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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A - Spring 2007 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil April 19, 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 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 Rose is selling tickets to her upcoming tuba performance.
She knows from experience that the number of tickets she sells will be
a linear function of the price that she sets for the tickets.
If she sets the price at \$20, she will sell 150 tickets.
If she sets the price at \$18.60, she will sell 162 tickets.

At what price will she make the most money?

\newp

\item Joey has a rectangular pizza that is 1 foot by 2 feet long. 
Joey wants to cut the pizza by making a straight slice through one
corner of the pizza.  
With a coordinate system imposed as shown in the figures below, 
we can represent the slice by the line $y=mx$.
Joey plans to eat the portion of the pizza below the slice (the
shaded region in the figures below).

Two possible slices are shown here:

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

The area of the shaded region
depends only on the \textbf{slope} of the slice.

\begin{enumerate}
\item Find the area of the shaded region when the slice has slope
$m=0.1$.
\vfil
\item Find the area of the shaded region when the slice has slope 
$m=1.3$.
\vfil
\item Express the area of the shaded region as a multi-part 
function of the slope $m$.
\vfil \vfil
\end{enumerate}
\newp

\item Sally is walking in a straight line through the Circular Forest, which has the shape
of a perfect circle.
She enters the forest at a point 10 km east and 4 km north of the center
of the forest.
She exits the forest at Point P and 
continues walking in the same direction.
Point P is due south of a point 3 km due east of the center of the forest.

When she is due south of the center of the forest, how far from the center
is she?

\newp

\item Let $f(x)=2x+3$ and $g(x)=|x|$.

\begin{enumerate}
\item Write the multipart rule for $g(f(x))$.
\vfil
\item Find all solutions to the equation
\[
g(f(x))=-3x+9.
\]
\end{enumerate}

\end{enumerate}



\end{document}


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