WebQuiz is a LATEX package for creating interactive web quizzes. The idea is that you write the quiz using LATEX and that WebQuiz creates the web page from this file. Anything that you can write using LATEX will be converted to HTML by WebQuiz. This includes, for example, mathematics and graphics written using pstricks. WebQuiz supports three different types of quiz questions:

1.

Multiple choice questions with a unique correct answer. (See 1)

2.

Multiple choice questions with several (or no) correct answers. (See 2)

3.

Questions that require the student to enter an answer, which can then be compared with the correct answer in several different ways. (See 3)

The use of WebQuiz is described in the next section. Later sections describe how each of the WebQuiz environments are used.

The discussion environment in WebQuiz can also be used to write Web Pages like this one (The pages you are reading here were written using WebQuiz.)

Once you have a WebQuiz file, you can run it through LATEX, in the usual way, to produce a readable version of your quiz. When you are happy with the quiz, use WebQuiz to create the HTML version. Note that the printable version of the quiz does not look like the web page; rather, it contains all of the information in an easily readable layout. If, for example, your quiz file is called quiz1.tex then you can use the following commands:

 
     > latex quiz1           % latex a quiz file 
     > pdflatex quiz1        % a PDF versio of the quiz 
     > xdvi quiz1            % view the quiz using xdvi 
     > dvips quiz1           % print the quiz 
     > webquiz quiz1         % converts the quiz to html
      

Converting the quiz to html can take quite a long time, particularly if a large number of images need to be created.

The basic structure of a WebQuiz file is as follows:

 
     \documentclass{webquiz} 
 
     \title{Quiz 1: Complex numbers} 
 
     \UnitCode{MATH1001} 
     \UnitName{Differential Calculus} 
     \UnitURL{/u/UG/JM/MATH1001/} 
     \QuizzesURL{/u/UG/JM/MATH1001/Quizzes/} 
 
     \begin{document} 
 
     \begin{discussion}[short heading][optional heading] 
        . . . % optional discussion 
     \end{discussion} 
 
     \begin{question} % question 1 
        . . . 
     \end{question} 
 
     \begin{question} % question 2 
        . . . 
     \end{question} 
     . 
     . 
     \end{document}
      

In the preamble of the LATEX file you can specify the unit code, the name of the unit of study, the location of the homepage for the unit and the index file for the quizzes for this unit; this is done using the commands \UnitCode, \UnitName, \UnitURL and \QuizzesURL respectively. If the command \QuizzesURL is omitted then the URL for the quiz index file is set to \UnitURL/Quizzes.

The title of the quiz can be set in the preamble using the \title command. Note that the \title command must appear before the \begin{document} command. As in any LATEX document, the preamble can define macros and load other LATEX packages the usual way .

By using the discussion environment you can summarise the material for the students or add introductory material for the quiz. For example, discussion environments can be used to recall that main concepts being covered by the quiz or to give references to the lecture notes for the unit. The syntax for the discussion environment is as follows:  

 
     \begin{discussion}[optional short heading][optional heading] 
      . . . 
     \end{discussion}
      

Anything you like (text, mathematics, …) can go inside discussion environments. The optional heading, which defaults to Discussion”, is used both as the section heading on the web page and as the heading in the side-menu on left hand side of the page. If a short heading is also given then it is used in the side-menu. The quiz can contain zero or more discussion items ( and zero or more quiz questions).

Questions are set inside a question environment. The text is followed by the answers.

WebQuiz supports three types of questions:

• Multiple choice questions with precisely one correct answer;
• Multiple choice questions with zero or more correct answers;
• Questions that require the students to enter an answer. Five difference comparison methods are available.

With each of these types of questions you can (and should) provide feedback to the students depending on whether their answer is correct or incorrect. Below we describe how to produce these different types of questions.

