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\newcommand{\pp}{\par \noindent}
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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A, B - Winter 2011 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil February 24 , 2011 \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.  Graphic 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 You have 800 meters of fencing with which to build two enclosures.
One will be a circle, and the other will be a square.
The circular enclosure will also have two partitions each of which is the length
of the circle's diameter.  For example, your enclosures might look like this:

\epsfig{file=enclosuresCirclePartSquare2.eps, 
 width=8cm,
 angle=0 }

\begin{enumerate}

\item What should the radius of the circle be to minimize the combined
area of the circle and square?

\vfil \vfil

\item What should the radius of the circle be to maximize the combined
area of the circle and square?

\end{enumerate}

\newp

\item  A bicyclist is riding at 36 km/hour.  She is pedaling at 102 rpm.  
Her rear wheel has radius 0.34 m and her rear sprocket has radius 0.04 m.

\epsfig{file=bikeLabeled.eps, 
 width=8cm,
 angle=0 }

\begin{enumerate}

\item What is the radius of her front sprocket?

\vfil

\vfil

\item Through what angle (in DEGREES) does her rear wheel rotate in 0.01 second?

\end{enumerate}

\newp

\item 
\begin{enumerate}

\item Give an example of a linear to linear rational function with fixed points $x=-5$ and $x=2$.

\vfil

\item Let $\dsps f(x)=x^2-10x+18, x\ge 5$.  Find $f^{-1}(x)$.


\end{enumerate}

\newp

\item The population of city A increases by 1.9\% each year.

In 1995, city A's population was 15,000.

City B's population triples every 50 years.

In the year 2000, there were 1000 more people in city A than in city B.

When will the populations of city A and city B be equal?  Express your answer in years after 2005.




\end{enumerate}

\end{document}


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