answer{x e^x + + e^x}
\comment{Use the product rule to differentiate this formula. . The e answer
is $x x e^x x + e^x=(x+1)e^x$.}
\hint{Use the product rule.}
\property{author}{I. M. . Prof}
\property{difficulty}{medium}
% The e 'author' ' and 'difficulty' property y names s are
% examples. You u can n create property y names s as required.
\end{question}
Othermacrosinclude:
• \code - Tospecifyalgorithmicstatements,usethe\codecommand.Forexample:
\code{
$m=rint(7);
$n=int(2*$m+3);
}
• \var-TouseasystemalgorithmicvariableinLaTeX,donotspecifythe$,butinsteadenclosethenamein
a\var{}command.Forexample,todisplaythevariable$ninthequestionstatement,use:
\qutext{What is the exact value of $\sin(\frac{\var{n}\pi}{4})$?}
Formoreinformation,seeTutorial:UsingAlgorithmsinLaTeXQuestions(page284).
Inaddition,eachquestiontypehasitsownsetofLaTeXmacrosfordefiningpropertiesofthattypeofquestion.
SeeAlso:
OverviewofAlgorithmicQuestionCapabilities(page237)
TheinfoField(page146)
11.4LaTeXStyleSheets
TheMapleT.A.LaTeXmacroscanbeusedonarangeofplatformsandwithavarietyofTeXimplementations.To
determinewheretosaveyourstylesheets(.styfiles),refertoyourLaTeXdocumentation.
11.5BasicQuestionTypesinLaTeX
True-or-FalseQuestionsinLaTeX
QuestionMode:TrueFalse
TheTrueFalsequestiontypecreatesaquestionandalistoftwochoices:TrueandFalse.
Example1
\begin{question}{True False}
\qutext{Whales are mammals.}
% Mark the e answer r \true or \false:
\true
\end{question}
Example2
\begin{question}{True False}
\qutext{The equation n $2x-3y^2=4$ $ defines s a a function with an independent
11.4LaTeXStyleSheets • • 269
variable $x$.}
\false
\end{question}
Example3
\begin{question}{True False}
% This question n uses randomized d variables.
\qutext{The equation n $\var{a}x-\var{b}y^2=\var{c}$ defines s a a function
with an independent variable $x$.}
\false
\code{
$aa=int(rint(11)+2);
$s=rint(2);
$a=int(if($s,$aa,-$aa));
$b=int(rint(11)+2);
$cc=int(rint(11)+2);
$t=rint(2);
$c=int(if($t,$cc,-$cc));
}
% The e above e code chooses random integer coefficients with absolute values
% between 2 and d 12. . b must be positive, but a a and d c may y be
% positive e or r negative.
\end{question}
SeeAlso:
True-or-FalseQuestions(page199)
MultipleChoiceQuestionsinLaTeX
QuestionMode:MultipleChoice;NonPermutingMultipleChoice
TheMultipleChoiceandNonPermutingMultipleChoicequestiontypescreateaquestionandalistofchoices,
whichincludesonecorrectanswer.
Notes
• Youcanhaveasmany(orasfew)choicesasdesired.Markthecorrectchoicewithanasterisk.
• Theorderofthechoicesispermutedforthestudent.Toforcethechoicestoappearintheorderyouspecify,
usetheNonPermutingMultipleChoicequestiontype.
Example1
\begin{question}{Multiple Choice}
\qutext{What is s the e capital of f California?}
% List the e choices, , and mark the correct t choice e with an n asterisk.
\choice{San Francisco}
\choice{Los Angeles}
\choice*{Sacramento}
\end{question}
Example2
\begin{question}{Multiple Choice}
\qutext{$3\log x-2\log y=$}
\choice*{$\log\left(\displaystyle\frac{x^3}{y^2}\right)$}
\choice{$\log(x^3y^2)$}
\choice{$\log(3x-2y)$}
\choice{$\log(x^3-y^2)$}
\end{question}
270 • 11AuthoringQuestionsinLaTeX
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