The syntax for a multiple choice question having precisely one correct answer is as follows:

 
   \begin{question} 
     . . .question text 
     \begin{choice} 
      \(in)correct . . . text for (in)correct option 
      \feedback   . . . feedback on response 
 
      \(in)correct . . . text for (in)correct option 
      \feedback   . . . feedback on response 
      . 
      . 
      . 
     \end{choice} 
   \end{question}
      

The different choices in a multiple choice question must be inside a choice environment. This environment behaves like a standard LATEX list environment except that instead of using \item for list item you use:

• \correct for a correct choice
• \incorrect for an incorrect choice
• \feedback to give feedback to the student when they select this choice

At most one \feedback response should be given for each \correct and each \incorrect response. The \feedback commands are optional; however, it is recommended that you use them because targeted feedback to the students based on their responses can be beneficial.

For example, the code below, when run through WebQuiz, produces 1 in the online manual quiz.  

 
  \begin{question} 
    The shaded region in the graph 
    \begin{center} 
      \begin{pspicture}(-3,-1.5)(3,4) 
       \pscircle[linewidth=1pt,linestyle=dashed,% 
                fillcolor=SkyBlue,fillstyle=solid](1,1){2} 
       \psaxes[linecolor=red,linewidth=1pt,labels=none]% 
       {->}(0,0)(-1.5,-1.5)(3.5,3.5) 
       \rput(3.75,0){$x$} 
       \rput(0,3.85){$iy$} 
       \rput(3,-0.4){3} 
       \rput(-0.4,3){3$i$} 
       \psdots(1,1) 
      \end{pspicture} 
    \end{center} 
    is equal to which of the following sets of complex numbers? 
    \begin{choice} 
      \incorrect $\{z \in \C : (z-1)^{2}+(z-(i+1))^{2}<2\}$ 
      \feedback  The equation of a circle in the complex plane with 
      centre $a+ib$ and radius $r$ is 
      \begin{displaymath} 
       \{z\in\C : |z-(a+ib)|<r \}. 
      \end{displaymath} 
 
      \incorrect $\{z \in \C : z+(i+1)<2\}$ 
      \feedback  You want the set of points whose \textit{distance} 
      from $1+i$ is less than $2$. 
 
      \correct  $\{z \in \C : |z-(i+1)|<2\}$ 
      \feedback  The graph shows the set of complex numbers whose 
      distance from $1+i$ is less than $2$. 
 
      \incorrect $\{z \in \C : |z-2|<|i+1-2|\}$ 
      \feedback  As $|i+1-2|=\sqrt 2$, this is the set of complex 
      numbers whose distance from $2$ is less than 
      $\sqrt 2$. 
 
      \incorrect None of the above. 
      \feedback The graph shows the set of complex numbers whose 
      distance from the centre of the circle is less than $2$. 
    \end{choice} 
  \end{question}
      

To allow multiple (or no) correct answer we add multiple as an optional argument to the choice environment:

 
   \begin{question} 
     . . .question text. . . 
     \begin{choice}[multiple] 
      \(in)correct . . . text for (in)correct option 
      \feedback   . . . feedback on response 
 
      \(in)correct . . . text for (in)correct option 
      \feedback   . . . feedback on response 
      . 
      . 
      . 
     \end{choice} 
   \end{question}
      

The only difference to the previous case is that zero or more \correct commands can appear.

For example, 2 below was typed into WebQuiz using the following commands:  

 
   \begin{question} 
     Which of the following numbers are prime? 
     \begin{choice}[multiple] 
      \incorrect 1 
      \feedback  By definition, a prime is a number greater than 1 
      whose only factors are 1 and itself. 
 
      \correct  19 
      \feedback  The only factors of 19 are 1 and itself. 
 
      \incorrect 6 
      \feedback  2 is a factor of 6 
 
      \correct  23 
      \feedback  The only factors of 23 are 1 and itself. 
 
      \correct  191 
      \feedback  The only factors of 191 are 1 and itself. 
     \end{choice} 
   \end{question}
      

By default, the choice environments puts the multiple choice options into one column format. Sometimes the options look better when listed in two or more columns, however, this should be used sparingly as multiple columns do not always display well if the quiz is viewed on a mobile device. By using the columns key word in a choice environment you can specify the number of columns in the HTML version of the quiz.

 
   \begin{question} 
     . . .question text. . . 
     \begin{choice}[multiple, columns=n]    . . . n columns 
      \(in)correct . . . text for (in)correct option 
      \feedback   . . . feedback on response 
 
      \(in)correct . . . text for (in)correct option 
      \feedback   . . . feedback on response 
      . 
      . 
      . 
     \end{choice} 
   \end{question}
      

If the optional argument [multiple] is not present, then the question admits precisely one correct answer.

