\documentclass[12pt]{report} 

\usepackage{palatino}
\usepackage{epsfig}

\pagestyle{empty} %%% this results in no pagenumbers (footer is empty}

\addtolength{\oddsidemargin}{-1.0in}
\addtolength{\evensidemargin}{-1.0in}
\addtolength{\textwidth}{1.5in}
\addtolength{\topmargin}{-0.5in}
\addtolength{\textheight}{1.0in}

\baselineskip=20pt

\newcommand{\dsps}{\displaystyle}
\newcommand{\pp}{\par \noindent}
\newcommand{\newp}{\vfil \eject}
%\newcommand{\newp}{\bigskip}

\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 D - Autumn 2007 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil October 18, 2007 \hfil \pp
\normalsize
\vfil
\medskip
\hfil Name: \hrulefill \hrulefill \hrulefill
\hspace{0.5in}
 Section: \hrulefill
\vfil
\begin{center}
{\large
\begin{tabular}{||c|c|r||} \hline 
 1 & 10 &\hspace{10mm} \hfil\\ \hline 
 2 & 10 &       \\ \hline
 3 & 10 &      \\ \hline
4 &  10 &    \\ \hline
Total & 40 & \\ \hline 
\end{tabular}
}
\end{center}
\vfil
\begin{itemize}
\item Complete all four questions. 
\item You may use a calculator during this
examination.  
Other electronic devices are not allowed, and should be
turned off and put away for the duration of the exam.
\item If you use a trial-and-error or guess-and-check method,
or read a numerical solution from a graph on your calculator
when an algebraic method is available, you will not receive full credit.
\item You may use one hand-written 8.5 by 11 inch page of notes.  Write
your name on your notesheet and turn it in with your exam.
\item Show all work for full credit.  
\item You have 50 minutes to complete the exam. 
\end{itemize}
\vfil
.

\newp

\begin{enumerate}


\item Robert starts walking due west from an oasis in the desert at noon.
His walking speed is 4 km/hr.

At 2 PM, Maria starts walking north from a point 3 km due east of the oasis.
She walks 5 km/hr.

When will Robert and Maria be 20 km apart?  Give your answer in hours after noon.

\newp

\item Jean is walking along a railroad track that passes through a forest.
The track is perfectly straight.  In the forest, there is a spring.
Jean starts walking on the track 5 km east and 2 km south of the spring.
He heads along the track to a point 4 km west and 3 km north of the spring.
During his walk, how close does he get to the spring?

\newp

\item Trapezio Pizzeria sells pizza in the shape of a trapezoid as shown below.

 \epsfig{file=multip01.eps, 
 width=11cm,
 angle=0 }
 
Suppose you make a cut through the pizza, parallel to the right edge and
$x$ cm from the left endpoint.

Express the area of the pizza to the left of the cut as a multipart function of $x$.

\newp

\item Ophelia has 300 meters of fencing with which to make two enclosures next to
a river.  The enclosures will be rectangular, but she will use the river for one side
of each enclosure, so no fencing is needed for that side.  
She wants the two enclosures to have the same width, and
have one enclosure be twice as long as the other enclosure.  An example of how she might
do this is shown in the figure.

 \epsfig{file=quad01.eps, 
 width=11cm,
 angle=0 }

What should the dimensions of the smaller enclosure be to make the
total combined area of the two enclosures as large as possible?


\end{enumerate}


\end{document}