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{\LARGE{
\hfil Math 120 A - Autumn 2016 \hfil \pp
\hfil Midterm Exam Number One\hfil  \pp
\hfil October 20th, 2016 \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 
 
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{\Huge
\begin{tabular}{||c|c|r||} \hline 
 1 & 15 &\hspace{10mm} \hfil\\ \hline 
 2 & 15 &       \\ \hline
 3 & 8 &       \\ \hline
 4 & 8 &      \\ \hline
5 & 14 &    \\ \hline
Total & 60 & \\ \hline 
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}
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\vfil
\begin{itemize}
\item This exam consists of FIVE problems on FIVE pages, including this cover sheet.
\item Show all work for full credit. 
\item You may use a TI-30X IIS calculator during this
exam.  Other calculators and electronic device are not permitted.
\item You do not need to simplify your answers.
\item If you use a trial-and-error or guess-and-check method
when a more rigorous method is available, you will not receive full credit.
\item If you write on the back of the page, please indicate that you have done so!
\item You may use one hand-written double-sided 8.5" by 11" page of notes.
\item You have 50 minutes to complete the exam.
\end{itemize}

\vfil
{\small --}

\newpage

\begin{enumerate}

\item {\bf [15 points]} Candela stands $10$ meters west and $16$ meters south of a gym. Spark stands $3$ meters east and $11$ meters north of the gym.\\[.1 in]
Candela walks due east until she is $17.8$ meters away from the gym. Then, she turns and walks in a straight line towards Spark.\\[.1 in]
How close does Candela get to the gym?

\newpage

\item {\bf [5 points per part]} Luke and Reva begin walking in the $xy$-plane at constant speeds at the same time.\\[.1 in]
Luke walks from $(3,5)$ to $(-2,4)$ in a straight line, reaching it in $10$ seconds.\\[.1 in]
Reva walks from $(-4,6)$ in a straight line. When Luke crosses the $y$-axis, Reva is at $(4,1)$.

\begin{enumerate}
\item Write parametric equations for Luke's position, $t$ seconds after he starts walking.
\vskip 2 in
\item Write parametric equations for Reva's position, $t$ seconds after she starts walking.
\vskip 3 in
\item When is Luke directly east of Reva?
\end{enumerate}

\newpage

\item {\bf [8 points]} Consider the following multipart function $f$:

$$f(x) = \begin{cases}
0 & \mbox{if } x \leq 0\\
x+5 & \mbox{if } 0 < x < 4\\
x^2+6 & \mbox{if }x \geq 4\\
\end{cases}$$

Find all solutions to the equation $f(x) = x^2-1$.

\vskip 3.5 in

\item {\bf [8 points]} Find all values of $d$ such that the vertex of $y = dx^2 + 5x + d + 1$ is on the $x$-axis.

\newpage


\item {\bf [14 points]} Ken sells sweaters. His profit is a quadratic function of the price he charges.\\[.1 in]
If he gives the sweaters away for free, he will {\bf lose} $\$100$.\\[.1 in]
If he charges $\$10$ per sweater, he will {\bf earn} $\$80$.\\[.1 in]
If he charges $\$20$ per sweater, he will {\bf earn} $\$180$.\\[.1 in]
How much will he earn by charging $\$33$ per sweater?

\end{enumerate}

\end{document}