Nicola L.C. Talbot
School of Computing Sciences
University of East Anglia
Norwich. Norfolk
NR4 7TJ. United Kingdom.
http://theoval.cmp.uea.ac.uk/~nlct/
26th August 2008
In addition to the answers and noanswers package options, it is also possible to show or suppress the solutions using \showanswers and \hideanswers, respectively. The boolean variable showanswers determines whether the answers should be displayed. You can use this value with the ifthen package to specify different text depending on whether the solutions should be displayed. For example:
Assignment 1\ifthenelse{\boolean{showanswers}}{ (Solution Sheet)}{}
Alternatively you can use \ifshowanswers...\else...
\fi:
Assignment 1\ifshowanswers\space (Solution Sheet)\fi
For longer passages, you can use the environments onlyproblem and onlysolution. For example:
\begin{onlyproblem}%
What is the derivative of $f(x) = x^2$?
\end{onlyproblem}%
\begin{onlysolution}%
$f'(x) = 2x$
\end{onlysolution}
The above will only display the question if showanswers
is false and will only display the solution if showanswers
is true. If you want the question to appear in the answer
sheet as well as the solution, then don't put the question in
the onlyproblem environment:
What is the derivative of $f(x) = x^2$?
\begin{onlysolution}%
Solution: $f'(x) = 2x$
\end{onlysolution}
NOTE: You can't use verbatim text in the body of the
onlyproblem or onlysolution environments.
If you need verbatim-like text, then try packages such as
alltt. Remember that you also can't use verbatim
text in command arguments.
The commands and environments described in this section are
provided to assist formatting problems and their solutions.
\begin{solution}text\end{solution}
\par\noindent\textbf{\solutionname}:text
where \solutionname defaults
to "Solution". Note that you must place the solution
environment inside the onlysolution environment or
between \ifshowanswers...\fi to ensure that it
is suppressed when the solutions are not wanted. (See
Showing and
Hiding Solutions.)
Note that the probsoln package will only define the solution environment if it is not already defined.
\begin{textenum}...\end{textenum}
\begin{onlyproblem}%
Differentiate the following:
\begin{textenum}
\item $f(x)=2^x$;
\item $f(x)=\cot(x)$
\end{textenum}
\end{onlyproblem}
\begin{onlysolution}
\begin{enumerate}
\item
\begin{align*}
f(x) &= 2^x = \exp(\ln(x^2)) =\exp(2\ln(x))\\
f'(x) &= \exp(2\ln(x))\times \frac{2}{x}\\
&= f(x)\frac{2}{x}
\end{align*}
\item
\begin{align*}
f(x) &= \cot(x) = (\tan(x))^{-2}\\
f'(x) &= -(\tan(x))^{-2}\times\sec^2(x)\\
&=-\csc^2x
\end{align*}
\end{enumerate}
\end{onlysolution}
In this example, the items in the question are brief, so an
enumerate environment would result in a lot of
unnecessary white space,
but the answers require more space, so an enumerate
environment is more appropriate. Since the textenum
environment uses the same counters as the enumerate
environment, the question and answer sheets use consistent
labelling. Note that there are other packages available on
CTAN that you can use to create in-line lists. Check the
TeX
Catalogue for
further details.
Under which of the following functions does $S=\{a_1,a_2\}$
become a probability space?
\begin{enumerate}
\incorrectitem $P(a_1)=\frac{1}{3}$, $P(a_2)=\frac{1}{2}$
\correctitem $P(a_1)=\frac{3}{4}$, $P(a_2)=\frac{1}{4}$
\correctitem $P(a_1)=1$, $P(a_2)=0$
\incorrectitem $P(a_1)=\frac{5}{4}$, $P(a_2)=-\frac{1}{4}$
\end{enumerate}
It is possible to construct a problem sheet with solutions using the commands described in the previous sections, however it is also possible to define a set of problems for later use. In this way you can create an external file containing many problems some or all of which can be loaded and used in a document. The probsoln package has a default data set labelled "default" in which you can store problems or you can create multiple data sets. You can then iterate through each problem in a problem set. You can use a previously defined problem more than once, which means that by judicious use of onlyproblem, onlysolution or the showanswers boolean variable in conjunction with \showanswers and \hideanswers, you can print the solutions in a different location to the questions (for example in an appendix).
\begin{defproblem}[n]{label}definition\end{defproblem}
If defproblem occurs in the document or is included via \input or \include, then the problem will be added to the default data set. If defproblem occurs in an external file that is loaded using one of the commands defined in Loading Problems From External Files then the problem will be added to the specified data set.
