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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A - Winter 2008 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil February 28, 2008 \hfil \pp
\normalsize
\vfil
\medskip
\hfil Name: \hrulefill \hrulefill \hrulefill
\hspace{0.5in}
 Section: \hrulefill
\vfil
\begin{center}
{\large
\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 You may use a calculator during this
examination.  
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,
or read a numerical solution from a graph on your calculator
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 Show all work for full credit.  
\item You have 50 minutes to complete the exam. 
\end{itemize}
\vfil
.

\newp

\begin{enumerate}

\item Paolo is running at a constant speed of 3 meters per second around a circular track.  
He runs clockwise around the track.
From his starting point, it takes him 82 seconds to reach the northernmost point of the
track.  He takes 305 seconds to complete
one lap of the track.  

After running for 12 minutes, how far (in a straight line) is he from the
westernmost point of the track?

\newp

\item Lucy's height is a linear-to-linear rational function of time.
Today, her height is 10 feet.  One year from today her height will be 15 feet.
Five years from today, her height will be 20 feet.

How tall will she be 30 years from today?

\newp

\item Graham had an accident, and injured his left foot.  As a result, 
his foot is swelling and
contracting in such a way that its length is a sinusoidal function of time.
One hour after his accident, his foot had swelled to its maximum length: 30 cm.  
It then decreased in length, reaching its minimum length, 22 cm, 10 hours after
the accident.

\begin{enumerate}
\item How long was his foot 3 hours after the accident?

\vfil

\item Find all times in the first 24 hours after the accident when his foot was
28.3 cm long.  Express these times in hours after the accident.


\end{enumerate}

\newp

\item Let 
\[
f(x) = \left\{ \begin{array}{ll}
	3-x & \mbox{if $x \ge 2$ } \\
	2-\frac{1}{2}x & \mbox{if $x<2$ } 
	\end{array}
	\right.
\]
and
\[
g(x) = |x+1|.
\]

	
\begin{enumerate}

\item (8 points) Write a multi-part rule for the function $h(x)= 3f(x) - g(x)$.
\vfil \vfil \vfil \vfil
\item (2 points) Is the function $h(x)$ one-to-one? Explain.

\end{enumerate}


\end{enumerate}


\end{document}




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