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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/exam-n/sample
Initial commit
Diffstat (limited to 'macros/latex/contrib/exam-n/sample')
-rw-r--r--macros/latex/contrib/exam-n/sample/Makefile23
-rw-r--r--macros/latex/contrib/exam-n/sample/cosmo1.tex93
-rw-r--r--macros/latex/contrib/exam-n/sample/cosmo2.tex60
-rw-r--r--macros/latex/contrib/exam-n/sample/cosmo3.tex50
-rw-r--r--macros/latex/contrib/exam-n/sample/dynamical1.tex96
-rw-r--r--macros/latex/contrib/exam-n/sample/dynamical2.tex24
-rw-r--r--macros/latex/contrib/exam-n/sample/dynamical3.tex59
-rw-r--r--macros/latex/contrib/exam-n/sample/excos1.tex46
-rw-r--r--macros/latex/contrib/exam-n/sample/fig/spiral.eps22
-rw-r--r--macros/latex/contrib/exam-n/sample/fig/spiral.pdfbin0 -> 1799 bytes
-rw-r--r--macros/latex/contrib/exam-n/sample/numerical1-solution.tex21
-rw-r--r--macros/latex/contrib/exam-n/sample/numerical1.tex58
-rw-r--r--macros/latex/contrib/exam-n/sample/numerical2.tex44
-rw-r--r--macros/latex/contrib/exam-n/sample/numerical3.tex46
-rw-r--r--macros/latex/contrib/exam-n/sample/sample_exam.tex65
-rw-r--r--macros/latex/contrib/exam-n/sample/sample_exam_solution.tex65
-rw-r--r--macros/latex/contrib/exam-n/sample/sample_mcq.tex87
17 files changed, 859 insertions, 0 deletions
diff --git a/macros/latex/contrib/exam-n/sample/Makefile b/macros/latex/contrib/exam-n/sample/Makefile
new file mode 100644
index 0000000000..253245e534
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/Makefile
@@ -0,0 +1,23 @@
+%.pdf: %.tex ../exam-n.cls
+ TEXINPUTS=..: pdflatex $<
+ if grep 'Rerun to get cross' ${<:.tex=.log}; then TEXINPUTS=..: pdflatex $<; else :; fi
+
+all: sample_exam.pdf
+
+sample_exam.pdf: numerical1-solution.pdf
+
+sample_exam_solution.pdf: sample_exam_solution.tex
+
+sample_exam_solution.tex: sample_exam.tex
+ rm -f $@
+ sed '1s/documentclass/documentclass[showsolutions]/' sample_exam.tex >sample_exam_solution.tex
+
+# This will depend somehow on the .dtx file in the parent directory,
+# but expressing that here second-guesses how that file is actually
+# generated, so skip this ('don't repeat yourself'; also, this is only
+# occasionally used while testing)
+../exam-n.cls:
+ cd ..; $(MAKE) exam-n.cls
+
+clean:
+ rm -f *.pdf *.log *.aux sample_exam_solution.tex
diff --git a/macros/latex/contrib/exam-n/sample/cosmo1.tex b/macros/latex/contrib/exam-n/sample/cosmo1.tex
new file mode 100644
index 0000000000..27045d026a
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/cosmo1.tex
@@ -0,0 +1,93 @@
+\documentclass[compose]{exam-n}
+
+\usepackage{graphics}
+\graphicspath{{fig/}}
+
+\begin{document}
+
+\begin{question}{20} \author{Reginald Q Whimsy}
+% Have a blank line here, to check that the question number remains
+% nicely lined up, even if there are lines between the environment
+% opening and the text.
+
+First, \emph{admire} the restful picture of a spiral in Fig.\ \ref{f:spiral},
+included as a graphic. Fully zenned up? Then let us begin\dots.
+\begin{figure}
+\ifbigfont
+ \includegraphics[width=\textwidth]{spiral}
+\else
+ \includegraphics{spiral}
+\fi
+\caption{\label{f:spiral}A spiral}
+\end{figure}
+
+\part Show that, under the action of gravity alone, the scale size
+of the Universe varies according to
+\begin{equation}
+\ddot{R}=-\frac{4\pi G \rho_0}{3R^2}
+\end{equation}
+\partmarks*{4}
+and that, consequently,
+\begin{equation*}
+\dot{R}^2=-\frac{8\pi G \rho_0}{3R}=-K.
+\partmarks*{3}
+\end{equation*}
+
+Express $K$ in terms of the present values of the Hubble constant
+$H_0$ and of the density parameter $\Omega_0$.
