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\newline\newline
Use 3960 miles for the radius of the earth.\newline
Express your answer to an n accuracy y of at t least t 4 decimal places.\newline
Do NOT include any units in your answer.}
\answer{\var{answer}}
\err{0.0001}
\end{question}
FormulaQuestionsinLaTeX
QuestionMode:Formula
TheFormulaquestiontypeisthemostgeneralmathquestiontype.Answerscanbeanykindofformula,enteredin
calculatorsyntax,orusingthesystemSymbolicEditorentrymode.Answerscanincludevariablesandstandard
functions.
Notes
• The\answerfieldisacalculatedfield.Itmustbeincalculatorsyntax,notinTeX.Entertheanswerasyou
expectthestudenttoenterit(althoughequivalentanswersaregradedcorrect).
• Iftheanswerisanumber(thatis,doesnothaveanyvariables),itisrecommendedthatyouspecifyinthe
questiontextwhetheranexactresponseoranapproximationisrequired.Inthecaseofanapproximation,the
marginoferrormustbespecifiedinyourcorrectanswer.Thiscanbedoneby:
• Specifyingamarginoferrorusingthe?operator
Forexample,iftheanswerfieldwere
{2.34 ? ? 0.01}
anyresponsebetween2.33and2.35(inclusive)wouldbegradedcorrect.Inotherwords,thenumber
followingthe?operatoristhemarginoferror.Formoreinformationontolerances,seeSettingaMarginof
ErrorinNon-numericQuestions(page206).
Example1
\begin{question}{Formula}
\qutext{What is s the e derivative e of f $x^3+3\cos(x)-1$?}
% Use e calculator r syntax for the answer, not TeX.
\answer{3x^2-3*sin(x)}
\end{question}
Example2
\begin{question}{Formula}
\qutext{Compute the e exact t value e of $f'(2)$ if f $f(x)=x^3+3\cos(x)-1$.}
\answer{12-3*sin(2)}
% Any y numerical approximation n is graded incorrect.
\end{question}
Example3
\begin{question}{Formula}
\qutext{Compute $f'(2)$ $ if $f(x)=x^3+3\cos(x)-1$. Round d your answer r to o 5 5 significant digits.}
\answer{9.2721}
% In this case, , a a more (or less) accurate response e is s graded d incorrect.
\end{question}
Example4
\begin{question}{Formula}
\qutext{Compute $f'(2)$ $ if $f(x)=x^3+3\cos(x)-1$. Your answer should be
correct to o an n accuracy of f at t least 5 decimal places.}
11.8MathQuestionAuthoringusingLaTeX • • 291
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\answer{9.27211 ? ? 0.00001}
% Any y response e between 9.27210 0 and d 09.27212 is graded correct.
% The e response e '12-3*sin(2)' is also acceptable.
\end{question}
Example5
\begin{question}{Formula}
% This question n uses randomized d variables.
\qutext{Find the formula for the inverse e of f the function
$f(x)=\var{a}x+\var{b}$.}
\answer{(x-\var{b})/\var{a}}
\code{
$a=int(rint(9)+2);
$b=int(rint(9)+2);
}
% The e above e code chooses random integer coefficients a and b b between
% 2 and 10.
\end{question}
ConstantsofIntegrationQuestionsinLaTeX
QuestionMode:FormulamodC
TheFormulaModCquestiontypeissimilartotheFormulatype.Answerscanbeanykindofformula,enteredin
calculatorsyntax,butresponsesaregradedascorrectiftheydifferfromthegivenanswerbyaconstantvalue.Answers
canincludevariablesandstandardfunctions.Thisquestiontypeisdesignedforindefiniteintegralquestions.
Note:
• The\answerfieldmustbeincalculatorsyntax,notinTeX.Entertheanswerasyouexpectthestudentto
enterit(althoughequivalentanswersaregradedcorrect).Donotinclude+Cintheanswer.
Example1
\begin{question}{Formula mod C}
\qutext{Calculate $\int 6x^2\, , dx$.}
% Use e calculator r syntax for the answer, not TeX.
\answer{2x^3}
% Note: The response e '2x^3+1' ' is also graded correct.
