Nicola L.C. Talbot
21st August 2007
| answers | Show the answers | |
| noanswers | Don't show the answers (default) |
[nargs]{label}{problem}{solution}
[nargs]{label}{problem}
\newproblem{quaddiff}{%
%This is the problem
\begin{displaymath}
f(x) = x^2 + 3x + 4
\end{displaymath}
}{%
%This is the solution
\begin{displaymath}
f'(x) = 2x + 3
\end{displaymath}
}
The following is an essay question, so doesn't come with a solution:
\newproblem*{inheritance}{Describe what is meant by the term
\emph{inheritance} in object-oriented programming. Use examples.}
The optional argument nargs specifies the number of
parameters this problem will take. By default this value is
0, but any value from 1 to 9 may be used. Each parameter is
referred to by #1, #2, ..., #9.
For example, the following problem, labelled sindiff,
takes one parameter:
\newproblem[1]{sindiff}{%
\(f(x) = \sin(#1x)\)
}{%
\(f'(x) = #1\cos(#1x)\)
}
The quaddiff problem shown above can be made more generic by using parameters:
\newcount\ctr
\newproblem[3]{diff:quad}{%
\(f(x) =
\ifnum#1=0
\else
\ifnum#1=1\else#1\fi x^2
\fi
\ifnum#2=0
\else
\ifnum#2>0 \ifnum#1=0 \else + \fi \fi
\ifnum#2=1\else#2\fi x
\fi
\ifnum#3=0
\else
\ifnum#3>0 \ifnum#2=0 \ifnum#1=0 \else + \fi \else + \fi\fi
#3
\fi\)
}{%
\(f'(x) =
\ifnum#1=0
\else
\ctr=2
\multiply\ctr by #1
\the\ctr x
\fi
\ifnum#2=0
\else
\ifnum#2>0 \ifnum#1=0 \else + \fi \fi
#2
\fi
% print 0 if both #1 and #2 are 0
\ifnum#1=0 \ifnum#2=0 0 \fi\fi
\)
}
The three parameters correspond to the coefficients. Note
that they must all be integers since TEX only performs
integer arithmetic.
To generate a database, simply create a .tex file where all the problems are defined using newproblem or newproblem*, and either \input it at the start of your document if you want to use specific problems, or pass it to \selectrandomly. This package comes with some sample databases, along with some sample documents that use these databases.
{label}
\useproblem{sindiff}{2} would produce the following:
\useproblem{diff:quad}{3}{0}{-2} would produce:
Suppose all the above problems are defined in the file probs.tex, then the following code will create a problem sheet with four questions in it:
\documentclass{article}
\usepackage{probsoln}
\input{probs}
\begin{document}
Differentiate the following functions with respect to $x$:
\begin{enumerate}
\item \useproblem{quaddiff}
\item \useproblem{sindiff}{4}
\item \useproblem{diff:quad}{2}{3}{1}
\item \useproblem{diff:quad}{0}{1}{2}
\end{enumerate}
\end{document}
The answer sheet can then be generated by passing the option
answers to the probsoln package.
To select all problems defined in a database, in the order in
which they were defined, use the command:
selectallproblems{filename}
For example, suppose the problems are defined in the file
easy.tex, then the following will create a problem sheet
which uses all these problems:
\documentclass[a4paper]{article}
\usepackage{probsoln}
\begin{document}
Differentiate the following functions:
\begin{enumerate}
\selectallproblems{easy}
\end{enumerate}
\end{document}
{filename}{n}
\begin{enumerate}
\selectrandomly{easy.tex}{4}
\end{enumerate}
will result in four numbered problems, selected at random
from the file easy.tex. (The .tex extension
may be omitted.) Each problem is followed by the command
endPSNitem which by default does nothing.
Multiple \selectrandomly commands may be used, however a different file must be used each time. For example:
\begin{enumerate}
\item Differentiate the following functions with respect to $x$:
\begin{enumerate}
\selectrandomly{samples/easy.tex}{3}
\selectrandomly{samples/args.tex}{1}
\end{enumerate}
\selectrandomly{samples/implicit.tex}{1}
\selectrandomly{samples/1stprncpl.tex}{1}
\end{enumerate}
This will result in a total of 6 problems, numbered 1(a),
1(b), 1(c), 1(d), 2 and 3.
If a randomly selected problem requires arguments, a message similar to the following will be displayed:
Problem diff:quad requires 3 argument(s), please specify (e.g. {5}{3}):
Enter the required arguments, where each argument is
enclosed in braces ({ }).
{n} specifies
the seed for the random number generator. For example,
if you are using selectrandomly,
\PSNrandseed{\year} will produce a different set of
problems each year, whereas \PSNrandseed{\time}
will produce a different set of problems each time you
LATEX the problem sheet (as long as you leave at least a
minute between runs.)