+\partmarks{3}
+\begin{solution}
+This can be solved by \emph{remembering} the solution
+\partmarks{3}
+\end{solution}
+
+\part In the early Universe, the relation between time and
+temperature has the form
+\begin{equation*}
+t=\sqrt{\frac{3c^2}{16\pi G g_{\rm eff}a}}\frac{1}{T^2},
+\end{equation*}
+where $a$ is the radiation constant. Discuss the assumptions
+leading to this equation, but do not carry out the mathematical
+derivation. Discuss the meaning of the factor $g_{\rm eff}$ , and
+find its value just before and after annihilation of electrons and
+positrons.
+\partmarks{6}
+\begin{solution}
+Before, well, geee; after\dots kazamm!
+\end{solution}
+
+\part
+Explain how the present-day neutron/proton ratio was established
+by particle interactions in the Early Universe. How is the ratio
+of deuterium to helium relevant to the nature of dark matter? It is
+\emph{crucially vital} to note
+that Table~\ref{t:dullness} is of absolutely no relevance to this question.
+\begin{table}
+\begin{tabular}{r|l}
+Column 1&and row 1\\
+More content&in row 2
+\end{tabular}
+\caption{\label{t:dullness}A remarkably dull table}
+\end{table}
+Finis.
+\begin{questiondata}
+Hubble's law: $v=H_0 D$
+\end{questiondata}
+\partmarks{4}
+\begin{solution}
+Explanations are superfluous; all that is, is.
+\begin{table}
+\begin{tabular}{r|l}
+First rows&are premier\\
+subsequent rows&are of secondary interest
+\end{tabular}
+\caption{\label{t:dullnessII}A table o'erbrimming with otioseness}
+\end{table}
+In addition, Table~\ref{t:dullnessII} adds nothing to the discussion,
+adds nothing to our understanding of our place in the cosmos, but it
+\emph{does} contribute slightly to the heat-death of the universe (can
+you work out how many deuterium nuclei decayed during the typing of
+this table?).
+\end{solution}
+\end{question}
+\end{document}
diff --git a/macros/latex/contrib/exam-n/sample/cosmo2.tex b/macros/latex/contrib/exam-n/sample/cosmo2.tex
new file mode 100644
index 0000000000..bb6c512b9d
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/cosmo2.tex
@@ -0,0 +1,60 @@
+\documentclass[compose]{exam-n}
+\begin{document}
+
+\begin{question}{30} \comment{by John Brown}
+Show by considering the Newtonian rules of vector and velocity
+addition that in Newtonian cosmology the cosmological principle
+demands Hubble's Law $v_r\propto r$.\partmarks{10}
+
+Prove that, in Euclidean geometry, the number $N(F)$ of objects
+of identical luminosity $L$, and of space density $n(r)$ at
+distance $r$, observed with radiation flux $\ge F$ is (neglecting
+other selection and redshift effects)
+\begin{equation*}
+N(F)=4\pi\int_0^{(\frac{L}{4\pi F})^{1/2}} n(r) r^2\ddd r.
+\end{equation*}
+\partmarks*{5}
+
+Use this to show that for $n=n_1=$constant at $r<r_1$ and
+$n=n_2=$constant at $r>r_1$,
+\begin{equation*}
+N(F) = N_1\left(\frac{F}{F_1}\right)^{-3/2}\qquad \text{for
+$F>F_1$},
+\end{equation*}
+and
+\ifbigfont
+ \begin{multline*}
+ N(F) =
+ N_1\left\{1+\frac{n_2}{n_1}\left[\left(\frac{F}{F_1}\right)^{-3/2}-1\right]
+ \right\}\\\text{for $F<F_1$},
+ \end{multline*}
+\else
+ \begin{equation*}
+ N(F) =
+ N_1\left\{1+\frac{n_2}{n_1}\left[\left(\frac{F}{F_1}\right)^{-3/2}-1\right]
+ \right\} \qquad \text{for $F<F_1$},
+ \end{equation*}
+\fi
+where $F_1=L/4\pi r_1^2$, $N_1=N(F_1)=\frac{4}{3}\pi r_1^3 n_1$.
+\partmarks{9}
+
+Reduce these two expressions to the result for a completely
+uniform density universe with $n_1=n_2=n_0$.
+\partmarks{3}
+
+% An itemized list followed by partmarks*
+Sketch how $n(F)$ would look in universes which are
+\begin{itemize}
+\item flat,
+\item open,
+\item and closed.