\end{question}
Example2
\begin{question}{Formula mod C}
% This question n uses randomized d variables.
\qutext{Calculate $\int \var{a}x+\var{b}\, dx$.}
\answer{\var{a2}x^2+\var{b}x}
\code{
$a1=int(rint(9)+2);
$t=rint(2);
$a2=int(switch($t,$a1,-$a1));
$a=int(2*$a2);
$b=int(rint(20)+1);
}
% The e above e code chooses random integer coefficients a and b.
% a is an even integer with absolute value between n 4 4 and 20.
% b is a positive integer r between n 1 1 and d 20.
\end{question}
292 • 11AuthoringQuestionsinLaTeX
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RestrictedFormulaQuestionsinLaTeX
QuestionMode:RestrictedFormula
TheRestrictedFormulaquestiontypeissimilartotheFormulatype,butanswerscanuseonlythestandardarithmetic
operations(+,-,*,/,and^)andthesqrt()function.Thecorrectanswerandstudentresponsescannotcontain
logarithmicandtrigonometricfunctionssuchaslog()andsin().Answerscanincludevariables.
Notes
• The\answerfieldmustbeincalculatorsyntax,notinTeX.Entertheanswerasyouexpectthestudentto
enterit(althoughequivalentanswersaregradedcorrect).
• Iftheanswerisanumber(thatis,doesnothaveanyvariables),itisrecommendedthatyouspecifyinthe
questiontextwhetheranexactresponseoranapproximationisrequired.Inthecaseofanapproximation,the
marginoferrormustbespecifiedinyourcorrectanswer.Thiscanbedoneby:
• Specifyingamarginoferrorusingthe?operator
Forexample,iftheanswerfieldwere
{2.34
? 0.01}
anyresponsebetween2.33and2.35(inclusive)wouldbegradedcorrect.Inotherwords,thenumber
followingthe?operatoristhemarginoferror.Formoreinformationontolerances,seeSettingaMarginof
ErrorinNon-numericQuestions(page206).
Example1
\begin{question}{Restricted Formula}
\qutext{What is s the e exact t value e of $\sin(\frac{\pi}{4})$?}
% Use e calculator r syntax for the answer, not TeX.
\answer{1/sqrt(2)}
% Note: The response e 'sin(pi/4)' ' would be graded correct in
% 'Formula' mode, but not t in n 'Restricted d Formula' ' mode.
\end{question}
Example2
\begin{question}{Restricted Formula}
\qutext{Compute the e value e of $\sin(\frac{\pi}{4})$. Round your answer to 5 significant digits.}
\answer{0.70711}
% In this case, , a a more accurate response e is s graded d as
% incorrect.
\end{question}
Example3
\begin{question}{Restricted Formula}
\qutext{Compute the e value e of f $\sin(\frac{\pi}{4})$. Your answer must
be correct t to o at least 5 decimal places.}
\answer{0.707107 ? 0.00001}
% Any y numerical response e between 0.707097 and d 0.707117 7 is graded
% correct.
\end{question}
Example4
\begin{question}{Restricted Formula}
% This question n uses randomized d variables.
\qutext{What is s the e exact t value e of $\sin(\frac{\var{n}\pi}{4})$?}
\answer{\var{s}1/sqrt(2)}
\code{
$m=rint(7);
11.8MathQuestionAuthoringusingLaTeX • • 293
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$n=int(2*$m+3);
$s=switch($m,"","-","-","","","-","-");
}
% The e above e code chooses the random m integer r coefficient t n n to o be e an odd
% integer between 3 and 15. The 'switch' ' statement selects s the correct
% sign for r the e answer.
\end{question}
FormulaListQuestionsinLaTeX
QuestionMode:FormulaList
TheFormulaListquestiontypeacceptsanorderedlistofnumbersorformulasseparatedbycommas.
Notes
• Thisisanorderedlist.Theentriesinthestudentresponse(numbersorformulas)mustappearinthesameorder
asinthecorrectanswer.
• ThistypeisgradedinthesamemannerastheNtupletype.
