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\begin{document}
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{\LARGE{
\hfil Math 120 A Spring 2018 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil April 19, 2018 \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 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 You start bicycling from a point $33$ meters due EAST of a fountain in a park and 
bicycle directly toward a point $56$ meters due NORTH of the fountain.  You bicycle at a constant speed of $13$
meters per second.

\begin{enumerate}
\item Impose a coordinate system with the fountain at the origin.
Give the parametric equations for your location $t$ seconds after you start bicycling.

\vfil

\item A bear starts moving at the same time that you do.  $t$ seconds after you start walking,
the bear's location is given by $x=1+3t, y  = 60-4t$.

Find the value of $t$ when you are closest to the bear.


\end{enumerate}

\newp

\item You are walking near the Circular Forest, which has the shape of a perfect circle
with a radius of $15$ km.  

You begin your walk $20$ km WEST and $5$ km SOUTH of the center of the forest and 
walk directly toward the easternmost point of the forest.  
You walk at a constant speed of $5$ km/hr.

How much time passes from the moment you enter the forest until you are
at the point where you are closest to the center of the forest?



\newp


\item You have a pizza shaped as shown in the figure below (dimensions
are in centimeters).
You are going to make a vertical cut through the pizza.
The cut will be located a distance $x$
centimeters from the left edge.

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

\begin{tikzpicture}[scale=0.5]
\tikzstyle{arrow}=[<->,>=stealth,very thick]
\draw[line width=3pt] (0,0) -- (10,0) -- (10,9) -- (4,3) -- (0,3)  -- cycle;
\draw[arrow] (-0.5,3) -- (-0.5,0);
\draw (-1.0,1.5) node {$3$};
\draw[arrow] (0,3.5) -- (4,3.5);
\draw (2.,4) node {$4$};
\draw[arrow] (10.5,0) -- (10.5,9);
\draw (11,4.5) node {$9$};
\draw[arrow] (0,-0.5) -- (10,-0.5);
\draw (5,-1.0) node {$10$};
\end{tikzpicture}

\newp

\item \begin{enumerate}
\item Let 
\[
f(x) = 
\begin{cases}
3x+1  & \text{ if } x\ge 1, \\
1-x & \text{ if } x < 1.
\end{cases}
\]
Find all values of $c$ such that $f(c)=c$.

\vfil

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


\end{enumerate}



\end{enumerate}

\end{document}


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