+\end{itemize}
+\partmarks*{3}
+
+\begin{solution}
+A sufficiently heavy weight will reduce expressions to completely
+uniform sheets of paper if it is placed on top of them.\partmarks3
+In a flat universe, $n(F)$ will look like n(F).\partmarks*3
+\end{solution}
+\end{question}
+\end{document}
diff --git a/macros/latex/contrib/exam-n/sample/cosmo3.tex b/macros/latex/contrib/exam-n/sample/cosmo3.tex
new file mode 100644
index 0000000000..b7b74c0107
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/cosmo3.tex
@@ -0,0 +1,50 @@
+\documentclass[compose]{exam-n}
+\begin{document}
+
+\begin{question}{30} \comment{by Andrew Davies}
+
+The Friedmann equations are written, in a standard notation,
+\begin{gather*}
+H^2 = \frac{8\pi G\rho}{3}-\frac{kc^2}{R^2}+\frac{\Lambda}{3},\\
+\Diffl {}t (\rho c^2R^3)=-p\Diffl {R^3}t,
+\end{gather*}
+Discuss briefly the meaning of each of $H$, $\rho$ , $k$ and
+$\Lambda$. \partmarks{4}
+
+Suppose the Universe consists of a single substance with equation
+of state $p=w\rho c^2$, where $ w=$constant. Consider the
+following cases, with $k=\Lambda=0$:
+
+\part For $w = 0$, find the relation between $R$ and $\rho$. Hence
+show that $H=\frac{2}{3t}$. What is the physical interpretation of
+this case?
+\partmarks{8}
+
+\part In the case $w=-1$ , show that $H = $constant and $R = A \exp(Ht)$,
+with $A$ constant.
+\partmarks{4}
+
+\part Explain how the case, $w=-1$, $k=\Lambda=0$, $\rho=0$ is
+equivalent to an empty, flat, Universe with a non-zero $\Lambda$.
+\partmarks{2}
+
+\part Consider a model Universe which contained matter with equation
+of state with $w = 0$ for $0 < t < t_0$, but which changes to
+$W=0$ for $t\ge t_0$ without any discontinuity in $H(t)$.
+Regarding this second stage as driven by a non-zero $\Lambda$ what
+is the value of $\Lambda$ if $t_0 = 10^{24}$\units{\mu s}? Define the
+dimensionless deceleration parameter, $q$, and find its value
+before and after $t_0$.
+\shout{Shout it loud: I'm a geek and I'm proud}
+\partmarks{8}
+
+Note: that's
+\[
+t_0=10^{24}\units{\mu s}\qquad\text{with a letter mu: $\mu$}.
+\]
+
+\part To what extent does this idealized model resemble the currently
+accepted picture of the development of our Universe?
+\partmarks{4}
+\end{question}
+\end{document}
diff --git a/macros/latex/contrib/exam-n/sample/dynamical1.tex b/macros/latex/contrib/exam-n/sample/dynamical1.tex
new file mode 100644
index 0000000000..e3a51a803b
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/dynamical1.tex
@@ -0,0 +1,96 @@
+\documentclass[compose]{exam-n}
+
+\begin{document}
+
+\begin{question}{20} \author{John Brown and Declan Diver}
+\part An earth satellite in a highly eccentric orbit of (constant)
+perigee distance $q$ undergoes a targential velocity impulse
+$-\Delta V$ at each perigee passage. By considering the mean rate
+of change of velocity at perigee, show that the mean rate of
+change of the semi-major axis $a$ ($\gg q$) satisfies
+\begin{equation*}
+\frac{1}{a^2} \Diffl at =
+\left(\frac{8}{GMq}\right)^{1/2}\frac{\Delta V}{T},
+\end{equation*}
+where $M$ is the Earth's mass and $T$ the orbital period.
+\partmarks{3}
+\begin{questiondata}
+You may assume $\displaystyle v^2(r)=GM\left(\frac{2}{r}-\frac{1}{a}\right)$.
+\end{questiondata}
+
+Using $T=2\pi(a^3/GM)^{1/2}$ show that with $a_0=a(0)$, (where
+$a(t)$ is the semimajor axis at time $t$)
+\begin{equation*}
+\frac{a(t)}{a_0}=\left[1-\frac{t\Delta V}{2^{1/2}\pi
+a_0(1-e_0)^{1/2}}\right]^2
+\end{equation*}
+\partmarks*{2}
+and
+\begin{equation*}
+\frac{T(t)}{T_0}=\left[1-\frac{t\Delta V}{2^{1/2}\pi
+a_0(1-e_0)^{1/2}}\right]^3
+\end{equation*}
+\partmarks*{1}
+and the eccentricity satisfies (with $e_0=e(0)$)
+\begin{equation*}
+e(t)=1-\frac{1-e_0}{\left[1-\frac{t\Delta V}{2^{1/2}\pi
+a_0(1-e_0)^{1/2}}\right]^2}.
+\end{equation*}
+\partmarks*{2}
+
+Show that, once the orbit is circular, its radius decays
+exponentially with time on timescale $m_0/2\dot{m}$ where $m_0$
+is the satellite mass and $\dot{m}$ the mass of atmosphere
+`stopped' by it per second. \partmarks{2}
+
+\part What is meant by (a) the sphere of influence of a star, and
+(b) the passage distance?
+\partmarks{2}
+
+Consider a system of $N$ identical stars, each of mass $m$.
