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%\markboth{Dr. Matthew M. Conroy - University of Washington}{Dr. Matthew M. Conroy - University of Washington}


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\begin{document}
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\vfil \noindent

{\LARGE{
\hfil Math 120 A - Autumn 2013 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil October 17, 2013 \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.  Graphing 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 You have a pizza shaped as shown below.

\begin{tikzpicture}[scale=0.7]
\tikzstyle{arrow}=[<->,>=stealth,very thick]
\draw (0,0) -- (0,4) -- (2,7) -- (8,7) -- (8,0) -- (0,0);
%\draw[line width=2pt] (2,7) arc (180:360:3);
\draw[arrow] (-0.5,0) -- (-0.5,4);
\draw (-0.9,2) node{4"};
\draw[arrow] (0,-0.5) -- (8,-0.5);
\draw (4,-0.8) node{8"};
\draw[arrow] (8.5,0) -- (8.5,7);
\draw (8.9,3.5) node{7"};
\draw[arrow] (2,7.5) -- (8,7.5);
\draw (5,7.8) node{6"};
\end{tikzpicture}

You are going to cut the pizza with a vertical cut $x$ inches from the left edge.

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

\newp

\item Terry and Jim are at a campsite in a desert.
At 6 AM, Terry leaves the campsite, cycling east at 20 km/hr.
At 7 AM, Jim leaves the campsite, cycling north at 18 km/hr.

\begin{enumerate}
\item When Terry and Jim are 80 km apart, for what length of time has Jim been cycling?
\vfil
\item There is a radio transmitter 50 km east and 20 km north of the campsite.
Terry can pick up the signal from the transmitter when he is within 40 km 
of the transmitter.  For what length of time will Terry Jim be able to pick up the signal?
\end{enumerate}

\newp

\item 
Malala lives inside the Circular Forest.
The forest has the shape of a circle, with a radius of 20 km.
Malala's house is 6 km due north of the center of the forest.
One day, she decides to walk to Stewart's house, which is 22 km east and 9 km south of
Malala's house.

%Malala walks at a constant speed of 4 km/hr.

\begin{enumerate}

\item Where is Malala when she is closest to the easternmost point of the forest? 
Give her location relative to the center of the forest.

\vfil

\item Is the location you gave in part (a) inside or outside the forest?
Be sure to show calculations supporting your answer.

\end{enumerate}


\newp

\item 

\begin{enumerate}

\item Let $f(x)=3x-x^2$.  Simplify the expression
\[
\frac{f(x+h)-f(x-h)}{h}
\]
far enough so that plugging in
$h = 0$ would be allowed. 

\vfil

\item Find the area of the triangle made by the $y$-axis, the line $y=8-x$ and
the line $y=3x$.

\end{enumerate}












\end{enumerate}

\end{document}


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