MathQuiz is a LATEX based system to create interactive web quizzes. The
idea is that you write the quiz using LATEX and that MathQuiz creates the web
page from this file. Anything which you can write using LATEX will be converted to
HTML by MathQuiz. This includes, for example, mathematics and graphics
written using PSTricks. MathQuiz supports three different types of quiz
questions:
Multiple choice questions with a unique correct answer. (See Question 1)
Multiple choice questions with several (or no) correct answers. (See
Question 2)
Questions which require a numerical answer. (See Question 3)
The use of MathQuiz is described in the next section. Later sections describe how
each of the MathQuiz environments are used.
The discussion environment in MathQuiz can also be used to write Web Pages
like this one (The pages you are reading here were written using MathQuiz.)
Basic Usage
Once you have a MathQuiz 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
mathquiz 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
> xdvi quiz1 % view the quiz using xdvi
> dvips quiz1 % print the quiz
> mathquiz 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.
MathQuiz files
The basic structure of a MathQuiz file is as follows:
The preamble of the LATEX file specifies the course 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. (Within the the School of
Mathematics and Statistics, there is also a package smsquiz.sty which sets the default
parameters from the course code.)
The title of the quiz should also be set in the preamble using the \tile command.
Note that the \title command must appear before the \begin{document}
command. In the preamble you can also define macros and load any packages that
you want in the usual way .
The discussion environment can be used to add comments or remarks to a quiz. For
example, it can be used to summarize the material being tested in the quiz or to give
references to the course notes. The syntax for the discussion environment is as
follows:
Anything you like (text, mathematics, …) can go inside discussion environments. The
optional title is used both as the section heading on the web page and as the heading
in the navigation bar which runs down the left hand side of the page. The headings
should not be too long as they have to fit in the left hand margin. By default, the
title is discussion. There can be several discussion environment, but they go all in
front of the questions.
Questions are set inside a question environment. The text is followed by the
answers.
MathQuiz supports three types of questions:
Multiple choice questions with precisely one correct answer;
Multiple choice questions with several or no correct answers;
Questions taking a numerical answer.
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.
Question 1
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
\response . . . feedback on response
\(in)correct . . . text for (in)correct option
\response . . . feedback on response
.
.
.
\end{choice}
\end{question}
The multiple choice responses for each question go inside a choice environment. The
correct answer goes after \correct, incorrect answers after \incorrect. Either can
be followed by a \response, providing comments on the students choice when
checking their answers. The \reponse commands are optional; however, it is
recommended that you use them as good feedback is very useful for the
students.
For example, Question 1 below was typed into MathQuiz using the following
commands:
\begin{question}
The shaded region in the graph
\begin{center}
\begin{pspicture}(-3,-1.5)(3,4)
\pscircle[linewidth=2pt,linestyle=dashed,%
fillcolor=blue,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 $\{z \in \C : (z-1)^{2}+(z-(i+1))^{2}<2\}$
\response 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 $\{z \in \C : z+(i+1)<2\}$
\response You want the set of points whose \textit{distance}
from $1+i$ is less than $2$.
\correct $\{z \in \C : |z-(i+1)|<2\}$
\response The graph shows the set of complex numbers whose
distance from $1+i$ is less than $2$.
\incorrect $\{z \in \C : |z-2|<|i+1-2|\}$
\response 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.
\response The graph shows the set of complex numbers whose
distance from the centre of the circle is less than $2$.
\end{choice}
\end{question}
Question 2
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
\response . . . feedback on response
\(in)correct . . . text for (in)correct option
\response . . . feedback on response
.
.
.
\end{choice}
\end{question}
The only difference to the previous case is that multiple (or no) \correct
commands may be used.
For example, Question 2 below was typed into MathQuiz using the following
commands:
\begin{question}
Which of the following numbers are prime?
\begin{choice}[multiple]
\incorrect 1
\response By definition, a prime is a number greater than 1
whose only factors are 1 and itself.
\correct 19
\response The only factors of 19 are 1 and itself.
\incorrect 6
\response 2 is a factor of 6
\correct 23
\response The only factors of 23 are 1 and itself.
\correct 191
\response The only factors of 191 are 1 and itself.
\end{choice}
\end{question}
Question 3
By default, the choice environments puts the multiple choice options into two
column format. Sometimes, however, the options look better when listed in a single
column and, sometimes, three or more columns are better. There is a more
general Choice environment which lets you specify the number of columns in
the HTML version of the quiz. Its syntax is similar to that of the choice
environment.
\begin{question}
. . .question text. . .
\begin{Choice}[multiple]{n} . . . n columns
\(in)correct . . . text for (in)correct option
\response . . . feedback on response
\(in)correct . . . text for (in)correct option
\response . . . 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, Question 3 below was typed into MathQuiz 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=blue,linewidth=2pt](1,2)(3,2)
\end{pspicture}
\end{center}
\begin{Choice}{1}
\incorrect $x=2\cos t + 1$, $y=3\sin t + 2$
\response 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=blue,linewidth=2pt]{0}{360}%
{t cos 2 mul 1 add t sin 3 mul 2 add}
\end{pspicture}
\end{center}
\correct $x=3\cos t + 1$, $y=2\sin t + 2$
\response The curve is an ellipse centre (1,2) with axes length 6
in the $x$ direction and 4 in the $y$ direction.