+
+\part Given that the change $\delta u$ in the speed of one such star
+due to the cumulative effect over time $t$ of many gravitational
+encounters with other stars in the system can be approximated by
+\begin{equation*}
+(\delta u)^2 \propto [\nu tm^2\log(p_{\rm max}/p_{\rm
+min})]/\bar{u},
+\end{equation*}
+where $\bar{u}$ is the rms mutual speed, $\nu$ is the stellar
+number density, and $p_{\rm max, min}$ are the maximum, minimum
+passage distances for the system, show that this leads to a natural
+time $T$ for the system, where
+\begin{equation*}
+T\propto\frac{\bar{u}u^2}{m^2\nu\log N}.
+\end{equation*}
+\partmarks*{5}
+
+\begin{questiondata}
+You may assume that the sphere of influence radius of a star is
+approximated by $(m/M)^{2/5}R$ where $R$ and $M$ are the radius
+and mass of the whole system respectively.
+\end{questiondata}
+
+\part Deduce that $T$ is the disintegration timescale for the system,
+by showing that a star with initial speed $u_0$ in a stable circular
+orbit reaches escape speed after time $T$.
+\partmarks{3}
+
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+Dummy text, to lengthen the question to the extent that it spreads across three pages.
+\end{question}
+\end{document}
diff --git a/macros/latex/contrib/exam-n/sample/dynamical2.tex b/macros/latex/contrib/exam-n/sample/dynamical2.tex
new file mode 100644
index 0000000000..517ae84920
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/dynamical2.tex
@@ -0,0 +1,24 @@
+\documentclass[final]{exam-n}
+\begin{document}
+
+\begin{question}{30} \comment{by John Brown}
+Give the equations of motion for $i=1,\ldots, N$ particles of
+masses $m_i$ and positions $r_i(t)$ under the action of mutual
+gravity alone in an arbitrary inertial frame.
+\partmarks{4}
+
+Use these to derive the following conservation laws of the system:
+
+\part Constancy of linear momentum -- i.e., centre of mass fixed in a
+suitable inertial frame. \partmarks{4}
+ \part Constancy of angular momentum. \partmarks{6}
+ \part Constancy of total energy. \partmarks{8}
+
+How many integrals of motion exist in total?
+\partmarks{2}
+
+Derive the moment of inertia of the system and demonstrate its
+relevance to criteria for escape of particles from the system.
+\partmarks{6}
+\end{question}
+\end{document}
diff --git a/macros/latex/contrib/exam-n/sample/dynamical3.tex b/macros/latex/contrib/exam-n/sample/dynamical3.tex
new file mode 100644
index 0000000000..abc51017ea
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/dynamical3.tex
@@ -0,0 +1,59 @@
+\documentclass[compose]{exam-n}
+\begin{document}
+
+\begin{question}{30} \comment{by Declan Diver}
+For a system of $N$ objects, each having mass $m_i$ and position
+vector $\mathbf{R}_i$ with respect to a fixed co-ordinate system,
+use the moment of inertia
+\[
+I=\sum_{i=1}^N m_i R_i^2
+\]
+to deduce the virial theorem in the forms
+\[
+\ddot{I}=4E_k+2E_G=2E_k+2E
+\]
+where $E_k$ and $E_G$ are respectively the total kinetic and
+gravitational potential energy, and $E$ is the total energy of
+the system.
+\partmarks{8}
+
+Given the inequality
+\ifbigfont
+ \begin{multline*}
+ \left(\sum_{i=1}^N
+ a_i^2\right) \left(\sum_{i=1}^N b_i^2\right) \\
+\ge \left(\sum_{i=1}^N \mathbf{a}_i\cdot\mathbf{b}_i\right)^2 \\
++ \left(\sum_{i=1}^N \mathbf{a}_i\times\mathbf{b}_i\right)^2
+ \end{multline*}
+\else
+ \begin{equation*}
+ \left(\sum_{i=1}^N
+ a_i^2\right) \left(\sum_{i=1}^N b_i^2\right) \ge \left(\sum_{i=1}^N
+ \mathbf{a}_i\cdot\mathbf{b}_i\right)^2 + \left(\sum_{i=1}^N
+ \mathbf{a}_i\times\mathbf{b}_i\right)^2
+ \end{equation*}
+\fi
+for arbitrary vectors $\mathbf{a}_i$, $\mathbf{b}_i$,
+$i=1,\ldots,N$, deduce the following relationship for the $N$-body
+system
+\begin{equation*}
+\frac{1}{4}\dot{I}^2+J^2\le 2IE_k,
+\end{equation*}
+where $\mathbf{J}$ is the total angular momentum of the system.
