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{\LARGE{
\hfil Math 120 A Spring 2017 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil April 20, 2017 \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
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{\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}
}
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\vfil
\begin{itemize}
\item Complete all four questions. 
\item Show all work for full credit. 
\item The only calculator you may use during this exam is
a TI-30XIIs.
All 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, two-sided, 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 Tristan and Iseult are traveling in the $xy$-plane.
They travel with constant speeds and directions along lines.
They both start at midnight.

Tristan start at the point $(10,-3)$ and at $2$ AM, Tristan's
location is $(7,8)$.

Iseult starts at the point $(5,4)$ and reaches the point 
$(11,6)$ at $3$ AM.

\begin{enumerate}
\item Find the parametric equations for Tristan's motion.
\vfil
\item Find the parametric equations for Iseult's motion.
\vfil
\item When will Tristan and Iseult be closest together?
Give your answer in hours after midnight.
\end{enumerate}

\newp

\item Anna is searching for buried treasure.  At noon, she starts
walking due East at 2 km per hour.  She walks due East for 3 hours,
and then turns and walks due North at 3 km per hour for 1 hour.
She then turns and walks due East again at 5 km per hour for 2 hours.

The path she follows looks like this:


\begin{tikzpicture}[scale=0.5]
\tikzstyle{arrow}=[->,>=stealth,very thick]
\draw[line width=3pt] (0,0) -- (6,0) -- (6,3) -- (16,3);
\draw (2,2.5) node {start};
\draw[arrow] (2,2) -- (0.2,0.2);
\end{tikzpicture}





Express her distance from her starting point as a multipart function of $t$,
the time since she started walking.


\newp

\item A particular radar buoy off the coast can detect any ship within a radius
of $10$ miles.   Erik is in his sailboat located $3$ miles north and $13$ miles
west of the buoy.  Erik sails due east at a constant speed of $8$ miles per hour. 
After $45$ minute, he turns due south and continues sailing at the same constant
speed forever. \\

How long (in hours) is Erik within the radar region?


\newp

\item For each of the functions below, 
find the expression for
\[
\frac{f(x+h)-f(x)}{h}.
\]
Simplify each of your expressions far enough so that plugging in
$h = 0$
would be allowed. 
\begin{enumerate}
\item $f(x)=1-3x$
\vfil
\item $f(x)=5x^2+x$
\vfil
\end{enumerate}

\end{enumerate}

\end{document}


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