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Table11.6:BasicSketchCriteria
sketchedfunctionmustpassthroughthepoint(xcoord,
ycoord)
goes_through(xcoord, ycoord)
sketchedfunctionmustbeincreasing
increasing
sketchedfunctionmustbedecreasing
decreasing
sketchedfunctionmustbeconcaveup
concave_up
sketchedfunctionmustbeconcavedown
concave_down
sketchedfunctionmustbelinear
linear
Torestrictacriteriontoaninterval[a,b],use\check[a,b]{criterion}.Thisoptionisignoredfor
goes_through.
Thecriterioncanalsobeabooleanexpression;usefulstatementsinthiscaseare:
returntheslopeofthecurveatthex-valuexval.
slope_at(xval)
returnthey-valueforthex-valuexval.
value(xval)
returntrueifexpr1isequaltoexpr2.Otherwise,it
returnsfalse.
expr1 == = expr2
returntrueifexpr1islessthanexpr2.Otherwise,it
returnsfalse.
expr1 < < expr2
returntrueifexpr1isgreaterthanexpr2.Otherwise,
itreturnsfalse.
expr1 > > expr2
booleanconstant
true
booleanconstant
false
Forexample,value(xcoord) == ycoordisequivalenttogoes_through(xcoord, ycoord).
Morethanone\checkstatementcanappear,inwhichcaseeverycriterionmustbesatisﬁed.
Syntax
\begin{sketch}[gridlines option]{xMin}{xMax}{yMin}{yMax}
\example{<point-list>}
\check{criterion1}
\check{criterion2}
\check{criterion3}
\end{sketch}
Example1
\begin{question}{sketch}
\qutext{Sketch the graph of the function n $y=x+1$.}
\begin{sketch}[4]{-2}{2}{-2}{2}
\example{-2,-1
1,2}
\check{linear}
\check{goes_through(0,1)}
\end{sketch}
\end{question}
Example2
Thisexampleusesrandomizedvariables.
\begin{question}{sketch}
\code{$a = = int(rand(2,6));$a2
= int($a*$a);
$xmax = int(2*$a);
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$x = sqrt(2)*$a;}
\qutext{Sketch the graph of the function n $y=x^2/\var{a2}$.}
\begin{sketch}[4]{-\var{xmax}}{\var{xmax}}{-4}{4}
\example{-\var{x},2
-\var{a},1
0,0
\var{a},1
\var{x},2}
\check{goes_through(0,0)}
\check{goes_through(-\var{a},1)}
\check{goes_through(\var{a},1)}
\check{slope_at(0)
== 0}
\check[-\var{x},0]{decreasing}
\check[0,\var{x}]{increasing}
\check{concave_up}
\end{sketch}
\end{question}
IncludingGraphicReferencesinLaTeXQuestions
IncludingGraphicsUsing\image
YoucaninsertanimageinaLaTeXquestion.The\imagemacroistherecommendedmethodforincludinggraphics
inaquestion.IftheﬁleisavailablelocallyasanEncapsulatedPostscript(epsorepsf)ﬁle,itisincluded(\image
calls\epsfigtoincludethegraphic).
Important:Donotexplicitlycall\epsfig.Using\epsfigdirectlydoesnotensurethatproperMapleT.A.code
results.
Toincludegraphics:
http://.../web/<class>/Public_Html/<folder>/...
where<class>isMapleT.A.'sinternalidentiﬁerforyourclass,and<folder>isthefolderthatcontainstheimages.
2. Insertthe\setImageBasedirectivenearthetopoftheLaTeXﬁletospecifythepathyoudeterminedinstep1.
Forexample,ifyourMapleT.A.classidentiﬁerismyclass,andyourgraphicsfolderisImages,usethedirective:
\setImageBase{web/myclass/Public_Html/Images}
3. Includegraphicsinaquestionusingthe \imagemacro.Theformatforthe\imagemacrois:
\image[extension]{filename}
Theextensionargumentisoptional.Itspeciﬁestheextensiontobeappendedtotheﬁlename(thesecondargument)
whenthequestionbankisconvertedtoMapleT.A.format.Thedefaultvalueisjpg.