+\partmarks{8}
+
+Assuming the system is isolated, use the virial theorem to deduce
+further the generalised Sundman inequality
+\begin{equation*}
+\frac{\dot{\sigma}}{\dot{\rho}}\ge 0,
+\end{equation*}
+in which $\rho^2=I$ and
+$\displaystyle\sigma=\rho\dot{\rho}^2+\frac{J^2}{\rho}-2\rho E $.
+\partmarks{8}
+
+Why does this inequality preclude the possibility of an
+$N$-fold collision for a system with finite angular momentum?
+\partmarks{6}
+
+\end{question}
+\end{document}
diff --git a/macros/latex/contrib/exam-n/sample/excos1.tex b/macros/latex/contrib/exam-n/sample/excos1.tex
new file mode 100644
index 0000000000..511902dc1a
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/excos1.tex
@@ -0,0 +1,46 @@
+\documentclass[compose]{exam-n}
+
+\multiplechoiceanswers{4}
+
+\begin{document}
+
+\begin{mcq}
+In 1908, where was there an airburst `impact'?
+\answer Tunguska
+\item Arizona
+\item Off the Mexican coast
+\item Swindon
+\begin{solution}
+The evidence for this is a dirty big hole in the ground in Siberia.
+\end{solution}
+\end{mcq}
+
+\begin{mcq}
+The fossil record suggests that mass extinction events occur once every how many years?
+\item 2.6 Billion Years
+\item 260 Million Years
+\item 26 Million Years % not marked as correct
+\item 4 Thousand Years after the dominant lifeform invents fire
+\end{mcq}
+
+\begin{mcq}
+The habitable zone of our Solar system extends over what distances from the Sun?
+\answer 0.6--1.5 AU
+\item 6--15 AU
+\item 60--150 AU
+\item 600--1500 AU
+% excess item, and a second \answer...
+\answer From the little bear's bed all the way through to daddy bear's
+ bed. This is known as the `Goldilocks zone'.
+\end{mcq}
+
+\begin{mcq}
+If the temperature of the Sun were to increase by 10\%, how would the
+position of the solar habitable zone change?
+\item It would move closer to the Sun.
+\answer It would move further from the Sun.
+\item It would move to Stornoway.
+%\item There would no longer be a habitable zone.
+\end{mcq}
+
+\end{document}
diff --git a/macros/latex/contrib/exam-n/sample/fig/spiral.eps b/macros/latex/contrib/exam-n/sample/fig/spiral.eps
new file mode 100644
index 0000000000..fcf91bb97d
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/fig/spiral.eps
@@ -0,0 +1,22 @@
+%!PS-Adobe-3.0 EPSF-3.0
+% Shrinking squares, cgl Feb 97
+% Adapted from http://www.ntg.nl/maps/pdf/19_12.pdf
+% this version...
+%%Creator: norman@astro.gla.ac.uk
+%%BoundingBox: 0 0 200 125
+/b 0.6180339887 def % (\sqrt5-1)/2
+/x 200 def
+/y x b mul def
+/square {
+ 0 y lineto y y lineto y 0 lineto
+ y 0 y 180 90 arcn y y translate
+} def
+0.35 setlinewidth
+16 {
+ 0 0 moveto square -90 rotate
+ /x y def /y x b mul def
+} repeat
+stroke
+
+%showpage
+
diff --git a/macros/latex/contrib/exam-n/sample/fig/spiral.pdf b/macros/latex/contrib/exam-n/sample/fig/spiral.pdf
new file mode 100644
index 0000000000..0119b77d38
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/fig/spiral.pdf
Binary files differ
diff --git a/macros/latex/contrib/exam-n/sample/numerical1-solution.tex b/macros/latex/contrib/exam-n/sample/numerical1-solution.tex
new file mode 100644
index 0000000000..b8862899a1
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/numerical1-solution.tex
@@ -0,0 +1,21 @@
+\documentclass{article}
+\usepackage{color}
+\begin{document}
+\color{red}
+\noindent This page and the following two should appear on separate pages (as
+opposed to superimposed on each other), and disappear when the
+noshowsolutions option is present.
+
+(In the real situation, the corresponding PDF would be a scan of a hand-written
+solution.)
+
+\fontsize{72}{72}\selectfont
+\centering
+Numerical 1 solution, page one
+\newpage
+\null\vskip\baselineskip
+Numerical 1 solution, page two
+\newpage
+\null\vskip2\baselineskip
+Numerical 1 solution, page three
+\end{document}
diff --git a/macros/latex/contrib/exam-n/sample/numerical1.tex b/macros/latex/contrib/exam-n/sample/numerical1.tex
new file mode 100644
index 0000000000..98157ebf68
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/numerical1.tex
@@ -0,0 +1,58 @@
+\documentclass[compose]{exam-n}
+\begin{document}
+
+\begin{question}{20} \author{Graham Woan}
+
+\part The recently-launched \emph{Swift} Gamma Ray Burst telescope is
+expected to detect about 200 bursts of gamma rays during its
+2-year lifespan. Explain why the Poisson distribution,
+\begin{equation*}
+P(n|\lambda)=\exp(-\lambda)\lambda^n /n!