For example, 3 below was typed into WebQuiz using the following commands:  

 
   \begin{question} 
     What are suitable parametric equations for this plane curve? 
     \begin{center} 
      \psset{unit=.6cm} 
      \begin{pspicture}(-2.5,-0.5)(5,5.5) 
        \psaxes[linecolor=red,linewidth=1pt,labels=none]% 
        {->}(0,0)(-2.5,-1.5)(5,5) 
        \psellipse[linecolor=SkyBlue,linewidth=2pt](1,2)(3,2) 
      \end{pspicture} 
     \end{center} 
 
     \begin{choice}[columns=1] 
      \incorrect $x=2\cos t + 1$, $y=3\sin t + 2$ 
      \feedback This is an ellipse with centre $(1,2)$ and with axes of 
      length $4$ in the $x$-direction and $6$ in the $y$-direction. 
      \begin{center} 
        \psset{unit=.6cm} 
        \begin{pspicture}(-2.5,-0.5)(5,5.5) 
          \psaxes[linecolor=red,linewidth=1pt,labels=none]% 
          {->}(0,0)(-2.5,-1.5)(5,5) 
          \parametricplot[linecolor=SkyBlue,linewidth=2pt]{0}{360}% 
          {t cos 2 mul 1 add t sin 3 mul 2 add} 
        \end{pspicture} 
      \end{center} 
 
      \correct $x=3\cos t + 1$, $y=2\sin t + 2$ 
      \feedback The curve is an ellipse centre (1,2) with axes length 6 
      in the $x$ direction and 4 in the $y$ direction. 
 
      \incorrect $x=3\cos t - 1$, $y=2\sin t - 2$ 
      \feedback This is an ellipse with centre $(-1,-2)$ and with axes 
      of length $6$ in the $x$-direction and $4$ in the $y$-direction. 
      \begin{center} 
        \psset{unit=.6cm} 
        \begin{pspicture}(-5,-4)(1,2) 
          \psaxes[linecolor=red,linewidth=1pt,labels=none]% 
          {<-}(0,0)(-4.5,-5.5)(1,2) 
          \parametricplot[linecolor=SkyBlue,linewidth=2pt]{0}{360}% 
          {t cos 3 mul 1 sub t sin 2 mul 2 sub} 
        \end{pspicture} 
      \end{center} 
 
      \incorrect $x=2\cos t - 1$, $y=3\sin t - 2$ 
      \feedback This is an ellipse with centre $(-1,-2)$ and with axes 
      of length $4$ in the $x$-direction and $6$ in the $y$-direction. 
      \begin{center} 
        \psset{unit=.6cm} 
        \begin{pspicture}(-4,-5)(1,2) 
          \psaxes[linecolor=red,linewidth=1pt,labels=none]% 
          {<-}(0,0)(-4.5,-5.5)(1,2) 
          \parametricplot[linecolor=SkyBlue,linewidth=2pt]{0}{360}% 
          { t cos 2 mul 1 sub t sin 3 mul 2 sub} 
        \end{pspicture} 
      \end{center} 
     \end{choice} 
   \end{question}
      

The final type of question that WebQuiz supports is a question that requires an answer, which can be a number or a string. The answer is typeset using the \answer macro. The \answer macro takes two arguments: an optional comparison method, which defaults to string, and the correct answer for the question:

 
   \answer[comparison method]{correct answer}
      

Feedback for correct and incorrect answers is given using the macros \whenRight and \whenWrong, respectively. The structure of questions with \answer’s is as follows:

 
       \begin{question} 
         . . .question text. . . 
         \answer[*][complex|integer|lowercase|number|string]{actual answer} 
         \whenRight . . . feedback when right (optional) 
         \whenWrong . . . feedback when wrong (optional) 
       \end{question}
      

See the WebQuiz manual for details of the different comparison types. For example, 4 below was typed into WebQuiz using the following commands:  

 
   \begin{question} 
     If the vectors $\vect{a}$ (of magnitude 8 units) and $\vect{b}$ 
     (of magnitude 3 units) are perpendicular, what is the value 
     of 
     \begin{displaymath} 
      |\vect{a} -2\vect{b}|~? 
     \end{displaymath} 
     (Hint: Draw a diagram!) 
 
