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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A - Spring 2006 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil April 20, 2006 \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 Triangolo Pizzeria sells pizza in the form of a triangle.  They are
shaped as shown in this figure:

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

Suppose you cut the pizza with a cut perpendicular to the long side
of the pizza.  Suppose the slice is $x$ inches from the leftmost point.

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

\newp

\item Jessie is planning to bicycle from Casserole to Needham.
The town of Lakewood is located 30 miles east and 25 miles north 
of Needham.  The town of Casserole is located 7 miles west and 10 miles
north of Lakewood.  
How close to Lakewood will she get on her trip?

\newp

\item What is the area of the largest rectangle that you can place in
the triangle shown?  One corner of the rectangle should be at the origin,
one side should be along the $x$-axis, one side along the $y$-axis, and
one corner should lie on the line shown.  The $x$- and $y$-intercepts of the
line are labeled in the figure.

A rectangle (not the largest one) fitting the criteria is shown in the picture.

\epsfig{file=triangle01.eps, 
 width=8cm,
 angle=0 }

\newp

\item Laura is hiking through the Circular Forest, which has the shape of
a circle with a 5 mile radius.  She will start her
trip 3 miles east and 4 miles north of the easternmost point
of the forest, and hike directly to the westernmost point, where
she will leave the forest.

For what distance will she walk through the forest?



\end{enumerate}




\end{document}


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