The command random{counter}{a}{b}
generates a random number from a to b and
stores it in the LATEX counter counter. For example,
to select 2, 3 or 4 problems from the file
implicit.tex:
\newcounter{numproblems}
\begin{enumerate}
\random{numproblems}{2}{4}
\selectrandomly{implicit.tex}{\value{numproblems}}
\end{enumerate}
(Note the use of \value.)
This command can also be used to generate random values for problems that take arguments. Consider the problem diff:quad defined earlier. Three counters can be defined to represent the three coefficients:
\newcounter{A}
\newcounter{B}
\newcounter{C}
Random values can now be assigned to these counters:
\random{A}{-5}{5}
\random{B}{-5}{5}
\random{C}{-5}{5}
Finally, the problem can be used (note the use of \arabic):
\useproblem{diff:quad}{\arabic{A}}{\arabic{B}}{\arabic{C}}
The command
doforrandN{n}{cmd}{list}{text} will apply
text for a random selection of n items in the
comma separated list. In each iteration the list
item is denoted by cmd. For example, suppose you
have three files called file1.tex,
file2.tex and file3.tex, and you want to
select 1 problem from two of the three files, then you can
do:
\doforrandN{2}{\file}{file1,file2,file3}{\selectrandomly{\file}{1}}
Note that it is also possible to do
\newcounter{numproblems}
\random{numproblems}{1}{3}
\selectrandomly{file\arabic{numproblems}}{1}
\random{numproblems}{1}{3}
\selectrandomly{file\arabic{numproblems}}{1}
however there is a possibility that the same file may be
selected twice which will cause an error.
The command showanswers will show the solutions from that point on. May be localised by placing within a group.
The command hideanswers will hide the solutions from that point on. May be localised by placing within a group.
The solution is placed inside the solution
environment. By default this environment simply does
\par\noindent\textbf{\solutionname:} at the start, where
solutionname
has the value: Solution. See the file sample3.tex, which
comes with this package, for an illustration of how to
customise the way in which the randomly selected problems are
displayed. This sample file randomly selects multiple choice
problems stored in the file tabmchoice.tex, and displays them
in a longtable environment. As from version 2.03, the package
will not define this environment if another package or class file has
already defined it.
The boolean variable showanswers is defined to be true if the answers are shown and false otherwise. You can therefore do something like:
\ifthenelse{\boolean{showanswers}}{\textbf{Solution Sheet}}{}
and Solution Sheet will be printed only if the
answers are displayed. (For more information on
\ifthenelse and \boolean see the
documentation for the ifthen package by
David Carlisle.)
The showanswers switch can also be used within the definition of a problem, if you want the question to appear differently if the solution is displayed. For example:
\newproblem{mc:prod}{%
Which of the following is the derivative of $x\sin(x)$?
(Circle the correct answer.)
\ifthenelse{\boolean{showanswers}}{}%
{\begin{description}
\item[A] $\sin(x)$
\item[B] $x\cos(x)$
\item[C] $\sin(x) + x\cos(x)$
\end{description}
}}{%
\begin{description}
\item[A] $\sin(x)$
\item[B] $x\cos(x)$
\item[\textcircled{C}] $\sin(x) + x\cos(x)$ (product rule).
\end{description}
}
If the solutions are not displayed, the question will appear
as
This is probably because you have lots of extraneous white space in your database. selectrandomly will input the entire file, so any extra space will be included. Try commenting out the extra space using %.
Each label identifier used in newproblem must be unique. Check to make sure you haven't used the same label more than once. Also check to make sure you haven't \inputed or randomly selected from the same file more than once. (Or \inputed and randomly selected from the same file.)
You need to define a problem before you can use it. Check to make sure you haven't mis-spelt it, and check to make sure you have \inputed the file in which it is defined.
You have asked for more problems than are defined within the specified file. All problems in that file will be selected.
You have asked to randomly select n items from a list that has less than n elements. For example, the following will generate this error:
\doforrandN{10}{\file}{file1,file2,file3}{%
\selectrandomly{\file}{1}}
In this case the list, file1,file2,file3 has only 3
elements, but the user has asked for 10 elements. If you type
`h' at the LATEX prompt it will tell you how many items it thinks
there are in the list. Remember that each item must be separated by a
comma.
Each problem selected using selectrandomly is proceeded by PSNitem which by default is defined as \item, and should therefore be placed in one of the list environments, such as enumerate. Alternatively, redefine PSNitem.
selectrandomly inputs the database twice, so any command definition will be read twice, causing an error. You can use the switch \iffirstpass to prevent the error. For example:
\iffirstpass
\newcommand{\mycmd}{}
\fi
It is generally not a good idea to put anything other than
newproblem commands within the database.