\incorrect $x=3\cos t - 1$, $y=2\sin t - 2$
\response 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=blue,linewidth=2pt]{0}{360}%
{t cos 3 mul 1 sub t sin 2 mul 2 sub}
\end{pspicture}
\end{center}
\incorrect $x=2\cos t - 1$, $y=3\sin t - 2$
\response 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=blue,linewidth=2pt]{0}{360}%
{ t cos 2 mul 1 sub t sin 3 mul 2 sub}
\end{pspicture}
\end{center}
\end{Choice}
\end{question}
Question 4
The final type of question that MathQuiz supports is a question which requires a
numerical as an answer. The numerical answer must be given in decimal
form. The answer is typeset using the \answer macro. That macro takes
two arguments, some text appearing in an answer box after the question
and the actual numerical answer. The text is optional. The syntax is
\answer[text after answer box]{numerical answer}. Then there is a
mechanism for providing feedback for correct and incorrect answers. This is done
using \whenRight and \whenWrong. Unlike the \response commands, the two
reponses \whenRight and \whenWrong are both mandatory for questions of this type.
The syntax is for such questions is as follows:
\begin{question}
. . .question text. . .
\answer[text after the answer box]{actual answer}
\whenRight . . . feedback when right
\whenWrong . . . feedback when wrong
\end{question}
For example, Question 4 below was typed into MathQuiz 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[units]{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}
Index Files
MathQuiz 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 MathQuiz file which
contains a —quizlist— environment. The syntax for this environment is as
follows:
\begin{quizlist}
\quiz[url1]{title for quiz 1}
\quiz[url2]{title for quiz 2}
. . .
\end{quizlist}
If no url is given as an optional argument to — then MathQuiz sets the url(s) to
quiz1.html, quiz2.html and so on.
Credits
MathQuiz is a HTML quiz preparation system which 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 being done by Eitan
Gurari’s TeX4ht and some python programs.
The LATEX component of MathQuiz was written by Andrew Mathas; the dtx file
was written by Daniel Daners; the python and javascripts were written by Andrew
Mathas and Don Taylor; and the extension of the system for use as a self
assessment test was written by Daniel Daners (see the following example
test).
Authors Daniel Daners, Andrew Mathas and Don Taylor.
Question 1
The shaded region in the graph
is equal to which of the following sets of complex numbers?
Not correct. Choice (a)
is false.
The equation of a circle in the complex plane with centre a + ib and radius r
is
Not correct. Choice (b)
is false.
You want the set of points whose distance from 1 + i is less
than 2.
Your answer is correct.
The graph shows the set of complex numbers whose
distance from 1 + i is less than 2.
Not correct. Choice (d)
is false.
As ∣i + 1 - 2∣ = , this is the set of complex numbers
whose distance from 2 is less than .
Not correct. Choice (e)
is false.
The graph shows the set of complex numbers whose distance from
the centre of the circle is less than 2.
Question 2
Which of the following numbers are prime?
There is at least one mistake.
For example, choice (a)
should be false.
By definition, a prime is a number
greater than 1 whose only factors are 1 and itself.
There is at least one mistake.
For example, choice (b)
should be true.
The only factors of 19 are 1 and itself.
There is at least one mistake.
For example, choice (c)
should be false.
2 is a factor of 6
There is at least one mistake.
For example, choice (d)
should be true.
The only factors of 23 are 1 and itself.
There is at least one mistake.
For example, choice (e)
should be true.
The only factors of 191 are 1 and itself.
Your answers are correct
False. By definition, a prime is a number
greater than 1 whose only factors are 1 and itself.
True. The only factors of 19 are 1 and itself.
False. 2 is a factor of 6
True. The only factors of 23 are 1 and itself.
True. The only factors of 191 are 1 and itself.
Question 3
What are suitable parametric equations for this plane curve?
Not correct. Choice (a)
is false.
This is an ellipse with centre (1,2) and with axes of
length 4 in the x-direction and 6 in the y-direction.
Your answer is correct.
The curve is an ellipse centre (1,2) with axes length 6 in
the x direction and 4 in the y direction.
Not correct. Choice (c)
is false.
This is an ellipse with centre (-1,-2) and with axes of
length 6 in the x-direction and 4 in the y-direction.
Not correct. Choice (d)
is false.
This is an ellipse with centre (-1,-2) and with axes of
length 4 in the x-direction and 6 in the y-direction.
Question 4
If the vectors a (of magnitude 8 units) and b (of magnitude 3 units) are
perpendicular, what is the value of
(Hint: Draw a diagram!)
Your answer is correct
The vectors a, , and a- 2b form the sides of a right-angled triangle, with
sides of length 8 and 6 and hypotenuse of length ∣a - 2b∣. Therefore by Pythagoras’
Theorem, .
Question
, this is the set of complex numbers
whose distance from 2 is less than 
.
, and a- 2b form the sides of a right-angled triangle, with
sides of length 8 and 6 and hypotenuse of length ∣a - 2b∣. Therefore by Pythagoras’
Theorem, 
.
right first
right
wrong