\documentclass[12pt]{report} 

\usepackage{palatino}
\usepackage{epsfig}
\usepackage[margin=0.8in]{geometry}

\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{patterns,arrows,snakes}

\pagestyle{empty} %%% this results in no pagenumbers (footer is empty}

\setlength{\parindent}{0in}
\setlength{\parskip}{0.05in}

\baselineskip=20pt

\tikzstyle{printersafe}=[snake=snake,segment amplitude=0 pt]

\newcommand{\dsps}{\displaystyle}
\newcommand{\pp}{\par \noindent}
\newcommand{\newp}{\vfil \eject}

\begin{document}
\noindent
\vfil \noindent

{\LARGE{
\hfil Math 120 C - Autumn 2017 \hfil \pp
\hfil Midterm Exam Number One\hfil  \pp
\hfil October 19th, 2017 \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 & 15 &\hspace{10mm} \hfil\\ \hline 
 2 & 15 &       \\ \hline
 3 & 15 &       \\ \hline
 4 & 15 &      \\ \hline
Total & 60 & \\ \hline 
\end{tabular}
}
\end{center}
\vfil
\begin{itemize}
\item This exam consists of FOUR 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]} Alex is at the {\em northernmost} point of a circular parking lot with radius $26$ feet.\\[.1 in]
Dylan stands $22.4$ feet west and $27$ feet south of the {\em southernmost} point of the parking lot.\\[.1 in]
Dylan walks due north until he hits the edge of the parking lot. Then, he turns and walks in a straight line towards the {\em easternmost} point of the parking lot.\\[.1 in]
How close does Dylan get to Alex?

\newpage

\item {\bf [5 points per part]} Chidi and Tahani are walking around the coordinate plane.\\[.1 in]
Chidi begins at the point $(6,-4)$ and walks towards $(-2,2)$ in a straight line at constant speed, reaching it in $10$ seconds.\\[.1 in]
Tahani begins at the point $(5,8)$ and also walks in as straight line at constant speed.\\[.1 in]
One second after Chidi crosses the $y$-axis, Tahani also crosses the $y$-axis at the same place.
\begin{enumerate}
\item Write parametric equations for Chidi's coordinates after $t$ seconds.
\vskip 2.5 in
\item {\em Where} and {\em when} does Chidi cross the $y$-axis?
\vskip 2.5 in
\item What is Tahani's speed?

\end{enumerate}

\newpage

\item Consider the following multipart function $f$:

$$f(x) = \begin{cases}
-2x-5 & \mbox{if } -4 \leq x < -1\\
-1 & \mbox{if } -1 \leq x \leq 2\\
1+\sqrt{4-(x-2)^2} & \mbox{if } 2 < x \leq 4\\
\end{cases}$$

\begin{enumerate}
\item {\bf [7 points]} Sketch a graph of $f(x)$ below.

\begin{center}
\begin{tikzpicture}
\draw [very thick, <->] (-4.5,0) -- (4.5,0) node[anchor = west] {$x$};
\draw [very thick, <->] (0,-4.5) -- (0,4.5) node[anchor=south] {$f(x)$};
\foreach \n in {-4,-3,...,4}
{
 \draw [thick, densely dotted, printersafe] (\n,-4.5) -- (\n,4.5) (-4.5,\n) -- (4.5,\n);
 \node [anchor = south west,scale=.7] at (0,\n) {\n};
 \node [anchor = south west,scale=.7] at (\n,0) {\n};
}
\end{tikzpicture}
\end{center}
\vskip .2 in
\item {\bf [8 points]} Find all values of $x$ such that $f(x) = \frac12x+1$.
\end{enumerate}

% Write a multipart function for this.
% Write a multipart function for the vertical distance from this graph to some other thing?

\newpage

\item The temperature in Paraboland is modeled by a quadratic function of time.\\[.1 in]
Right now, the temperature is $20^\circ$.\\[.1 in]
In $2$ days, the temperature will be $27^\circ$.\\[.1 in]
In $10$ days, the temperature will be $51^\circ$.
\begin{enumerate}
\item {\bf[12 points]} Write a function $f(x)$ for the temperature in Paraboland $x$ days from now.
\vskip 6.5 in
\item {\bf[3 points]} What will the maximum temperature be?
\end{enumerate}

\end{enumerate}

\end{document}