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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A, B - Winter 2011 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil January 27, 2011 \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}
{\Huge
\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 Show all work for full credit. 
\item You may use a scientific calculator during this
examination.  Graphic 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 You have 50 minutes to complete the exam. 
\end{itemize}
\vfil
.

\newp

\begin{enumerate}

\item Josephine is sailing near a radar buoy which can detect
anything within 8 km of the buoy.  She starts sailing from
a point 7 km WEST and 9 km SOUTH of the buoy.  She sails NORTH for
one hour, then turns and sails EAST for 30 km.  

She sails at a constant speed of 6 km/hr.

How much time was she within 8 km of the buoy?

\newp

\item You are going to cut a pizza which is shaped as shown below.

\epsfig{file=pizza01a.eps, 
 width=11cm,
 angle=0 }

You wish to make a straight cut through the lower left corner, labeled $P$.
We are interested in the area below the cut, which is shaded in the figure.

Impose a coordinate system with P at the origin.

\begin{enumerate}
\item If the cut has a slope of 0.6, what is the area of the pizza 
below the cut?

\vfil

\item Suppose the cut has slope $m$.  Write the area of the pizza
below the cut as a multipart function of $m$.

\vfil


\end{enumerate}

\newp

\item Jo is moving linearly in the $xy$-plane at a constant speed.
She starts from the point $(3,1)$ and moves along the line 
$y=-3x+10$ at a speed of 2 units per second, heading toward the $y$-axis.

\begin{enumerate}
\item Write parametric equations for Jo's location $t$ seconds after
starting.

\vfil

\item Express Jo's distance from the point $(5,8)$ as a function of $t$.
\end{enumerate}

\newp

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

\begin{enumerate}

\item Simplify the expression 
\[
\frac{f(x-h)-f(x+2h)}{h}
\]
far enough so that plugging in $h=0$ would be allowed.

\vfil

\item Find all solutions to the equation
\[
g(x)=-2x-8.
\]

\end{enumerate}

\end{enumerate}

\end{document}


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