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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A - Winter 2006 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil January 26, 2006 \hfil \pp
\normalsize
\vfil
\medskip
\hfil Name: \hrulefill \hrulefill \hrulefill
\hspace{0.5in}
 Section: \hrulefill
\vfil
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{\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 questions. 
\item You may use a calculator during this
examination.  
Other electronic devices are not allowed, and should be
turned off 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.
\item Show all work for full credit.  
\item You have 50 minutes to complete the exam. 
\end{itemize}
\vfil
.

\newp

\begin{enumerate}

\item 
Susan is on a hike.  She begins 
her trip from a point 2 km east of the southernmost point of 
a circular forest with a radius of 6 km.  She heads directly toward
the westernmost point of the forest.  However, when she reaches a point
due south of the center of the forest, she changes direction and heads west 
until she leaves the forest.

Impose a coordinate system with the center of the forest at the origin.
What are the coordinates of the point where she leaves the forest?

\newp

\item 
Alice is going into business selling pizzas shaped like the
polygon in the figure below.  The coordinates indicate the 
vertices (corners) of the polygon pizza.  The units are inches.

 \epsfig{file=pizza01.eps, 
 width=11cm,
 angle=0 }
 
If a vertical cut is made in the pizza, $x$ inches from the
left edge of the pizza, determine the area of the pizza to
the left of the cut as a multipart function of $x$.



\newp

\item The populations of the towns of Ribbit and Croak are each
linear functions of time.  In 1980, there were 40,000 people in Ribbit,
and in 2000, there were 48,000 people in Ribbit.
In 1990, Croak's population was one quarter the population of
Ribbit, while in 1995 its population was one half that of Ribbit's.

When will the population of Croak be 10,000 more than the population
of Ribbit?


\newp

\item Juliet is deciding how much to charge for the tickets to
a concert.  She knows from past experience that the amount of
money she makes from the sale of the tickets will be a quadratic
function of the ticket price.  
Obviously, if she charges nothing, she will make no money.
If she charges \$1, she will make \$100.
If she charges \$2, she will make \$180.

\begin{enumerate}
\item How much should she charge to make the most money?
\vfil \vfil \vfil
\item What is the largest amount of money she could make?
\end{enumerate}



\end{enumerate}




\end{document}


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