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\begin{document}
\noindent
\vfil \noindent

{\LARGE{
\hfil Math 120 B - Winter 2018 \hfil \pp
\hfil Midterm Exam Number One\hfil  \pp
\hfil January 25th, 2018 \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 & 12 &\hspace{10mm} \hfil\\ \hline 
 2 & 12 &       \\ \hline
 3 & 12 &       \\ \hline
 4 & 12 &      \\ \hline
 5 & 12 &      \\ \hline
Total & 60 & \\ \hline 
\end{tabular}
}
\end{center}
\vfil
\begin{itemize}
\item This exam consists of FIVE problems on THREE double-sided pages.
\item Show all work for full credit. 
\item You may use a TI-30X IIS calculator during this
exam. Other calculators and electronic devices are not permitted.
\item You do not need to simplify your answers, except on problem \#5.
\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 \textbox{Draw a box} around your final answer to each problem.
\item {\bf Do not write within 1 centimeter of the edge!} Your exam will be scanned for grading.
\item If you run out of room, write on the back of the last page and indicate that you have done so. If you still need more room, ask your TA for an extra page to staple to your exam.
\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}

%%% Section B:

\item {\bf [12 points]} Anthony and Carmela stand at the southwest and northwest corners (respectively) of an intersection, and Bobby stands 30 feet east of the northeast corner of the intersection. The streets are 30 feet wide.\\[.1 in]
Anthony walks in a straight line towards Bobby at a speed of 4 feet per second, paying no attention to traffic laws or common sense.\\[.1 in]
At the point when Anthony is closest to Carmela, Carmela yells at him for jaywalking.\\[.1 in]
Anthony immediately speeds up and walks the rest of the way towards Bobby at a speed of 8 feet per second.\\[.1 in]
How long does he spend walking, in total?
\vspace{-.4 in}
\begin{flushright}\begin{tikzpicture}[scale=.03]
\draw (-20,0) -- (0,0) -- (0,-20)
(-20,30) -- (0,30) -- (0,50)
(30,50) -- (30,30) -- (90,30)
(30,-20) -- (30,0) -- (90,0);
\fill [pattern=north east lines] (-20,30) -- (-20,35) -- (-5,35) -- (-5,50) -- (0,50) -- (0,30) -- cycle
(-20,0) -- (0,0) -- (0,-20) -- (-5,-20) -- (-5,-5) -- (-20,-5) -- cycle
(30,-20) -- (30,0) -- (90,0) -- (90,-5) -- (35,-5) -- (35,-20) -- cycle
(30,30) -- (90,30) -- (90,35) -- (35,35) -- (35,50) -- (30,50) -- cycle;
\draw [fill=black] (0,0) circle (3) node[below right,scale=.8] {\textsf{A}};
\draw [fill=black] (0,30) circle (3) node[above right,scale=.8] {\textsf{C}};
\draw [fill=black] (70,30) circle (3) node[below right,scale=.8] {\textsf{B}};
\end{tikzpicture}\end{flushright}

\newpage

\item {\bf [12 points]} The populations of Mashon and Vercer grow linearly over time.\\[.1 in]
In the year 2000, there were 6 thousand people in Mashon. The population of Mashon grows by 5 thousand people every 10 years.\\[.1 in]
In the year 2004, the population of Vercer was half the population of Mashon. In the year 2018, the population of Vercer was 1 thousand less than the population of Mashon.\\[.1 in]
When will the populations of Mashon and Vercer be equal? Round your answer to the nearest year.

\newpage

\item {\bf [6 points per part]} Fungo is walking around the coordinate plane.\\[.1 in]
At time $t=0$, Fungo begins walking from the point $(7,0)$ towards the point $(-5,9)$ at a constant speed, reaching it in $5$ seconds.
\begin{enumerate}
\item Write parametric equations for Fungo's coordinates after $t$ seconds.
\vskip 3 in
\item A puddle is growing, centered at the origin. After $t$ seconds its radius is $2t$ units.\\[.1 in]
How much time will Fungo spend inside the puddle?
\end{enumerate}

\newpage

\item {\bf [12 points]} Here's a graph of $f(x)$, consisting of a quarter-circle and two straight lines.
\vspace{-.2 in}
\begin{center}
\begin{tikzpicture}[auto,scale=.8, line width=2pt]

\foreach \x in {-4,-3,...,5} \draw [printersafe, line width=1pt,densely dotted] (\x,-3.2)--(\x,4.2);
\foreach \x in {-4,-3,...,5} \draw (\x+.2,.19) node {\scriptsize \x};
\foreach \y in {-3,-2,...,4} \draw [printersafe, line width=1pt,densely dotted] (-4.2,\y)--(5.2,\y);
\foreach \y in {-3,-2,...,4} \draw (.2,\y+.19) node {\scriptsize \y};

\draw [line width = 1.5 pt, <->] (-4.6,0) -- (5.5,0);
\draw [line width = 1.5 pt, <->] (0,-3.6) -- (0,4.6);

\draw (5.7,0) node {$x$};
\draw (0,4.9) node {$f(x)$};

\draw (-3,2) arc (180:270:3)
(0,3) -- (3,-2)
(3,2) -- (4,2);
\draw [fill=black,line width=1 pt] (-3,2) circle (.09)
(0,-1) circle (.1)
(3,-2) circle (.1)
(4,2) circle (.1);
\draw [fill=white,line width=1 pt] (0,3) circle (.09)
(3,2) circle (.1);
\end{tikzpicture}
\end{center}
\vspace{-.2 in}
Write the multipart rule for $f(x)$.
\vskip 2 in

\item {\bf [12 points]} Let $g(x) = x^2+x-2$. Simplify the following expression as much as possible: \[\dfrac{g(x+h)-g(x-h)}{h}\]

\end{enumerate}

\end{document}