\documentclass[12pt]{article}
\usepackage{fullpage,amsmath,amssymb}
%\usepackage[normalem]{ulem}
\pagestyle{empty}

\def\bbZ{{\mathbb Z}}

\begin{document}

\begin{center}

\vfill

\noindent{\bf Do not turn this page until instructed.}

\vfill

{\large Math 267 Advanced Ordinary Differential Equations}

\vfill

{\LARGE Sample Term Test}

\vfill

University of Toronto, October 19, 2012

\vfill

\noindent{\bf Solve the 3 of the 4 problems on the other side of this page. }\\
Each problem is worth 34 points.\\You have fifty minutes to
write this test.

\vfill

\noindent{\bf Notes.}

\begin{itemize}
\item No outside material other than stationary and a basic calculator
(not capable of displaying text) is allowed.
\item {\bf Neatness counts! Language counts!} The {\em ideal} written
solution to a problem looks like a page from a textbook; neat and clean
and made of complete and grammatical sentences. Definitely phrases like
``there exists'' or ``for every'' cannot be skipped. Lectures are mostly
made of spoken words, and so the blackboard part of proofs and
calculations given during lectures often omits or shortens key
phrases. The ideal written solution to a problem does not do that.
\end{itemize}

\end{center}

\vfill

\centerline{\bf Good Luck!}

\vfill

\newpage

\noindent{\bf Solve 3 of the following 4 problems. } Each problem
is worth 34 points. You have fifty minutes. {\bf Neatness counts!
Language counts!}

\vfill \noindent{\bf Problem 1. } Solve the following two differential
equations:
\begin{enumerate}
\item Linear non-homo similar to HW.
\item Exact similar to HW.
\end{enumerate}

\vfill \noindent{\bf Problem 2. }
\begin{enumerate}
\item State precisely (without proof) the theorem about existance and
uniqueness of solutions for {\em systems} of ordinary differential
equations of order 1.
\item Show how the above theorem implies an existance and
uniqueness theorem for ordinary differential
equations of arbitrary order.
\end{enumerate}

\vfill \noindent{\bf Problem 3. } CoV similar to HW.

\vfill \noindent{\bf Problem 4. }
\begin{enumerate}
\item State what is the ``improved Euler method'' for solving the
differential equation $\phi'=f(x,\phi)$ with initial condition
$\phi(x_0)=y_0$ using step size $h$.
\item Compute the single-step approximation for $\phi(1)$, given that
$\phi$ satisfies $\phi'=-\phi$ and $\phi(0)=1$, using the improved
Euler method.
\end{enumerate}

\vfill

\begin{center}
\bf Warning: The real exam will be similar to this sample, to
my opinion. Your opinion may be significantly different.
\end{center}

\vfill

\end{document}