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\begin{document}
\noindent
\vfil \noindent

{\LARGE{
\hfil Math 120 A Winter 2017 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil January 26, 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
\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 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 Paula and Nikita are moving in the $xy$-plane. They both move along straight lines
at constant speeds, and they both start at the same time.

Paula starts from the point $(0,3)$ and heads directly toward the point $(-5,-2)$, reaching
that point in $5$ seconds.

Nikita starts from the point $(4,0)$ and heads directly toward the point $(-10,0)$,
reaching it in $2$ seconds.

Let $t$ be the time since they started moving.  

Find the values of $t$ when Nikita and Paula are a distance of $5$ units apart.


\newp

\item 
Sam is walking near the Circular Forest.  

The Circular Forest has the shape of a circle, with radius of 17 km.  

Sam begins walking from a point $12$ km west and $13$ km south  of the center of the forest.

Sam heads directly toward a point $5$ km east of the easternmost point of the forest.

\begin{enumerate}

\item Where does Sam exit the forest? State how many kilometers east and how many kilometers south of the
center of the forest the exit point is.

\vfil \vfil

\item On Sam's walk, where is Sam when Sam
is closest to the center of the Circular Forest? 
Give the location as so many kilometers east and so many kilometers south of the
center of the forest.
\end{enumerate}


\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) -- (10,4) -- (3,4) -- (0,9) -- (0,0);
\draw (-1.25,4.5) node {$9$};
\draw (5,-1.25) node {$10$};
\draw[arrow] (4.75,4) -- (4.75,0);
\draw (5.25,2.5) node {$4$};
\draw (3,3) -- (3,4);
\draw[arrow] (3,3.5) -- (0,3.5);
\draw (1.5,3.) node {$3$};
\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);
\end{tikzpicture}




\newp 

\item \begin{enumerate}

\item Let $g(x)=7x^2+x$.  
Assume $h$ is not zero, and simplify the following expression as much as possible.
\[
\frac{g(x+h)-g(x)}{h}
\]

\vfil

\item Find the center and radius of the circle defined by the following equation.

\[
x^2-\frac{4}{3}x+y^2+10y=\frac{95}{9}.
\]
\end{enumerate}



\end{enumerate}

\end{document}


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