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\begin{document}
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\vfil \noindent

{\LARGE{
\hfil Math 120 A, B Autumn 2012 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil October 18, 2012 \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
.

\newp

\begin{enumerate}

\item Below is the graph of a multipart function, $f(x)$, which is composed of 
a straight line and two circular arcs.  The function's domain is $0 \le x \le 10$.

\begin{tikzpicture}[auto,scale=1.9, line width=2pt]

\draw (-1.0,0) -- (6,0);
\draw (0,-1.0) -- (0,4.0);

\draw (2,3) arc (0:-180:1) ;

\draw (2,3) -- (3,1);
 
\draw (5,3) arc (90:180:2);

\def \vShift{0.05};
\def \lilShift{0.35};
\def \micShift{0.01};

\draw (5+\lilShift,3) node {$(10,6)$};
\draw (3,1-\lilShift) node {$(6,2)$};
\draw (2+\lilShift,3) node {$(4,6)$};
\draw (0-\lilShift,3) node {$(0,6)$};

\draw (5.5,-0.25) node {$x$};
\draw (-0.25,3.75) node {$y$};

\def \circRad{0.05};
\fill[black] (0,3) circle(\circRad);
\fill[black] (2,3) circle(\circRad);
\fill[black] (3,1) circle(\circRad);
\fill[black] (5,3) circle(\circRad);

\end{tikzpicture}

 Write the multipart rule for this function.


\newp

\item Titus and Ophelia are moving in the $xy$-plane.  They both move along straight lines at constant speeds.
The coordinates of the $xy$-plane are given in meters (e.g., the point $(1,0)$ is one meter to the right of the origin).

Titus leaves the origin and heads toward the point $(5,12)$ at a rate of 3 meters per second.

At the moment Titus leaves the origin, Ophelia starts moving from the point $(5,-4)$ and heads toward the point $(3,2)$.  She will
reach the $x$-axis after 2 seconds.

\begin{enumerate}

\item Give parametric equations for the location of Titus $t$ seconds after he starts moving.
\vfil
\item Give parametric equations for the location of Ophelia $t$ seconds after she starts moving.

\end{enumerate}

\newp

\item Renaldo is walking near the Circular Forest, a forest in the shape of a perfect circle with radius 9 km.
Renaldo walks at a constant speed of 2 km/hr.
Renaldo starts walking south from a point 5 km west and 1 km north of the northernmost point of the forest.
After entering the forest, he continues walking for one hour, then turns 
and walks west
until he leaves the forest.

For what length of time was Renaldo in the forest?

\newp

\item You are reading a book.  Five days from now, you will have 200 page left to read.
Ten days from now, you will have 150 pages left to read.
Twenty days from now, you will have 125 pages left to read.

Suppose the number of pages you have left to read is a quadratic function of time.

When, in the next two weeks, will you have 175 pages left to read?  

Give your answer in days from now (a non-whole number is okay!).

\end{enumerate}

\end{document}


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