The contents of the defproblem environment should be the text that defines the problem. This may include any of the commands defined in Showing and Hiding Solutions and General Formatting Commands.
The problem may optionally take n arguments (where n is from 0 to 9). The arguments can be referenced in the definition via #1,...,#9. If n is omitted then the problem doesn't take any arguments. The following example defines a problem with one argument:
\begin{defproblem}[1]{diffsin}
Differentiate $f(x)=\sin(#1x)$.
\begin{onlysolution}%
\begin{solution}
$f'(x) = #1\cos(#1x)$
\end{solution}
\end{onlysolution}
\end{defproblem}
\newproblem[1]{diffsin}{%
\(f(x) = \sin(#1x)\)
}{%
\(f'(x) = #1\cos(#1x)\)
}
is equivalent to
\begin{defproblem}[1]{diffcos}%
\(f(x) = \cos(#1x)\)
\begin{onlysolution}%
\begin{solution}%
\(f'(x) = -#1\sin(#1x)\)
\end{solution}%
\end{onlysolution}%
\end{defproblem}
(In this example, the argument will need to be a positive number
to avoid a double minus in the answer. If you want to perform
floating point arithmetic on the arguments, then try the
fp package.)
NOTE: Verbatim text must not be used in the contents of defproblem or in any of the arguments to \newproblem or \newproblem*. If you need verbatim-like text consider using \texttt or the alltt package.
Once you have defined a problem using defproblem or
\newproblem (see
Defining a
Problem), you can later display the problem
using:
For example, in the previous section the problem diffcos was defined to have one argument, so it can be used as follows:
\useproblem{diffcos}{3}
This will be equivalent to:
\(f(x) = \cos(3x)\)
\begin{onlysolution}%
\begin{solution}%
\(f'(x) = -3\sin(3x)\)
\end{solution}%
\end{onlysolution}%
You can store all your problem definitions (see Defining New Problems) in an external file. These problems can all be appended to the default data set by including the file via \input or they can be appended to other data sets using one of the commands described below. Once you have loaded all the required problems, you can iterate through the data sets using the commands described in Iterating Through Datasets. Note that the commands below will create a new data set, if the named data set doesn't exist.
\loadselectedproblems{diffsin,diffcos}{derivatives}
will only load the problems whose labels are diffsin
and diffcos, respectively. All the other problems in
the file will remain undefined.
NOTE: It is generally not a good idea to place anything in filename that is not inside the body of defproblem or in the arguments to \newproblem or \newproblem*. All the commands in this section input the external file within a local scope, so commands definitions would need to be made global to have any effect. In addition, \loadrandomproblems has to load each file twice, which means that anything outside a problem definition will be parsed twice.
Once you have defined all your problems for a given data set, you can use an individual problem with \useproblem (see Using a Problem) but it is more likely that you will want to iterate through all the problems so that you don't need to remember the labels of all the problems you have defined.
\begin{enumerate}
\foreachproblem{\item\thisproblem}
\end{enumerate}
\begin{enumerate}
\foreachdataset{\thisdataset}{%
\foreachproblem[\thisdataset]{\item\thisproblem}}
\end{enumerate}
Suppose I have two external files called derivatives.tex and probspaces.tex which define problems using both onlyproblem and onlysolution for example:
\begin{defproblem}{cosxsqsinx}%
\begin{onlyproblem}%
$y = \cos(x^2)\sin x$.%
\end{onlyproblem}%
\begin{onlysolution}%
\[\frac{dy}{dx} = -\sin(x^2)2x\sin x + \cos(x^2)\cos x\]
\end{onlysolution}%
\end{defproblem}
I can write a document that creates two data sets, one for
the derivative problems and one for the problems about
probability spaces. I can then use \hideanswers and
iterate through the require data set to produce the problems.
