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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A - Winter 2008 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil January 31, 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 Gloria is selling tickets to her glockenspiel concert, and she is trying to 
decide what the ticket price should be.
She knows from past experience that the number of tickets she will sell
is a linear function of the ticket price.  If the ticket price is
\$2, she will sell 1000 tickets.  If the ticket price is \$17.34, she will sell
200 tickets.

What should Gloria set the ticket price at for her to make the most money?

\newp

\item The Circular Forest has the shape of a circle with an 8 km radius.
Wally starts walking due WEST from a point 12 km EAST and 3 km NORTH of the
center of the forest.  He walks for 6 km, then turns and walks due SOUTH
and leaves the forest.

Wally walked at a constant speed of 4 km/hr. How much time did Wally spend in the forest?

\newp


\item A piece of paper has the shape and dimensions shown in the following figure.

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

Suppose the paper is cut with a vertical slice $x$ cm from the left
edge of the paper.

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

\newp


\item A number $k$ is said to be a {\textbf{fixed point}} 
for a function $f(x)$ if 
\[
f(k)=k.
\]

\begin{enumerate}

\item Find all fixed points of the function $\dsps f(x)=\left|\frac{1}{2}x-4\right|$.

\vfil \vfil

\item Let $f(x)=3x-1$ and $g(x)=5x+8$.  Find all fixed
points of the function 
\[
h(x) = f(g(x)).
\]

\end{enumerate}




\end{enumerate}


\end{document}