+\end{equation*}
+is appropriate to describe the probability of detecting $n$
+bursts, and carefully explain the significance of the parameter
+$\lambda$. Table~\ref{t:excess} has absolutely nothing to do with
+this question, and its presence here is proof positive of the existence of
+aliens who wish to do us typographical harm.\partmarks{4}
+
+% This table is here to check that the table in the _solution_ to the
+% previous question doesn't cause the table counter to be
+% incremented. This should be Table 2, whether or not solutions are
+% being shown.
+\begin{table}
+\begin{centering}
+\begin{tabular}{r|l}
+\hline
+left&right\\
+\hline
+\end{tabular}
+\caption{\label{t:excess}This is a table}
+\end{centering}
+\end{table}
+
+Given the above, estimate the probability that \emph{Swift} will
+detect more than three bursts on any particular calendar day.
+% Fill up the line, so that we check that (default) \partmarks doesn't
+% include \@partmarksspace, since (default) \partmarks is now fully in
+% the margin.
+Blah. Blah. Blaah. Fill the line.\partmarks{6}
+
+\part Explain how Bayesian inference uses the observed number of
+bursts to infer the true burst rate at the sensitivity limit of
+\emph{Swift}, and explain the significance of the posterior
+probability distribution for $\lambda$. \partmarks{5}
+\begin{solution}
+\includepdf[pages=-]{numerical1-solution.pdf}
+\end{solution}
+
+Assuming that the posterior, $p$, for $\lambda$ can be
+approximated as a gaussian, show that, quite generally, the
+uncertainty in $\lambda$ inferred from \emph{Swift} will be
+\begin{equation*}
+\sigma \simeq \left( -\frac{\partial^2\ln p}{\partial
+\lambda^2}\Big|_{\lambda_0} \right)^{-1/2},
+\end{equation*}
+where $\lambda_0$ is the most probable value of $\lambda$.
+\partmarks{5}
+\end{question}
+\end{document}
diff --git a/macros/latex/contrib/exam-n/sample/numerical2.tex b/macros/latex/contrib/exam-n/sample/numerical2.tex
new file mode 100644
index 0000000000..0843f1bc6e
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/numerical2.tex
@@ -0,0 +1,44 @@
+\documentclass[compose]{exam-n}
+\begin{document}
+
+\begin{question}{30} \comment{by Graham Woan}
+Two variables, $A$ and $B$, have a joint Gaussian probability
+distribution function (pdf) with a negative correlation
+coefficient. Sketch the form of this function as a contour plot
+in the $AB$ plane, and use it to distinguish between the most
+probable joint values of $(A,B)$ and the most probable value of
+$A$ given (a different) $B$. \partmarks{5}
+
+\label{q:numerical2}
+Note that this is question \ref{q:numerical2} on p.\pageref{q:numerical2}.
+
+Explain what is meant by \emph{marginalisation} in Bayesian
+inference and how it can be interpreted in terms the above plot.
+\partmarks{5}
+
+Doppler observations of stars with extrasolar planets give us data
+on $m\sin i$ of the planet, where $m$ is the planet's mass and
+$i$ the angle between the normal to the planetary orbit and the
+line of sight to Earth (i.e. the orbital inclination), which can
+take a value between 0 and $\pi/2$ .
+
+Assuming that planets can orbit stars in any plane, show that the
+probability distribution for $i$ is $p(i) = \sin i$.
+\partmarks{5}
+
+A paper reports a value for $m\sin i$ of $x$, subject to a Gaussian
+error of variance $\sigma^2$. Assuming the mass has a uniform
+prior, show that the posterior probability distribution for the mass
+of the planet is
+\begin{equation*}
+p(m|x)\propto\int_0^1\exp\left[-\frac{\left(x-m\sqrt{1-\mu^2}\right)^2}{2\sigma^2}\right]
+\ddd \mu,
+\end{equation*}
+where $\mu=\cos i$.
+\partmarks{9}
+
+Determine the corresponding expression for the posterior pdf of
+$\mu$, and explain how both are normalised.
+\partmarks{6}
+\end{question}
+\end{document}
diff --git a/macros/latex/contrib/exam-n/sample/numerical3.tex b/macros/latex/contrib/exam-n/sample/numerical3.tex
new file mode 100644
index 0000000000..2354c5db6f
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/numerical3.tex
@@ -0,0 +1,46 @@
+\documentclass[compose]{exam-n}
+\begin{document}
+
+\begin{question}{30} \comment{by Graham Woan}
+Distinguish between frequentist and Bayesian definitions of
+probability, and explain carefully how parameter estimation is
+performed in each regime.\partmarks{10}
+
+\label{q:numerical3}
+Note that this is question \ref{q:numerical3} on
+p.\pageref{q:numerical3}. It's the one after question~\ref{q:numerical2}.