Ifthefilenameargumentisaﬁlenamewithanextension,theﬁrstargumentisignored.Ifthefilenameargument
isaﬁlenamewithoutanextension,the.epsextensionisusedinpreviewmode,andextension(orthedefault
.jpg)isusedinproductionprocessing.
Sample1
\image{graphic}
Placestheﬁlegraphic.epsfromthecurrentdirectoryinthedvioutputinpreviewmode.Inproduction
processing,itproducesanimagetagpointingtographic.jpginthedirectoryspeciﬁedby\setImage-
Base.
282 • 11AuthoringQuestionsinLaTeX
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Sample2
\image[gif]{graphic}
Placestheﬁlegraphic.epsfromthecurrentdirectoryinthedvioutputinpreviewmode.Inproduction
processing,itproducesanimagetagpointingtographic.gifinthe \setImageBasedirectory.
Sample3
\image{graphic.pct}
Doesnotplacetheﬁlegraphic.pctinthedvioutput.Inproductionprocessing,itproducesanimage
tagpointingtographic.pctinthe\setImageBasedirectory.
Notes
• Whilethe\epsfigmacroallowsvariousoptions,forexample,width,\imagedoesnotsupportanyoptions.
EncapsulatedPostscriptﬁlesappearatfullsizeinthedviﬁle.
• Theconversiontoolsdonotprovidegraphicconversionservices.Youmustusethird-partytoolstoproduce
webimageﬁles.
Example
YouwillalsoneedtosettheimagebaseforyourLaTeXﬁleasdescribedabove.
\begin{question}{Numeric}
\qutext{Quadrilateral $ABCD$ $is circumscribed d about a circle, as shown, with h$AB$=\var{a} } cm, and$CD$=\var{b} cm. . Find the e perimeter of the quadrilateral. \image{quad.gif}} \code{$a=range(5,25);
$b=range($a+1,$a+5);$ans=2*(($a)+($b));}
\answer{$ans}[cm] \end{question} LabelingGraphicsinLaTeXQuestions LabeledGraphics-labelgraphicEnvironment Thelabelgraphicenvironmentallowsyoutoaddtextlabelstographics(gifandjpgﬁles). ToaddtextlabelstographicsinyourLaTeXquestion: 1. SelectalocationinyourMapleT.A.classwebsiteforgraphicsﬁles.Itisrecommendedthatyouuseadistinct folderfortheimagesineachquestionbank.UploadthegraphictoafolderonyourMapleT.A.classwebsite.For informationonuploading,seeUploadingImagesandReferenceFilestotheClassWebSite(page88).Afterup- loadinggraphicsﬁles,youcanclicktheiconbesideaﬁletoseeitsfullpath,whichwillhavetheform http://.../web/<class>/Public_Html/<folder>/... where<class>isMapleT.A.'sinternalidentiﬁerforyourclass,and<folder>isthefolderthatcontainstheimages. 2. Insertthe\setImageBasedirectivenearthetopoftheLaTeXﬁletospecifythepathyoudeterminedinstep1. Forexample,ifyourMapleT.A.classidentiﬁerismyclass,andyourgraphicsfolderisImages,usethedirective: 11.6AdvancedQuestionTypesinLaTeX • • 283 C# PDF Convert: How to Convert Tiff Image to PDF File Tiff to PDF. |. Home ›› XDoc.Converter ›› C# Converter: Tiff to PDF. .net convert pdf to tiff; convert pdf file to tiff online XDoc.Converter for .NET, Support Documents and Images Conversion converter SDK supports various commonly used document and image file formats, including Microsoft Office (2003 and 2007) Word, Excel, PowerPoint, PDF, Tiff, how to convert pdf to tiff format; compare pdf to tiff \setImageBase{web/myclass/Public_Html/Images} 3. Toincorporatetheimageﬁleintoaquestion,usethelabelgraphicenvironment.The\begin{labelgraph- ic}commandtakesthreearguments: i. Thenameoftheimageﬁle. ii. Thewidthoftheimageﬁleinpixels. iii.Theheightoftheimageﬁleinpixels. Todeterminethewidthandheightofthegraphic,useathird-partygraphicsapplication(forexample,Microsoft Paint). • Tolabelthegraphic,usethe\grlabelmacro.The\grlabelmacrotakesthreearguments: i. Thetextofthelabel. ii. Thex-coordinateofthelabel,inpixels. iii.They-coordinateofthelabel,inpixels. • Thex-andy-coordinatesaremeasuredfromtheupperleftcornerofthegraphic. • Morethanone\grlabelcommandcanbeused. Note:Withoutany\grlabelcommands,thelabelgraphicenvironmentonlyincorporatestheimageﬁleintoaquestion. Toincludeagraphic,itisrecommendedthatyouusethe\imagemacro.Formoreinformationontheimagemacro,seeIncluding GraphicReferencesinLaTeXQuestions(page282). Example Note:Forthisexampletoworkasis,youmustﬁrstuploada309x256pixelGIFimageLabeledGraphic.gif toyourMapleT.A.classwebsite.YouwillalsoneedtosettheimagebaseforyourLaTeXﬁleasdescribedabove. \begin{question}{Multi Formula} \qutext{Suppose that you u throw w a a rock from the top p of f a a \var{h} } m m cliff with a velocity y of f \var{v} m/s s in n the three directions shown. Neglecting aerodynamic drag, use the e principle of f work and energy to determine the velocity of the e rock as s it hits the e ground d in n the e upward, horizontal, and downward angles, , respectively. \begin{labelgraphic}{LabeledGraphic.gif}{309}{256} \grlabel{$h m}{80}{174}
\grlabel{$angle}{200}{134} \grlabel{$angle}{200}{97}
\end{labelgraphic}}
\code{$angle=rand(10,50,2);$h=rand(7,14,2);
$v=rand(8,17,2);$ansa=sig(3, sqrt(2*9.8*$h +$v^2));
$ansb=$ansa;
$ansc=$ansa;
$tol=lsu(2,$ansa);}
\answer{($ansa ?$tol)*m/s;($ansb ? ?$tol)*m/s;($ansc c ?$tol)*m/s}
\end{question}
11.7Tutorial:UsingAlgorithmsinLaTeXQuestions
AlgorithmicQuestions
Randomizedvariablescanbeincorporatedintoanyquestion.Rulesandrecommendationsforeffectiveuseofrandomized
variablesaregivenbelow,illustratedbyrelatedexamples.
284 • 11AuthoringQuestionsinLaTeX
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• Thecodethatcreatesandmanipulatestherandomizedvariablesiscontainedinthe\code{}sectionofthe
question.Eachvariableinthecodesectionisdesignatedwitha$symbol,suchas$m,$ans,and$b2.The
ﬁrstcharacterafterthe$symbolmustbealetter.Eachcodestatementisoftheform$variable=expression;
Separatemultiplevariabledeﬁnitionswithasemicolon.
quence.
Theusualarithmeticoperationsandfunctionscanbeusedintheexpressionportionofthecodestatement.
However,unlikemostotherprogramminglanguages,variablescannotberedeﬁnedintermsofthemselves(for
example,thestatement$a=$a+1;isnotallowed).Foradescriptionoftheadditionalfunctionsthatcanbe
usedinthecodesections,seeFunctionswithinAlgorithms(page239).
• Tousethevariablesinothersectionsofthequestion,enclosetheminthe\varmacro.Forexample,torefer
tothevariable$a,use: \var{a} Inthefollowingexamples,aFormulaquestionisdesignedthroughaseriesofreﬁnements. Example1 \begin{question}{Formula} \qutext{Find the solution n of f the linear equation$\var{a}x+\var{b}=\var{c}$.} \answer{(\var{c}-\var{b})/\var{a}} \code{$a=rint(12)+1;
$b=rint(12)+1;$c=rint(12)+1;
}
\end{question}
Theabovecoderandomlydeterminesintegercoefﬁcients$a,$b,and$cbetween1and12.Theansweris calculatedinthe\answersection. Althoughtheaboveexampledoesnotcauseerrors,thereareseveralsideeffects: • Theanswerisdisplayedintheform(7-3)/5(forexample).Thisprovidesanindicationofthemethodfor obtainingtheanswer,whichmaybeinappropriate. • Theaboveformatcanreturnanswersoftheform(7-7)/5,whichismorecomplicatedthanthesimpliﬁed form,0. Toavoidtheseissues,rewritethisexampleasfollows,usinganewvariable$ans(sothatyoureturnonly
Example2
ReﬁnementofExample1.
