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\begin{document}
\noindent
\vfil \noindent

{\LARGE{
\hfil Math 120 A, B Winter 2013 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil January 31, 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  Shin and Hannah are lost in the desert.
Shin is 5 km north and 3 km east of Hannah.
At the same time, they both begin walking due east.
Shin walks at 2 km/hr, and Hannah walks at 3 km/hr.

\begin{enumerate}
\item When will they be 10 km apart? Give your answer in hours after they start walking.
\vfil
\item When will the line through their locations be perpendicular to the
line through their starting locations? Give your answer in hours after they start walking.

\end{enumerate}

\newp

\item Alice stood at the southernmost point on the edge of a circular lake.  

The lake had a radius of 3 km.

She then dove into the lake and swam in a straight line toward a point 7 km west and 6~km north of the center of the lake.

When she reached the edge of the lake she stopped swimming.

\begin{enumerate}

\item What was the length of her swim (in kilometers)?
\vfil \vfil
\item Consider the point on her swim where she was closest to the westernmost point of the lake.
How far west of the center of the lake was that point?

\end{enumerate}

\newp

\item You are going to cut a piece of sheet steel with a vertical cut $x$ cm from its left edge.
The steel is shaped as shown in the figure below.  All dimensions are in cm.

\begin{tikzpicture}[scale=0.5]
\tikzstyle{arrow}=[<->,>=stealth,very thick]
\draw[line width=3pt] (0,0) -- (10,0) -- (10,8) -- (4,5) -- (0,9) -- (0,0);
\draw (-1.25,4.5) node {$9$};
\draw (5,-1.25) node {$10$};
\draw (11.25,4) node {$8$};
\draw (4.25, 5) -- (5.25,5);
\draw[arrow] (4.75,5) -- (4.75,0);
\draw (5.25,2.5) node {$5$};
\draw (4,4.75) -- (4,3.75);
\draw[arrow] (4,4.25) -- (0,4.25);
\draw (2,3.75) node {$4$};
\draw (-1.25,9) -- (-0.25,9);
\draw (-1.25,0) -- (-0.25,0);
\draw[arrow] (-0.75,0) -- (-0.75,9);
\draw (0,-0.25) -- (0,-1.25);
\draw (10,-0.25) -- (10,-1.25);
\draw[arrow] (0,-0.75) -- (10,-0.75);
\draw (10.25,8) -- (11.25,8);
\draw (10.25,0) -- (11.25,0);
\draw[arrow] (10.75,0) -- (10.75,8);
\end{tikzpicture}

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

\newp

\item 
\begin{enumerate}
\item Let $f(x)=3x^2+2x-5$. Simplify the expression below as much as possible:
\[
\frac{f(x+h)-f(x-h)}{h}
\] 

\vfil

\item Let $g(x)=3x-|4-x|$.  Find all solutions to the equation $g(a)=10+\frac{5}{2}a$.
\end{enumerate}


\end{enumerate}

\end{document}


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