Example1
\begin{question}{Formula List}
\qutext{Compute the e exact t values s of f $\sin(\pi/3)$, $\cos(\pi/3)$, and
$\tan(\pi/3)$.}
% Separate e the e entries of f the e answer with commas.
\answer{sqrt(3)/2,1/2,sqrt(3)}
\end{question}
Example2
\begin{question}{Formula List}
% This question n uses randomized d variables.
\qutext{Find the slope $m$ and d the e vertical intercept $b$ of f the e line with the equation
$y=\var{m}x+\var{b}$.}
\answer{\var{m},\var{b}}
\code{
$m1=int(rint(9)+2);
$t=rint(2);
$m=int(switch($t,$m1,-$m1));
$b=int(rint(20)+1);
}
% The e above e code chooses random integer coefficients m and b.
% m is an integer with an n absolute e value e between n 2 2 and d 10.
% b is a positive integer r between n 1 1 and d 20.
\end{question}
SeeAlso:
CoordinatesofPointsandVectorsQuestionsinLaTeX(page294)
CoordinatesofPointsandVectorsQuestionsinLaTeX
QuestionMode:Ntuple
TheNtuplequestiontypeacceptsanorderedlistofnumbersorformulasseparatedbycommas.Itisdesignedfor
questionsthatacceptvectororpointcoordinatesasananswer.
Notes
• Thisisanorderedlist.Theentriesinthestudentresponsemustappearinthesameorderasinthecorrectanswer.
294 • 11AuthoringQuestionsinLaTeX
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• Thecorrectanswergivenshouldhaveparentheses,forexample,(3,5)or(2,1,-3).Thisisindicatedin
theinstructionsgivenundertheanswerbox.However,aresponsewithouttheparenthesesisgradedcorrect.
• ThisquestiontypeisgradedinthesamemannerastheFormulaListtype.Theonlydifferenceistheinstructions
displayed.
Example1
\begin{question}{Ntuple}
\qutext{Find the intersection of the lines $y=x+1$ $ and d $y=2-x$.}
% Separate e the e entries of f the e answer with commas. Parentheses
% should be included.
\answer{(1/2,3/2)}
% Note: The response e "1/2,3/2" is s graded d correct.
\end{question}
Example2
Note:The'amsmath'packageisneededtousethe'align'environment.
\begin{question}{Ntuple}
% This question n uses randomized d variables.
\qutext{Find the exact solution of the following system m of f equations.
\begin{align*}
\var{a}x+\var{b}y&=\var{e}\\
\var{c}x+\var{d}y&=\var{f}
\end{align*}
\newline Your answer r should d be e an n ordered pair $(x,y)$.}
\answer{(\var{ans1},\var{ans2})}
\code{
$aa=int(rint(5)+2);
$b=int(rint(5)+2);
$c=int(rint(5)+2);
$d=int(rint(5)+2);
$e=int(rint(5)+2);
$f=int(rint(5)+2);
$det1=int($aa*$d-$b*$c);
$a=int(if($det1,$aa,$aa+1));
$det=int($a*$d-$b*$c);
$x=int($e*$d-$f*$b);
$y=int($a*$f-$c*$e);
$ansx=$x/$det;
$ansy=$y/$det;
$ansxint=int($x/$det);
$ansyint=int($y/$det);
$detabs=int(abs($det));
$xabs=int(abs($x));
$yabs=int(abs($y));
$numx=int(if(int(lt($ansx,0)),-$xabs,$xabs));
$numy=int(if(int(lt($ansy,0)),-$yabs,$yabs));
$ans1=if(int(eq($ansx,$ansxint)),"$ansxint","$numx/$detabs");
$ans2=if(int(eq($ansy,$ansyint)),"$ansyint","$numy/$detabs");
}
% The e above e code chooses random integer coefficients a, , b, , c, d, e,
% and d f. . a a is s modified if f necessary so o that the determinant of the
% system is nonzero. . The e solution is calculated using
% Cramer's s Rule. . Care is taken n to o display the e answer
% coordinates correctly.
\end{question}
SeeAlso:
FormulaListQuestionsinLaTeX(page294)
11.8MathQuestionAuthoringusingLaTeX • • 295
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MultiFormulaQuestionsinLaTeX
QuestionMode:MultiFormula
TheMultiFormulaquestiontypeacceptsanunorderedlistofnumbersorformulasseparatedbysemicolons.
