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\newcommand{\dsps}{\displaystyle}
\newcommand{\pp}{\par \noindent}
\newcommand{\newp}{\vfil \eject}

\begin{document}
\noindent
\vfil \noindent

{\LARGE{
\hfil Math 120 B - Autumn 2013 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil October 17, 2013 \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 You may use a scientific calculator during this
examination.  Graphing calculators are not allowed.
Also, 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
{\small (Version 1)}

\newp

\begin{enumerate}

\item Devra's swimming pool has a radius of 9 meters. She stands 7 meters west and 5 meters south of the westernmost point of the pool, and begins running toward the easternmost point of the pool. Once Devra reaches the pool, she continues towards the easternmost point, swimming at a speed of 2 meters per second, and exits the pool once she reaches the end.

How much time does Devra spend swimming across the pool?

\newp

\item Beverley is 12 feet north and 6 feet west of Avon, and Chelsea is 1 foot west and 5 feet south of Beverley.

Avon walks straight towards Beverley. When he reaches the point on his path which is closest to Chelsea, he turns and walks east for 4 feet, and then turns one more time and walks straight back to where he originally started.

How far does Avon walk, in total?

\newp

\item Iphigenia and Ethelbert awoke one morning to find themselves on a rather large piece of graph paper. Not knowing what else to do in this situation, they decided to at least make a math problem out of it.

Iphigenia stood at $(6,2)$ and Ethelbert stood at the origin. Then, at the same time, they both began walking:

Iphigenia headed towards the $y$-axis (walking parallel to the $x$-axis) at a constant speed of 4 units per second.

Ethelbert headed straight towards Iphigenia's starting position, reached it 3 seconds later, and kept on walking in a straight line at a constant speed.

\begin{enumerate}

\item What are Iphigenia's parametric equations of motion?
\vfil
\item What are Ethelbert's parametric equations of motion?
\vfil
\item Give a formula for the distance between Iphigenia and Ethelbert after $t$ seconds.
\vfil 
\end{enumerate}

\newp

\item Below is the graph of a multipart function, $f(x)$, composed of one quarter-circular arc and two straight lines.

\begin{center}
\begin{tikzpicture}[auto,scale=1.2, line width=2pt]

\draw (-5.0,0) -- (6,0);
\draw (0,-1.0) -- (0,7.0);

\draw (-1,2) arc (0:90:3) ;

\draw (-1,2) -- (1,1);
\draw (1,1) -- (4,6);
 
\def \vShift{0.05};
\def \lilShift{0.35};
\def \micShift{0.01};

\draw (-4,\lilShift+5) node {$(-4,5)$};
\draw (-1-\lilShift,2-\lilShift) node {$(-1,2)$};
\draw (1,-\lilShift+1) node {$(1,1)$};
\draw (4,\lilShift+6) node {$(4,6)$};

\draw (5.5,-0.25) node {$x$};
\draw (-0.25,5.75) node {$y$};

\def \circRad{0.05};
\fill[black] (-4,5) circle(\circRad);
\fill[black] (-1,2) circle(\circRad);
\fill[black] (1,1) circle(\circRad);
\fill[black] (4,6) circle(\circRad);

\end{tikzpicture}
\end{center}

\begin{enumerate}
\item Write the multipart rule for this function.
\vfil
\item Find all values of $x$ for which $f(x) = 4$.
\end{enumerate}

\end{enumerate}

\end{document}


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