\documentclass[12pt]{report}
\usepackage{palatino}
\usepackage{epsfig}
\pagestyle{empty} %%% this results in no pagenumbers (footer is empty}
\addtolength{\oddsidemargin}{-0.875in}
\addtolength{\evensidemargin}{-0.875in}
\addtolength{\textwidth}{1.75in}
\addtolength{\topmargin}{-0.5in}
\addtolength{\textheight}{2.0in}
\baselineskip=20pt
\newcommand{\dsps}{\displaystyle}
\newcommand{\pp}{\par \noindent}
\newcommand{\newp}{\vfil \eject}
\begin{document}
\noindent
\vfil \noindent
\large
\hfil Math 120 - Autumn 2011 \hfil \pp
\hfil Final Exam\hfil \pp
\hfil December 10, 2011 \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
5 & 10 & \\ \hline
6 & 10 & \\ \hline
7 & 10 & \\ \hline
8 & 10 & \\ \hline
Total & 80 & \\ \hline
\end{tabular}
}
\end{center}
\vfil
\begin{itemize}
\item Complete all questions.
\item Show all work for full credit.
\item You may use a scientific calculator during this
examination. Graphing calculators are not allowed.
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.
\item You have 170 minutes to complete the exam.
\end{itemize}
\vfil
.
\newp
\begin{enumerate}
\item You have 300 meters of fencing with which to build two enclosures.
One will be a square, and the other will be a rectangle where the length
of the base is exactly twice the length of the height.
\begin{enumerate}
\item Give the dimensions of the square and rectangle that \textbf{minimize} the combined area.
\vfil \vfil
\item What is the \textbf{maximum} combined area?
\vfil
\end{enumerate}
\newp
\item Erika is measuring the height of a tree. She is standing on the ground at some distance from the tree and measures an angle of
63 degrees to the top of the tree. She walks 20 feet further away from the tree and measures an angle of 50 degrees to the top of the
tree (this is her second measurement).
A year later she comes back to check on the tree and it has grown.
She measures the angle from the same location as the second
measurement from the year before and now gets an angle of 52
degrees.
How much taller is the tree?
\newp
\item A weight is attached to a spring suspended from the ceiling.
The height $h(t)$ of the weight is a sinusoidal function of time
$t$. At time $t=5$ seconds, the weight is at its lowest height of
15 cm. The weight next reaches its highest height of 37 cm at time
$t=9.4$ seconds.
During the first 20 seconds, how much time is the weight above 28 cm?
\newp
\item
\begin{enumerate}
\item Let $\displaystyle f(x) = \frac{x+1}{2x}$ and $g(x) = 7x-1$.
Find the inverse of $h(x) = f(g(x))$.
\vfill
\item Find all linear functions $f(x)$ such that the function $g(x) = f(f(x))$
has the properties $g(1) = 10$ and $g(2) = 14$.
\vfill
\end{enumerate}
\newp
\item William took a walk near the Circular Dunes.
The Circular Dunes is a perfect circle, with a radius of 7 km.
William began his walk from a point 11 km due north of the center
of the Dunes. He walked due east for one hour, and then due south for
three hours. He then walked due west until he left the Dunes.
William walked at a constant speed of 3 km/hr.
\begin{enumerate}
\item For what length of time
was William in the Dunes?
\vfil
\item Suppose William had walked in a straight line from the point where he
entered the Dunes to the point where he exited. If he continued along that line,
how far west of the center of the Dunes would he be when he was due west of the center?
\end{enumerate}
\newp
\item Rosetta is growing a bamboo plant in her apartment.
The height of the plant is a linear-to-linear function of time.
Thirty days ago, the plant was 14 cm high.
Today, the plant is 18 cm high.
The plant always increases in height, and will approach (but never exceed)
a height of 32 cm.
\begin{enumerate}
\item Find a function representing the height of the plant as a function of time.
\vfil
\item Rosetta also has a fast-growing cactus. Today, its height is 9 cm.
The cactus grows at a constant rate of 1 cm per day.
When will the cactus and the bamboo plant be the same height? Give your answer
in days after today.
\end{enumerate}
\newp
\item The population of the city of Alk increases by 17 percent every 12 years.
In 2010, the population of Alb was 8,000.
The population of the city of Bem doubles in the length of time it takes for the
city of Alk to triple. In 2005, there were 15,000 people in Bem.
When will the cities have the same population? Give your answer in years after
2010.
\newp
\item Maria is riding a ferris wheel. Her linear speed is 5 meters per second.
After the ride starts, it takes Maria 8 seconds to reach the highest point on the ride.
It takes 18.5 seconds from when the ride starts for Maria to reach the lowest point
on the ride. The highest point of the ride is 36 meters off the ground.
How high above the ground is Maria 120 seconds after the ride starts?
\end{enumerate}
\end{document}
% \epsfig{file=pizza01.eps,
% width=11cm,
% angle=0 }