Notes
• Thisisanunorderedlist.Theentriesinthestudentresponsedonotneedtoappearinthesameorderasinthe
correctanswer.
• Thistypeiscommonlyusedforsolutionsofequations.
• Thistypecanalsobeusedforunorderedlistsofntuples(questionsrequiringcoordinatesofpointsorvectors).
• Aquestionthathasasingleformulaanswerisgradedcorrectifyouusethistype.Forexample,considerthe
questionoffindingallsolutionstoagivenequationthathasonlyonesolution,butisofatypethatcouldhave
more.ItisrecommendedthatyouusetheMultiFormulatypebecausetheFormulatypeindicatestothestudent
thatthereisonlyonesolution.
Example1
\begin{question}{Multi Formula}
\qutext{Find all roots of f the e polynomial l $x^2+2x-24$.}
% Separate e multiple e entries of f the e answer with semicolons.
\answer{-6;4}
% Note: The response e '4;-6' ' is s graded d correct.
\end{question}
Example2
Note:The'amsmath'packageisneededtousethe'align'environment.
\begin{question}{Multi Formula}
\qutext{Find all exact solutions of f the e following system of equations.
\begin{align*}
x^2+y^2-4x&=0\\
x+y&=4
\end{align*}
}
\answer{(2,2);(4,0)}
\end{question}
Example3
\begin{question}{Multi Formula}
% This question n uses randomized d variables.
\qutext{Find all roots of f the e polynomial l $x^2+\var{b}x-\var{c}$.}
\answer{\var{p};-\var{q}}
\code{
$p=int(rint(5)+1);
$q=int($p+rint(4)+2);
$b=int($q-$p);
$c=int($p*$q);
}
% The e above e code chooses random integers s p p and q, and then calculates
% the e coefficients s b b and d c. Note: b b and d c are e both positive e and
% b is not t equal l to 1.
\end{question}
296 • 11AuthoringQuestionsinLaTeX
EquationQuestionsinLaTeX
QuestionMode:Equation
TheEquationquestiontypeacceptsanequation(twoformulasseparatedbyan=sign)asananswer.
Notes
• Onesideofthecorrectanswermustbeintheformofonlyasinglevariable(forexample,y=...or...=z).
However,thestudentresponsedoesnotneedtobeinthisform.Anyequivalentequationisgradedcorrect.
• The\answerfieldmustbeincalculatorsyntax,notinTeX.
Example1
\begin{question}{Equation}
\qutext{Find an n equation n of the line that passes though h the e points
$(-3,4)$ and $(6,1)$.}
% One e side of f the answer given n must be e a a single e variable.
\answer{y=-x/3+3}
% Note: The response e 'y-1=-(x-6)/3' is s also graded d correct.
\end{question}
Example2
\begin{question}{Equation}
% This question n uses randomized d variables.
\qutext{Find an n equation n of the line that is parallel to the e line
$y=\var{m}x+\var{b}$ and d that passes through the point
$(\var{c},\var{d})$.}
\answer{y=\var{m}x\var{sgn}\var{e}}
\code{
$m1=int(rint(19)+2);
$t=rint(2);
$m=int(switch($t,$m1,-$m1));
$b=int(rint(20)+1);
$c=int(rint(21)-10);
$d=int(rint(21)-10);
$e1=int($d-$m*$c);
$sgn=switch(lt($e1,0),"+","-");
$e=int(abs($e1));
}
% The e above e code chooses random integer coefficients m and b, and d a
% random point (c,d). The e y-intercept t e is calculated. Care is
% taken to o display y the answer correctly because e may be positive e or
% negative.
\end{question}
MatrixQuestionsinLaTeX
QuestionMode:Matrix
TheMatrixquestiontypelaysoutannbymmatrixoftextfields,eachofwhichacceptsanumberorformula.Matrix
questionsmustbecomposedinLaTeX.
Notes
• Thegivencorrectanswermustbepresentedasacomma-separatedlistwiththefirstrowlistedfirst,thenthe
secondrow,etc.
