\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}{2.0in}

\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 A - Spring 2009 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil April 23, 2009 \hfil \pp
\normalsize
\vfil
\medskip
\hfil Name: \hrulefill \hrulefill \hspace{0.5in} Student ID no. : \hrulefill

\vfil

\hfil Signature: \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 scientific calculator during this
examination.  Graphing calculators are not allowed.
Also, 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
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
\hfill.

\newp

\begin{enumerate}


\item Carlos is hiking near the Circular Forest, a forest in the shape of a
perfect circle.  The forest has a radius of 9 km.  Carlos begins hiking from
a point 14 km WEST and 7 km SOUTH of the center of the forest.  He begins
hiking DUE EAST, but when he reaches the edge of the forest, he turns and
hikes NORTH.  He hikes NORTH for 5 km, then turns and hikes WEST until he
leaves the forest.

Carlos hikes at a constant 4 km per hour.  How much time did he spend in the
forest?

\newp

\item In the figure below, the circle is centered at the origin.
The line $L$ is tangent to the circle: it intersects the circle at exactly
one point, $P$.  The line L also passes through the point A.

\epsfig{file=tangent01.eps, 
 width=8cm,
 angle=0 }

If the circle has a radius of 11, and $A$ is the point $(26,0)$, find the coordinates
of point $P$.

\newp



\item Alice has a peach orchard.  She knows from past experience that the
number of kilograms of peaches produced per tree is a linear function of the number of
trees in the orchard.  If she has 100 trees, the trees will produce
96 kg of peaches per tree.  Reducing the number of trees by 10 will increase
the kilograms produced per tree by 8.

What is the maximum possible total number of kilograms of peaches her orchard
can produce?

\newp

\item 
\begin{enumerate}

\item (5 points) Let $g(x)=|x-3|-\frac{1}{2}x$.  Find all solutions to the equation
\[
g(x) = 2-5x
\]

\vfil \vfil

\item (5 points) Let $f(x) = 8x-7$.  Find a function $h(x)$ such that $h(h(x))=f(x)$.

\end{enumerate}






\end{enumerate}





\end{document}


% \epsfig{file=pizza01.eps, 
% width=11cm,
% angle=0 }