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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.}
\err{0.0001}
\end{question}
FormulaQuestionsinLaTeX
QuestionMode:Formula
functions.
Notes
questiontextwhetheranexactresponseoranapproximationisrequired.Inthecaseofanapproximation,the
• Specifyingamarginoferrorusingthe?operator
{2.34 ? ? 0.01}
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.
\end{question}
Example2
\begin{question}{Formula}
\qutext{Compute the e exact t value e of $f'(2)$ if f $f(x)=x^3+3\cos(x)-1$.}
% 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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% 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
$f(x)=\var{a}x+\var{b}$.}
\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
canincludevariablesandstandardfunctions.Thisquestiontypeisdesignedforindeﬁniteintegralquestions.
Note:
Example1
\begin{question}{Formula mod C}
\qutext{Calculate $\int 6x^2\, , dx$.}
% Use e calculator r syntax for the answer, not TeX.
% 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 $\int \var{a}x+\var{b}\, dx$.}
\code{
$a1=int(rint(9)+2);$t=rint(2);
$a2=int(switch($t,$a1,-$a1));
$a=int(2*$a2);
$b=int(rint(20)+1); } % The e above e code chooses random integer coefficients a and b. % a is an even integer with absolute value between n 4 4 and 20. % b is a positive integer r between n 1 1 and d 20. \end{question} 292 • 11AuthoringQuestionsinLaTeX Online Merge PDF files. Best free online merge PDF tool. Merge PDF, Multiple PDF files. Then press the button below and download your PDF. Also you can add more PDFs to combine them and merge them into one single break pdf file into multiple files; pdf merger VB.NET TWAIN: Scanning Multiple Pages into PDF & TIFF File Using one convenient multi-page document file, like PDF and TIFF This VB.NET TWAIN pages scanning control add-on is an efficient solution to scan multiple pages into pdf merge; pdf combine pages RestrictedFormulaQuestionsinLaTeX QuestionMode:RestrictedFormula TheRestrictedFormulaquestiontypeissimilartotheFormulatype,butanswerscanuseonlythestandardarithmetic operations(+,-,*,/,and^)andthesqrt()function.Thecorrectanswerandstudentresponsescannotcontain logarithmicandtrigonometricfunctionssuchaslog()andsin().Answerscanincludevariables. Notes • The\answerﬁeldmustbeincalculatorsyntax,notinTeX.Entertheanswerasyouexpectthestudentto enterit(althoughequivalentanswersaregradedcorrect). • Iftheanswerisanumber(thatis,doesnothaveanyvariables),itisrecommendedthatyouspecifyinthe questiontextwhetheranexactresponseoranapproximationisrequired.Inthecaseofanapproximation,the marginoferrormustbespeciﬁedinyourcorrectanswer.Thiscanbedoneby: • Specifyingamarginoferrorusingthe?operator Forexample,iftheanswerﬁeldwere {2.34 ? 0.01} anyresponsebetween2.33and2.35(inclusive)wouldbegradedcorrect.Inotherwords,thenumber followingthe?operatoristhemarginoferror.Formoreinformationontolerances,seeSettingaMarginof ErrorinNon-numericQuestions(page206). Example1 \begin{question}{Restricted Formula} \qutext{What is s the e exact t value e of$\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
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.
\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
$y=\var{m}x+\var{b}$.}
\code{
$m1=int(rint(9)+2);$t=rint(2);
$m=int(switch($t,$m1,-$m1));
$b=int(rint(20)+1); } % The e above e code chooses random integer coefficients m and b. % m is an integer with an n absolute e value e between n 2 2 and d 10. % b is a positive integer r between n 1 1 and d 20. \end{question} SeeAlso: CoordinatesofPointsandVectorsQuestionsinLaTeX(page294) CoordinatesofPointsandVectorsQuestionsinLaTeX QuestionMode:Ntuple TheNtuplequestiontypeacceptsanorderedlistofnumbersorformulasseparatedbycommas.Itisdesignedfor questionsthatacceptvectororpointcoordinatesasananswer. Notes • Thisisanorderedlist.Theentriesinthestudentresponsemustappearinthesameorderasinthecorrectanswer. 294 • 11AuthoringQuestionsinLaTeX VB.NET Create PDF from images Library to convert Jpeg, png images Turn multiple image formats into one or multiple PDF file. images As New List(Of REImage) images.Add(New REImage example shows how to build a PDF document with acrobat merge pdf files; build pdf from multiple files C# PDF: C#.NET PDF Document Merging & Splitting Control SDK C#.NET Sample Codes to Merge Multiple PDF Files. C#.NET PDF Merger & Splitter SDK FAQs. Q 1: Using this C#.NET PDF merger & splitter control add-on, can I add pdf together one file; attach pdf to mail merge • Thecorrectanswergivenshouldhaveparentheses,forexample,(3,5)or(2,1,-3).Thisisindicatedin theinstructionsgivenundertheanswerbox.However,aresponsewithouttheparenthesesisgradedcorrect. • ThisquestiontypeisgradedinthesamemannerastheFormulaListtype.Theonlydifferenceistheinstructions displayed. Example1 \begin{question}{Ntuple} \qutext{Find the intersection of the lines$y=x+1 and d $y=2-x$.}
% Separate e the e entries of f the e answer with commas. Parentheses
% should be included.
% 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 $(x,y)$.}
\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
• Thistypeiscommonlyusedforsolutionsofequations.
• Thistypecanalsobeusedforunorderedlistsofntuples(questionsrequiringcoordinatesofpointsorvectors).
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.
% 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*}
}
\end{question}
Example3
\begin{question}{Multi Formula}
% This question n uses randomized d variables.
\qutext{Find all roots of f the e polynomial l $x^2+\var{b}x-\var{c}$.}
\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
secondrow,etc.
numberofrowsandnisthenumberofcolumns.
11.8MathQuestionAuthoringusingLaTeX • • 297
• MapleSyntaxquestionscanalsobeusedforquestionsthatwillhaveamatrixresponse,andprovidemore
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:
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}
\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}
QuestionMode:Maple
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