     \answer[number]{10} 
     \whenRight The vectors $\vect{a}$, \(-2\vect{b}\), and 
     $\vect{a} - 2\vect{b}$ form the sides of a right-angled 
     triangle, with sides of length $8$ and $6$ and 
     hypotenuse of length $|\vect{a} -2\vect{b}|$. Therefore 
     by Pythagoras’ Theorem, 
     \(|\vect{a} -2\vect{b}|=\sqrt{8^2+6^2}=10\). 
 
     \whenWrong Draw a diagram and then use Pythagoras’ theorem. 
   \end{question}
      

WebQuiz also provides a mechanism for creating a web page containing an index of all quizzes for a given Unit of Study. This is done with a WebQuiz file that contains a quizindex environment. The syntax for this environment is as follows:

 
   \begin{quizindex} 
     \quiz[url1]{title for quiz 1} 
     \quiz[url2]{title for quiz 2} 
     . . . 
   \end{quizindex}
      

If no URL is given as an optional argument to \quiz then WebQuiz sets the url(s) to quiz1.html, quiz2.html and so on.

WebQuiz was written and developed in the School of Mathematics and Statistics at the University of Sydney. The system is built on LATEX with the conversion from LATEX to HTML using Eitan Gurari’s TeX4ht, and Michal Hoftich’s make4ht.

To write quizzes using WebQuiz it is only necessary to know LATEX, however, the WebQuiz system has three components:

• A LATEX document class file, webquiz.cls, and a TEX4ht configuration file, webquitexz.cfg, that enable the quiz files to be processed by LATEX and TEX4ht, respectively.
• A python program, webquiz, that translates the XML file that is produced by TEX4ht into HTML.
• Some Javascript and CSS that controls the quiz web page.

The LATEX component of WebQuiz was written by Andrew Mathas and the python, CSS and Javascript code was written by Andrew Mathas (and Don Taylor), based on an initial prototype of Don Taylor’s from 2001. Since 2004 the program has been maintained and developed by Andrew Mathas. Although the program has changed substantially since 2004, Don’s idea of using TEX4ht, and some of his code, is still in use.

Thanks are due to Bob Howlett for general help with CSS and, for Version 5, to Michal Hoftich for technical advice.

The shaded region in the graph is equal to which of the following sets of complex numbers?

	(a)	$\left\{z\in ℂ:{\left(z-1\right)}^2+{\left(z-\left(i+1\right)\right)}^2<2\right\}$
	(b)	$\left\{z\in ℂ:z+\left(i+1\right)<2\right\}$
	(c)	$\left\{z\in ℂ:|z-\left(i+1\right)|<2\right\}$
	(d)	$\left\{z\in ℂ:|z-2|<|i+1-2|\right\}$
	(e)	None of the above.

Which of the following numbers are prime?

	(a)	1
	(b)	19
	(c)	6
	(d)	23
	(e)	191

What are suitable parametric equations for this plane curve?

	(a)	$x=2cost+1$, $y=3sint+2$
	(b)	$x=3cost+1$, $y=2sint+2$
	(c)	$x=3cost-1$, $y=2sint-2$
	(d)	$x=2cost-1$, $y=3sint-2$

If the vectors $\mathbf{a}$ (of magnitude 8 units) and $\mathbf{b}$ (of magnitude 3 units) are perpendicular, what is the value of $|\mathbf{a}-2\mathbf{b}|$ ? (Hint: Draw a diagram!)

Answer:  units