Later, I can use \showanswers and iterate over all problems defined in both data
sets to produce the chapter containing all the answers. When
displaying the questions, I have taken advantage of the fact that
I can cross-reference items within an enumerate environment,
and redefined \theenumi to label the questions according to
the chapter. The cross-reference label is constructed from
the problem label and is referenced in the answer section to
ensure that the answers have the same label as the questions.
\documentclass{report}
\usepackage{probsoln}
\begin{document}
\hideanswers
\chapter{Differentiation}
% randomly select 25 problems from derivatives.tex and add to
% the data set called 'deriv'
\loadrandomproblems[deriv]{25}{derivatives}
% Display the problems
\renewcommand{\theenumi}{\thechapter.\arabic{enumi}}
\begin{enumerate}
\foreachproblem[deriv]{\item\label{prob:\thisproblemlabel}\thisproblem}
\end{enumerate}
% You may need to change \theenumi back here
\chapter{Probability Spaces}
% randomly select 25 problems from probspaces.tex and add to
% the data set called 'spaces'
\loadrandomproblems[spaces]{25}{probspaces}
% Display the problems
\renewcommand{\theenumi}{\thechapter.\arabic{enumi}}
\begin{enumerate}
\foreachproblem[spaces]{\item\label{prob:\thisproblemlabel}\thisproblem}
\end{enumerate}
% You may need to change \theenumi back here
\appendix
\chapter{Solutions}
\showanswers
\begin{itemize}
\foreachdataset{\thisdataset}{%
\foreachproblem[\thisdataset]{\item[\ref{prob:\thisproblemlabel}]\thisproblem}
}
\end{itemize}
\end{document}
This package provides a pseudo-random number generator that is used by \loadrandomproblems.
\PSNrandseed{\time}
or to generate a different set of random numbers every year you
LaTeX your document:
\PSNrandseed{\year}
\newcount\myseed
\PSNgetrandseed{\myseed}
\newcount\myreg
\PSNrandom{\myreg}{10}
\newcounter{myrand}
\random{myrand}{3}{8}
\doforrandN{2}{\thisfile}{file1,file2,file3}{%
\loadrandomproblems{1}{\thisfile}}
Version 3.0 of the probsoln package completely changed the structure of the package, but the commands described in this section have been provided to maintain compatibility with earlier versions. The only problems that are likely to occur are those where commands are contained within groups. This will effect any commands that are contained in external files that are outside of the arguments to \newproblem and \newproblem*. However, since the external files had to be parsed twice in order to load the problems, this shouldn't be an issue as adding anything other than problem definitions in those files would be problematic anyway.
The other likely difference is where the random generator is used in a group. This includes commands such as \selectrandomly. For example, if your document contained something like:
\begin{enumerate}
\selectrandomly{file1}{8}
\item Solve the following:
\begin{enumerate}
\selectrandomly{file2}{4}
\end{enumerate}
\selectrandomly{file3}{2}
\end{enumerate}
Then using versions prior to v3.0 will produce a different
set of random numbers since the second \selectrandomly
is in a different level of grouping. If you want to ensure
that the document produces exactly the same random set with
the new version as with the old version, you will need to
get and set the random number seed. For example, the above
would need to be modified so that it becomes:
\begin{enumerate}
\selectrandomly{file1}{8}
\item Solve the following:
\newcount\oldseed
\PSNgetrandseed{\oldseed}
\begin{enumerate}
\selectrandomly{file2}{4}
\end{enumerate}
\PSNrandseed{\oldseed}
\selectrandomly{file3}{2}
\end{enumerate}
Note that in both the above cases, a new data set is created with the same name as the file name.