\begin{question}{Formula}
\qutext{Find the solution n of f the linear equation
$\var{a}x+\var{b}=\var{c}$.}
\code{
$a=rint(12)+1;$b=rint(12)+1;
11.7Tutorial:UsingAlgorithmsinLaTeXQuestions • • 285
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$c=rint(12)+1;$ans=($c-$b)/$a; } \end{question} Thereisanotherproblem.Thevariable$acanequal1,inwhichcasetheequationhastheform1x+5=8.To
avoidthissituation,imposetheconditionthat$abeanintegerbetween2and12. Although$ccanbe0ornegative,if$bis0ornegativetheequationisagainunsimpliﬁed.Generalizethe codetoallow$ctobeanyintegerbetween-12and12.
Example3
\begin{question}{Formula}
\qutext{Find the solution n of f the linear equation
$\var{a}x+\var{b}=\var{c}$.}
\code{
$a=rint(11)+2;$b=rint(12)+1;
$c=rint(25)-12;$ans=($c-$b)/$a; } \end{question} Thereisanotherproblem.Theanswer$ansisa(potentiallyinexact)ﬂoating-pointnumber,forexample,
aﬂoating-pointevaluation.
Example4
\begin{question}{Formula}
\qutext{Find the solution n of f the linear equation
$\var{a}x+\var{b}=\var{c}$.}
\code{
$a=rint(11)+2;$b=rint(12)+1;
$c=rint(25)-12;$num=$c-$b;
$ans="$num/$a"; } \end{question} Note:Writing$ans="($c-$b)/$a";displaysanswersoftheform(11-6)/3.First,calculatethenumeratorand storeitasanintegerin$num,andthencreatethefractionwiththestring"$num/$a".
Example5
Finalreﬁnementofthequestion.
\begin{question}{Formula}
\qutext{Find the solution n of f the linear equation
$\var{a}x+\var{b}=\var{c}$.}
\code{
$a=rint(11)+2;$b=rint(12)+1;
$c=rint(25)-12;$num=$c-$b;
286 • 11AuthoringQuestionsinLaTeX
$ans=frac($num,$a); } \end{question} Thestringreturnedbythefraccommandisareducedfraction. Example6-QuestionwithaPlot \begin{question}{Formula} \qutext{Enter the expression plotted below. Give only the expression itself, omitting any "y=" or "f(x)=" from your answer. \newline \var{plot}.} \answer{x^2+\var{a}x+\var{b}} \code{$a=rint(2, 9);
$b=rint(1, 9);$plot=plotmaple("plot(x^2+$a*x+$b, x=-10..10)");
}
\end{question}
maplecommand.Formoreinformation,seeplotmaple(text)(page247).
Usethefollowingguidelinesforalgorithms:
• Deﬁnerandomizedvariablessothatyouavoidexpressionslike1x,0x,x+-3,or-3/-4.Ifthesevaluesare
required,writethequestionsothattheydisplayproperly.
mayneedtousestrings,asshowninexamples4and5.
11.8MathQuestionAuthoringusingLaTeX
TheLaTeXauthoringmethodisidealforcreatingsophisticatedmathquestioncontent.Thismethodsupportsthefol-
lowingmathquestiontypes.
