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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A, B - Winter 2010 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil January 28, 2010 \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}
}
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\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 Aiman and Hue are walking in the $xy$-coordinate plane, with units in kilometers. They move
at constant speeds and they move linearly (i.e., their paths are straight lines).
Aiman starts walking from the origin. Aiman will reach the
point $(4,6)$ after walking for 4 hours.

Hue started walking at the same time as Aiman.  She started from the point $(-2,5)$
and will reach the point $(8,1)$ after walking for 5 hours.

\begin{enumerate}

\item Write parametric equations for the coordinates of Aiman, $t$ hours after she starts walking.

\vfil

\item Write parametric equations for the coordinates of Hue, $t$ hours after she starts walking.

\vfil \vfil

\item After how many hours of walking will Aiman and Hue be 4 kilometers apart for the first time?
\end{enumerate}

\vfil \vfil

\newp

\item Aidan is walking in a straight line from his house to Cahal's house.  Aidan's house 
is 5 km due east of Barra's house.  Cahal's house is 1 km east and 15 km south of Barra's house.

On Aidan's walk, how close does he come to Barra's house?

\newp

\item The figure below shows the graph of a multipart function, $f(x)$.  The graph consists of two line segments and
a quarter circle.  The coordinates of the labeled are as shown in the table below.

\begin{tabular}{l l}
A & (0,2) \\
B & (8,5) \\
C & (11,8) \\
D & (16,3) 
\end{tabular}

The figure is not to scale.

 \epsfig{file=multipart01.eps, 
 width=11cm,
 angle=0 }

Write the multipart rule for the function, $f(x)$.


\newp

\item For both parts of this problem, $f(x)=-2x^2-6x+11$.

\begin{enumerate}

\item What are the largest and smallest values of $f(x)$ for $x$ in the interval $-2 \le x \le 5$?

\vfil

\item Suppose $h \ne 0$.  Simplify the expression 
\[
\frac{f(x+h)-f(x-h)}{h}
\]
as much as possible.

\vfil

\end{enumerate}

\end{enumerate}

\end{document}


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