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\begin{document}
\noindent
\vfil \noindent

{\LARGE{
\hfil Math 120 A - Winter 2015 \hfil \pp
\hfil Midterm Exam Number One\hfil  \pp
\hfil January 29th, 2015 \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 & 15 &\hspace{10mm} \hfil\\ \hline 
 2 & 15 &       \\ \hline
 3 & 15 &      \\ \hline
4 & 15 &    \\ \hline
Total & 60 & \\ \hline 
\end{tabular}
}
\end{center}
\vfil
\begin{itemize}
\item This exam consists of FOUR problems on FIVE pages, including this cover sheet.
\item Show all work for full credit. 
\item You may use a scientific calculator during this
exam.  Graphing calculators are not permitted.
Also, other electronic devices are not allowed, and should be
turned off and put away for the duration of the exam.
\item You do not need to simplify your answers.
\item If you use a trial-and-error or guess-and-check method
when a more rigorous method is available, you will not receive full credit.
\item If you write on the back of the page, please indicate that you have done so!
\item You may use one hand-written double-sided 8.5" by 11" page of notes.
\item You have 50 minutes to complete the exam.
\end{itemize}

\vfil
{\small --}

\newpage

\begin{enumerate}

\item {\bf[15 points]} Siddhi stands 2 kilometers east and 0.66 kilometers north of the {\bf center} of a circular lake with radius $1.3$ kilometers.\\[.1 in]
First, she walks {\bf due west} until she reaches the edge of the lake. Then swims in a straight line towards the {\bf westernmost point} of the lake.\\[.1 in]
How close does Siddhi come to the center of the lake?

\newpage

\item Arthur is walking around the coordinate plane.\\[.1 in]
At time $t=0$, he begins at the point $(5,-2)$. He walks in a straight line towards the point $(-7,6)$ at a constant speed, reaching it in $8$ seconds.

\begin{enumerate}
\item {\bf[4 points]} Give parametric equations for Arthur's coordinates $t$ seconds after he begins walking.
\vskip 2 in
\item {\bf[6 points]} Find all times when Arthur is exactly $4$ units away from the origin.
\vskip 3 in
\item {\bf[5 points]} Arthur drops his wallet $2$ seconds after crossing the $y$-axis. Where is it?
\end{enumerate}

\newpage

\item Consider the function $f(x)$ shown in the graph below:

\begin{center}
\begin{tikzpicture}[auto,scale=.9, line width=2pt]

\foreach \x in {-5,-4,...,4} \draw [line width=1pt,densely dotted] (\x,-2.2)--(\x,5.2);
\foreach \x in {-5,-4,...,4} \draw (\x+.2,.19) node {\scriptsize \x};
\foreach \y in {-2,-1,...,5} \draw [line width=1pt,densely dotted] (-5.2,\y)--(4.2,\y);
\foreach \y in {-2,-1,...,5} \draw (.2,\y+.19) node {\scriptsize \y};

\draw [<->] (-5.6,0) -- (4.5,0);
\draw [<->] (0,-2.6) -- (0,5.6);

\draw (4.7,0) node {$x$};
\draw (0,5.9) node {$f(x)$};

\draw [<-] (-5.3,4) -- (1,4);
\draw [->] (1,-1) -- (3.25,5.75);

\draw[line width=1 pt, fill=black] (1,4) circle (.1);
\draw[line width=1 pt, fill=white] (1,-1) circle (.1);
\end{tikzpicture}
\end{center}
\begin{enumerate}
\item {\bf[4 points]} State the domain and range of $f(x)$.
\vskip 1 in
\item {\bf[5 points]} Write the multipart rule for $f(x)$.
\vskip 1.5 in
\item {\bf[6 points]} Find all solutions to the equation $f(x) = 6-x^2$
\end{enumerate}

\newpage

\item The temperature in the city of Pleasantville is a quadratic function of time.\\[.1 in]
Today, the temperature is $70^\circ$ Fahrenheit.\\[.1 in]
$5$ days from now, the temperature will be $67^\circ$ Fahrenheit.\\[.1 in]
$10$ days from now, the temperature will be $68^\circ$ Fahrenheit.
\begin{enumerate}
\item {\bf[10 points]} Write a function $f(t)$ for the temperature $t$ days from now.
\vskip 5 in
\item {\bf[4 points]} When does Pleasantville reach its minimum temperature?\\[.1 in]What is that temperature?
\vskip 1.8 in
\item {\bf[1 point]} Your friends are thinking of visiting in 30 days. How will the weather be?
\end{enumerate}

\end{enumerate}

\end{document}