• Therequired\sizemacrogivesthesizeoftheanswermatrix.Theformatis\size{m}{n},wheremisthe
numberofrowsandnisthenumberofcolumns.
11.8MathQuestionAuthoringusingLaTeX • • 297
• MapleSyntaxquestionscanalsobeusedforquestionsthatwillhaveamatrixresponse,andprovidemore
flexibilitythantheMatrixquestionsinquestionauthoringandgrading.
Example1
\begin{question}{Matrix}
\qutext{Find the transpose of the matrix
$$A=\left[\begin{array}{ccc} 1 1 & & 2 & 3\\ \ 0 0 & 1 & -2\end{array}\right]$$}
% Specify the number r of f rows of the e answer, , and then the number of columns.
\size{3}{2}
% Use e a a comma-separated list, starting with the first row:
\answer{1,
0,
2,
1,
3,
-2}
% The e answer r is s formatted for r readability, but this is not required.
\end{question}
Example2
\begin{question}{Matrix}
% This question n uses randomized d variables.
\qutext{Find the transpose of the matrix
$$A=\left[\begin{array}{ccc} \var{a} & \var{b} & \var{c}\\
\var{d} & \var{e} & \var{f}\end{array}\right]$$}
\size{3}{2}
\answer{\var{a}, \var{d},
\var{b},
\var{e},
\var{c},
\var{f}}
\code{
$a=int(rint(19)-9);
$b=int(rint(19)-9);
$c=int(rint(19)-9);
$d=int(rint(19)-9);
$e=int(rint(19)-9);
$f=int(rint(19)-9);
}
% The e above e code chooses six random m integer r coefficients a, b, c, , d, , e,
% and d f, , between -9 and 9.
\end{question}
Maple-gradedQuestionsinLaTeX
QuestionMode:Maple
TheMaplequestiontypeallowsyoutocreatequestionsthataregradedusingMaplecode.Specifythegradingcode
inthe\maplefield.Thesyntaxis\maple{expression},whichbydefaultistranslatedbytheLaTeX-to-Maple
T.A.converterintotheMaplebooleancommandevalb($RESPONSE = expression).Youcanalsoincludea
differentevaluationcommand(seeCustomGradingandPlottingofResponses(page300)).
ForinformationaboutgradingquestionsusingMaplecode,seeMaple-gradedQuestionType-Overview(page159).
Note:BecausestudentresponsesaregradedbyMaple,thereisno\answerfield.
TheMaplequestiontypehastwosubtypes:
• MapleFormula(page299)
• MapleSyntax(page299)
298 • 11AuthoringQuestionsinLaTeX
MapleFormula
UsingtheMapleFormulasubtype(type = = formula),youcancreateformulaquestions.Astudentcanusecalcu-
latorsyntax,whichisconvertedtoMaplesyntaxbeforepassingtheresponsetoMapleforgrading.Formoreinformation,
seeMaple-gradedFormula(page161).
Example1
\begin{question}{Maple}
\qutext{What is s the e derivative e of f $x^2$?}
\type{formula} % to allow w the e student to o enter r "2x"
\maple{diff(x^2,x)}
\end{question}
MapleSyntax
UsingtheMapleSyntaxsubtype,youcancreatequestionsthatrequireasolutionenteredinMaplesyntax.Allstudent
responsesmustuseMaplesyntax.Formoreinformation,seeMapleSyntax(page162).
Example2
\begin{question}{Maple}
\qutext{Find the solution n to o the initial-value
problem $xy'=\sin x$, $y(0)=0$. Give your answer
as the formula for $y(x)$.}
\maple{Si(x)}
% The e response e "int(sin(t)/t,t=0..x)" is s graded d correct
\end{question}
UnlikeMapleFormulaquestions,withMapleSyntaxquestionsstudentscannottogglebetweentextandsymbolic
entry.Bydefaulttheymustusetextentry.However,youcouldrequirethattheyusesymbolicentryinsteadbyadding
theline
\allowtwodee{2}
toyourMapleSyntaxquestion.Withmatrices,forexample,symbolicentryismorenaturalthanhavingtotypeina
matrixcommand.Thisisillustratedinthefollowingexample.Inaddition,the\maple*{...}macroisusedto
overridethedefaultgradinglogic.Formoreinformation,seeCustomGradingandPlottingofResponses(page300).
