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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 C - Autumn 2010 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil October 21, 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
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{\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 The city of Arb is 10 km NORTH and 4 km WEST of the city of Ott.

The city of Bim is 25~km EAST and 7 km SOUTH of Ott.

The city of Cup is 2 km EAST and 5 km SOUTH of Ott.

If you travel along a straight line from Arb to Bim, how close do you come to Cup?


\newp

\item Fred is moving at a constant speed along a line in the xy-plane.
He starts from the point $(-5,3)$ and heads directly toward the point $(13,-9)$, reaching
it after 6 seconds.

\begin{enumerate}
\item Give Fred's parametric equations of motion.

\vfil

\item Determine all times when Fred is a distance of 2 units from the origin.

\end{enumerate}
\vfil

\newp

\item Abby and Zev are at a campsite in a desert.  At 7 AM, Zev wakes up and starts walking
NORTH at 4 km per hour.  At 8 AM, Abby wakes up and starts walking EAST at 5 km per hour.
At 10 AM, Zev changes his speed, and continues walking NORTH at 3 km per hour. 

Express the distance between Abby and Zev as a multipart function of the time, $t$,
that Zev has been walking. You need only consider $t\ge0$.

\newp 

\item The function $f(x)$ is quadratic.  The vertex of the graph of $f(x)$ is the point $(-5,-3)$.
The graph of $f(x)$ passes through the point $(-4,-5)$.

\begin{enumerate}
\item Express $f(x)$ in the form $f(x)=ax^2+bx+c$.
\vfil
\item Simplify the expression 
\[
\frac{f(x+r)-f(x+2r)}{r}
\]
as far as possible.  Assume $r$ is a non-zero constant.

\end{enumerate}
\vfil

\end{enumerate}

\end{document}


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