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\begin{document}
\noindent
\vfil \noindent

{\LARGE{
\hfil Math 120 A - Winter 2016 \hfil \pp
\hfil Midterm Exam Number One\hfil  \pp
\hfil January 28th, 2016 \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 Electra stands $40$ feet west and $15$ feet north of the center of a circular puddle and begins running east at a speed of $10$ feet per second.\\[.1 in]
After $t$ seconds, the puddle has a radius of $8t$ feet.
\begin{enumerate}
\item {\bf[12 points]} From when she enters to when she leaves, how much time does Electra spend running through the puddle?
\vskip 6.5 in
\item {\bf[3 points]} While Electra is running through the puddle, how far does she run?
\end{enumerate}

\newpage

\item {\bf[15 points]}  Consider the following cake, which definitely isn't supposed to be a larger cake that I stole a piece from:
\vspace{-.3 in}
\begin{center}\begin{tikzpicture}[scale = .5]
\begin{scope}
\draw [clip] (0,0) -- (10,0) -- (10,2) -- (6,8) -- (0,8) -- cycle;
\node [black!70] at (5,6) {\huge HAPPY};
\node [black!70] at (5,4) {\huge BIRTHDAY};
\node [black!70] at (5,2) {\huge HAROLD!};
\draw [snake=zigzag,segment length = 13 pt] (.3,.3) -- (9.7,.3) -- (9.7,7.7) -- (.3,7.7) -- cycle;
\end{scope}

\draw [very thick] (0,0) -- (10,0) -- (10,2) -- (6,8) -- (0,8) -- cycle;

\draw [<->,very thick,densely dotted,printersafe] (0,8.5) -- node[above] {6 in.} (6,8.5);
\draw [<->,very thick,densely dotted,printersafe] (-.5,0) -- node[left] {8 in.} (-0.5,8);
\draw [<->,very thick,densely dotted,printersafe] (0,-.5) -- node[below] {10 in.} (10,-.5);
\draw [<->,very thick,densely dotted,printersafe] (10.5,0) -- node[right] {2 in.} (10.5,2);

\end{tikzpicture}\end{center}
\vspace{-.15 in}
Suppose I make a cut $x$ inches from the left end of the cake. Write a multipart function $f(x)$ for the area to the left of the cut, with domain $0 \leq x \leq 10$. Notice that there are two possible shapes I could get, depending on where I make the cut:
\vspace{-.1 in}
\begin{center}\begin{tikzpicture}[scale = .4]
\draw [very thick] (0,0) -- (10,0) -- (10,2) -- (6,8) -- (0,8) -- cycle;

\draw [pattern = north west lines, pattern color=black!70] (0,0) -- (4,0) -- (4,8) -- (0,8) -- cycle;

\draw [<->,very thick,densely dotted,printersafe] (0,-.5) -- node[below] {$x$ in.} (4,-.5);
\end{tikzpicture} \qquad \qquad \qquad \begin{tikzpicture}[scale = .4]
\draw [very thick] (0,0) -- (10,0) -- (10,2) -- (6,8) -- (0,8) -- cycle;

\draw [pattern = north west lines, pattern color=black!70] (0,0) -- (7,0) -- (7,6.5) -- (6,8) -- (0,8) -- cycle;

\draw [<->,very thick,densely dotted,printersafe] (0,-.5) -- node[below] {$x$ in.} (7,-.5);
\end{tikzpicture}
\end{center}

\newpage

\item Jareth stands at the point $(8,1)$, and walks towards the point $(-1,4)$ in a straight line at constant speed.\\[.1 in]
Jareth reaches the point on his path closest to the origin 8 seconds into his journey.

\begin{enumerate}
\item {\bf[6 points]} What is Jareth's speed, in units per second?
\vskip 5 in
\item {\bf[5 points]} Give parametric equations for Jareth's coordinates after $t$ seconds.
\vskip 2 in
\item {\bf[4 points]} When does Jareth cross the $y$-axis?
\end{enumerate}

\newpage

\item Phileas is going on a hot air balloon ride. His height above the ground after $t$ minutes is a quadratic function of $t$.\\[.1 in]
He begins from a platform at a height of 76 meters.\\[.1 in]
The balloon reaches its maximum height after 30 minutes.\\[.1 in]
After 80 minutes, he finally lands (at a height of 0 meters).
\begin{enumerate}
\item {\bf[11 points]} Give a function $f(t)$ for Phileas's height above the ground after $t$ minutes.
\vskip 5.5 in
\item {\bf[4 points]} Find all times during Phileas's journey when he is at a height of exactly 100 meters.
\end{enumerate}

\end{enumerate}

\end{document}