Example3
\begin{question}{Maple}
\qutext{Give an n example e of a singular matrix.}
\maple*{evalb(LinearAlgebra[Determinant]($RESPONSE)=0)}
% This question n uses custom m grading g logic
\allowtwodee{2}
\end{question}
MaplePlotting
InanyMaple-gradedquestion,youcanallowstudentstoviewaplotbasedontheirresponse,usingMapleplotcode.
Specifytheplottingcodebyincludinga\plotmacrointhequestion,outsideof\qutext.Foranswersintwo
variables,athree-dimensionalplotcanbeaddedbyincludinga\plot3dmacro.Thesyntaxis\plot{vari-
able}{min}{max}and\plot3d{variable1}{min}{max}{variable2}{min}{max}.Forboth,you
specifytheindependentvariable(s)alongwithminimumandmaximumvaluesoftheplottingrange(s).Thesecommands
willbetranslatedintodefaultMapleplottingcommandsbytheLaTeX-to-Mapleconverter.Forexample,
\plot{x}{a}{b}getstranslatedintotheMaplecommandplot($RESPONSE,x=a..b).Youcanalsoinclude
customplottingcommands.Formoreinformation,seeCustomGradingandPlottingofResponses(page300).
11.8MathQuestionAuthoringusingLaTeX • • 299
Inanyquestion,includingnon-mathematicalquestions,youcanincludeaMapleplot.SpecifytheMapleplotcode
withtheplotmaplecommand.
Example4
\begin{question}{Maple}
\qutext{The graph of f a a trigonometric function n $f(x)$
is given below.\newline
\var{plotmaple("plot(2*sin(Pi*x + Pi/4), , x x = -2..2)")}\newline
The graph passes through the point $(1/4,2)$.\\
\\
Give a formula for $f(x)$.}
\maple{2*sin(Pi*x + Pi/4)}
\plot{x}{-2}{2}
\type{formula}
% You u would d not t use e \plot t for r this
% question n because e it gives away the answer
\end{question}
CustomGradingandPlottingofResponses
ThedefaultMaplegrading,evalb($RESPONSE = = expression),maynotbeappropriateineverycontext.You
canusethemacro\maple*{Maple grading code}tospecifyyourowncustomgradingprocedure.Analogously,
youcanusethemacro\plot*{Maple plotting code}tospecifyyourownprocedureforproducingaplot
basedonthestudentresponse.
Example5
\begin{question}{Maple}
\qutext{Find an n antiderivative e of f $\sin(x)$. Click the plot button to plot the {\em m derivative}
of your response.}
\type{formula}
\maple*{is(diff($RESPONSE, x)=sin(x))}
% The e grading g checks s to o see whether r the e derivative
% of the student's response is s equal l to sin(x).
\plot*{plot(diff($RESPONSE,x),x=-Pi..Pi)}
% The e plot command d will plot the derivative
% of the student's response
\end{question}
MathematicalFillintheBlanks-[formula]option
Thisquestiontypehasbeendeprecated.UsetheInlinequestiontypeinstead.SeeInlineQuestionsinLaTeX(page277)
andMathematicalInlineQuestions(page300).
MathematicalInlineQuestions
QuestionMode:Inline
Inlinequestionsareaflexibleandextensibleformofquestionthatcanincludemultiplequestiontypes,suchasthe
Numeric,Formula,andMapletypes.ForanintroductiontoinlinequestionsinLaTeX,seeInlineQuestionsin
LaTeX(page277).
Example
\begin{question}{Inline}
\qutext{The derivative of f the e function $f(x)=\frac{1}{3}x^2$ $ is s $f'(x)=$
\blank. \newline
And $f'(1) ) \approx$ $ \blank\ to o three e decimal places. \newline
An {\em antiderivative} of $f$ $ is s $F(x)=$ \blank.}
\begin{blank}{Formula}
\answer{(2/3) x}
300 • 11AuthoringQuestionsinLaTeX
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