+
+A square ccd with $M\times M$ pixels takes a dark frame for
+calibration purposes, registering a small number of electrons in
+each pixel from thermal noise. The probability of there being $n_i$
+electrons in the $i$th pixel follows a Poisson distribution, i.e.
+\begin{equation*}
+ P(n_i|\lambda) = \exp(-\lambda)\lambda^{n_i}/n_i!,
+\end{equation*}
+where $\lambda$ is the same constant for all pixels. Show that the
+expectation value of is $\langle n_i \rangle = \lambda$.
+\partmarks{5} [You may assume the relation $\sum_0^\infty \frac{x^n}{n!}=\exp(x)$.]
+
+Show similarly that
+\begin{equation*}
+ \langle n_i(n_i-1) \rangle = \lambda^2.
+\end{equation*}
+and hence, or otherwise, that the variance of $n_i$ is also
+$\lambda$.
+\partmarks{5}
+
+The pixels values are summed in columns. Show that these sums,
+$S_j$, will be drawn from a parent probability distribution that is
+approximately
+\begin{equation*} p(S_j|\lambda)=\frac{1}{\sqrt{2\pi
+M\lambda}}\exp\left[-\frac{(S_j-M\lambda)^2}{2M\lambda}\right],
+\end{equation*}
+clearly stating any theorems you use.
+\partmarks{5}
+
+Given the set of $M$ values $\{S_j\}$, and interpreting the above
+as a Bayesian likelihood, express the posterior probability for
+$\lambda$, justifying any assumptions you make.
+\partmarks{5}
+\end{question}
+\end{document}
diff --git a/macros/latex/contrib/exam-n/sample/sample_exam.tex b/macros/latex/contrib/exam-n/sample/sample_exam.tex
new file mode 100644
index 0000000000..98031e6091
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/sample_exam.tex
@@ -0,0 +1,65 @@
+\documentclass{exam-n}
+%\documentclass[largefont]{exam-n}
+%\documentclass[hugefont,sansserif]{exam-n}
+%\documentclass[mtpro2,showsolutions]{exam-n}
+%\documentclass[mtpro2,showsolutions,sansserif]{exam-n}
+%\documentclass[draft,showsolutions,sansserif]{exam-n}
+
+% Note: this sample question dates from an earlier phase, in which
+% `paper n' would contain a bundle of questions from various courses.
+% That's why the \coursetitle doesn't match the broad range of
+% subjects being 'examined'.
+%
+% Several of the questions are gibberish.
+%
+% This collection of questions has in part turned into an informal
+% regression test for the class file.
+
+\examdate{Wednesday, 23 May 2007}
+\examtime{9:30 -- 10:45 (1 course)\\9:30 -- 12:00 (2 courses)}
+
+\exambanner{Examination for the degrees of \BSc\,
+ \MSci\ and \MA\ on the honours standard }
+
+\degreedescriptions{Physics 3\\Chemical Physics 3\\Physics with
+ Astrophysics 3\\Theoretical Physics 3M\\Joint Physics 3}
+\schoolcoursecode{P304D and P304H}
+\universitycoursecode{PHYS3031 and PHYS4025}
+\coursetitle{Quantum Mechanics}
+
+\usepackage{pdfpages}
+
+\rubric{Candidates should answer Questions 1 and 2 (10~marks each),
+ \linebreak\textbf{and either} Question 3 \textbf{or} Question 4 (30~marks).
+ \linebreak The content of this sample exam derives from real
+ questions, but the result is in many cases test gibberish.}
+%\norubric
+
+\numquestions{13}
+
+\usepackage{graphicx} % for graphic in dynamical1
+
+\begin{document}
+\maketitle
+
+\section{I}
+\includequestion{cosmo1}
+\includequestion{numerical1}
+\includequestion{dynamical1}
+
+\section{II}
+\includequestion{cosmo2}
+\subsection{Cosmology question number 3}
+\includequestion{cosmo3}
+\includequestion{excos1} % four multiple-choice questions
+
+\section{III}
+% Override the question number, to test/demo this
+\includequestion[99]{numerical2}
+\includequestion{numerical3}
+
+\section{IV}
+\includequestion{dynamical2}
+\includequestion{dynamical3}
+
+\end{document}
diff --git a/macros/latex/contrib/exam-n/sample/sample_exam_solution.tex b/macros/latex/contrib/exam-n/sample/sample_exam_solution.tex
new file mode 100644
index 0000000000..853bccbce9
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/sample_exam_solution.tex
@@ -0,0 +1,65 @@
+\documentclass[showsolutions]{exam-n}
+%\documentclass[largefont]{exam-n}
+%\documentclass[hugefont,sansserif]{exam-n}
+%\documentclass[mtpro2,showsolutions]{exam-n}
+%\documentclass[mtpro2,showsolutions,sansserif]{exam-n}
+%\documentclass[draft,showsolutions,sansserif]{exam-n}
+
+% Note: this sample question dates from an earlier phase, in which
+% `paper n' would contain a bundle of questions from various courses.