DimensionedFormula(MapleFormula(page299))
Numeric(NumericQuestionsinLaTeX(page288))
MultiFormula(MultiFormulaQuestionsin
LaTeX(page296))
Formula(FormulaQuestionsinLaTeX(page291))
Equation(EquationQuestionsinLaTeX(page297))
FormulamodC(ConstantsofIntegrationQuestionsin
LaTeX(page292))
Matrix(MatrixQuestionsinLaTeX(page297))
RestrictedFormula(RestrictedFormulaQuestionsin
LaTeX(page293))
LaTeX(page298))
FormulaList(FormulaListQuestionsin
LaTeX(page294))
InlineMathResponseAreas(MathematicalInline
Questions(page300))
Ntuple(CoordinatesofPointsandVectorsQuestionsin
LaTeX(page294))
OtherMathQuestionFeatures
• Graphplottingapplet-\graphand\multigraphmacros(GraphPlottinginLaTeXQuestions(page279))
• Includinggraphics-\imagemacro(IncludingGraphicReferencesinLaTeXQuestions(page282))
• Labeledgraphics-labelgraphicenvironment(LabelingGraphicsinLaTeXQuestions(page283))
11.8MathQuestionAuthoringusingLaTeX • • 287
SeeAlso:
Overview:AuthoringMethodsforQuestionBanks(page75)
MathQuestionTypesComparisonTable(page153)
NumericQuestionsinLaTeX
QuestionMode:Numeric
TheNumericquestiontypeacceptseitheranumberindecimalorscientiﬁcnotation,oranumberwithunitsforan
Becauseitisnaturaltospecifytheunitsafterthenumber,youcanusetheformat:
Notes:
]".
systempresentsthestudentwithasingletextﬁeldinwhichtoenteraresponse(withoutunits).Ifyouspecify
twotextﬁelds.Astudentmustenterthenumericalpartoftheresponseintheﬁrstﬁeldandtheunitsinthe
secondﬁeld
• Youmustuserecognizedunits.
• Todeﬁneacustomlistofunitsinaquestionbank,usethe\TableOfUnitscommandafterbeginninga
topicintheLaTeXdocument(thatis,after\begin{topic}andbefore\begin{question}{...}).
The\TableOfUnitscommandtakestworequiredarguments,inthefollowingorder:
tablename-tablename,consistingoflower-caseletters(a-z)withnospaces.Usethetablenametoreference
thetableinthedocument.
units_list-thelistofacceptableunits.UnitsaredeﬁnedwithstatementsdeﬁningtheunitsintermsofSI
unitsorpreviouslydeﬁnedunits.Eachstatementmustendwithasemicolon.Forexample:
cm = 0.01m;
mm = 0.1cm;
ThebaseSIunitsare:
m(meter)
kg(kilogram)
s(second)
A(amp)
K(kelvin)
288 • 11AuthoringQuestionsinLaTeX
cd(Candela)
• Touseacustomlistofunitsinaquestion,usethe\units{tablename}commandinthebodyofthe
question,wheretablenameisthetablename(theﬁrstargumentto\TableOfUnits).
Important:Becausethesystemconvertsbetweensystemsofunitsusinginexactconversionfactors,itisrecommendedthatyou
acceptresponsesinamarginoferrorinquestionswithunits.
instructionsandexamples.
Ifyoudonotspecifyanyothercommands,thisbehaviorisused.
ﬁeldandcontainthespeciﬁednumberofsigniﬁcantdigits.Specifythenumberofsigniﬁcantdigitsusingthe
\digits{n}command,wherenisthenumberofsigniﬁcantdigits.Forexample,using\digits{3}with
tolerance.Specifytheabsolutetoleranceusingthe\err{error}command,whereerroristheabsolutetolerance.
withinaspeciﬁedtoleranceinthenthsigniﬁcantdigit.Specifythetoleranceusingthe\err{k}and\digits{n}
commands,wherekisthetoleranceinthenthsigniﬁcantdigit.Forexample,using\err{2}and\digits{3}
percenterror.Specifythepercenttoleranceusingthe\perc{error}command,whereerroristhepercent.
• Considerthefollowingrecommendationswhenusingthisquestiontype.
1. Ingeneral,allowsometoleranceinastudentresponse.
3. Iftheuseofunitsisnotanimportantpartofthequestion(thatis,youarenottestingthestudent'sabilitytoconvert
intermsofaunityouspecify.
Example1
\begin{question}{numeric}
\qutext{Compute the e exact t value e of the function $f(x)=3x^4-2x^2-1$
at
$x=2.1$.}
\qutext{Compute the e value e of f $\log_{10}(45)$. . Round d your answer to 5