+% That's why the \coursetitle doesn't match the broad range of
+% subjects being 'examined'.
+%
+% Several of the questions are gibberish.
+%
+% This collection of questions has in part turned into an informal
+% regression test for the class file.
+
+\examdate{Wednesday, 23 May 2007}
+\examtime{9:30 -- 10:45 (1 course)\\9:30 -- 12:00 (2 courses)}
+
+\exambanner{Examination for the degrees of \BSc\,
+ \MSci\ and \MA\ on the honours standard }
+
+\degreedescriptions{Physics 3\\Chemical Physics 3\\Physics with
+ Astrophysics 3\\Theoretical Physics 3M\\Joint Physics 3}
+\schoolcoursecode{P304D and P304H}
+\universitycoursecode{PHYS3031 and PHYS4025}
+\coursetitle{Quantum Mechanics}
+
+\usepackage{pdfpages}
+
+\rubric{Candidates should answer Questions 1 and 2 (10~marks each),
+ \linebreak\textbf{and either} Question 3 \textbf{or} Question 4 (30~marks).
+ \linebreak The content of this sample exam derives from real
+ questions, but the result is in many cases test gibberish.}
+%\norubric
+
+\numquestions{13}
+
+\usepackage{graphicx} % for graphic in dynamical1
+
+\begin{document}
+\maketitle
+
+\section{I}
+\includequestion{cosmo1}
+\includequestion{numerical1}
+\includequestion{dynamical1}
+
+\section{II}
+\includequestion{cosmo2}
+\subsection{Cosmology question number 3}
+\includequestion{cosmo3}
+\includequestion{excos1} % four multiple-choice questions
+
+\section{III}
+% Override the question number, to test/demo this
+\includequestion[99]{numerical2}
+\includequestion{numerical3}
+
+\section{IV}
+\includequestion{dynamical2}
+\includequestion{dynamical3}
+
+\end{document}
diff --git a/macros/latex/contrib/exam-n/sample/sample_mcq.tex b/macros/latex/contrib/exam-n/sample/sample_mcq.tex
new file mode 100644
index 0000000000..268417ff7d
--- /dev/null
+++ b/macros/latex/contrib/exam-n/sample/sample_mcq.tex
@@ -0,0 +1,87 @@
+\documentclass[draft]{exam-n}
+
+\examdate{Today}
+\examtime{Now! -- \emph{you're late!}}
+
+\exambanner{Multiple-choice exam}
+
+\degreedescriptions{Various degrees}
+\schoolcoursecode{MCQ123}
+\universitycoursecode{AssDes101}
+\coursetitle{Assessment Design Strategies}
+
+\rubric{Candidates should choose answers randomly where they feel
+ unable to speculate wildly.}
+
+\multiplechoiceanswers{4}
+
+\begin{document}
+\maketitle
+
+\begin{mcq}
+Which is the first answer in this list?
+\answer Answer one
+\item Answer two
+\item Answer three
+\item Answer four
+\end{mcq}
+
+\begin{mcq}
+How many answers are in this list?
+\item one
+\item two
+\item three
+\answer four
+\end{mcq}
+
+\begin{mcq}
+Which is the incorrect answer in this list?
+\item Correct answer
+\item Another correct answer
+\answer The wrong answer
+\item A final correct answer
+\end{mcq}
+
+\begin{mcq}
+What is the nature of existence?
+\item All good things come to those who wait
+\item The universe makes sense
+\answer Error is inevitable
+\item Om
+\end{mcq}
+
+\begin{mcq}
+How many roads must a man walk down?
+\item Three
+\answer Oooh, I wouldn't walk down there -- it's terribly windy.
+\item Can I introduce you to the notion of the tuning fork?
+\item Third left, then second right, and the nature of existence is
+ available from the leprechaun in the little lane just after the bend
+ in the road.
+\end{mcq}
+
+\begin{mcq}
+How many questions are there in this test?
+\item Six
+\answer Eight
+\item Ten
+\item Twelve
+\end{mcq}
+
+\begin{mcq}
+Is this a reasonable question?
+\item no
+\item yes
+\item is this an answer?
+\answer if you say so
+\end{mcq}
+
+\begin{mcq}
+What is the most important thing about examinations?
+\item They are an accurate measure of understanding
+\item They are repeatable and reliable
+\answer They are nicely formatted
+\item They are stress-free occasions which everyone enjoys.
+\end{mcq}
+
+\end{document}