% Exam Template for UMTYMP and Math Department courses
%
% Using Philip Hirschhorn's exam.cls: http://www-math.mit.edu/~psh/#ExamCls
%
% run pdflatex on a finished exam at least three times to do the grading table on front page.
%
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% These lines can probably stay unchanged, although you can remove the last
% two packages if you're not making pictures with tikz.
\documentclass[11pt]{exam}
\RequirePackage{amssymb, amsfonts, amsmath, latexsym, verbatim, xspace, setspace}
%\RequirePackage{tikz, pgflibraryplotmarks}
\RequirePackage{tikz}
\usetikzlibrary{plotmarks}
% By default LaTeX uses large margins. This doesn't work well on exams; problems
% end up in the "middle" of the page, reducing the amount of space for students
% to work on them.
\usepackage{tabularx}
\usepackage{graphicx}
\usepackage[margin=2.5cm,a4paper]{geometry}
% Here's where you edit the Class, Exam, Date, etc.
\newcommand{\class}{YAP501E - Engineering Mathematics}
\newcommand{\term}{Fall 2014}
\newcommand{\examnum}{FINAL EXAM}
\newcommand{\examdate}{December 24th, 2014}
\newcommand{\timelimit}{80 Minutes}
\newcommand{\questionspace}{0.7cm}
% For an exam, single spacing is most appropriate
\singlespacing
% \onehalfspacing
% \doublespacing
% For an exam, we generally want to turn off paragraph indentation
\parindent 0ex
\begin{document}
% These commands set up the running header on the top of the exam pages
\pagestyle{head}
\firstpageheader{}{}{}
\runningheader{\class}{\examnum\ - Page \thepage\ of \numpages}{\examdate}
\runningheadrule
\begin{tabularx}{\textwidth}{X r}
\textbf{\class} & \textbf{\examdate} \\
\textbf{\term}&\\
\textbf{Time allowed: \timelimit} &\\
\end{tabularx}\\
\rule[1ex]{\textwidth}{.1pt}
This exam contains 3 problems. Check to see if any of the questions are missing. Enter all requested information on the top of your answer sheet(s). You are required to show your work on each problem on the answer sheet. You may not use your books and notes during the exam.
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%
% See http://www-math.mit.edu/~psh/#ExamCls for full documentation, but the questions
% below give an idea of how to write questions [with parts] and have the points
% tracked automatically on the cover page.
%
%
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\vspace{0.3cm}
\begin{center}
\bfseries \examnum
\end{center}
\vspace{0.1cm}
\begin{questions}
% -----------------------------------------------------------------
\question Find the solution of the initial value problem:
\begin{equation*}
(x+2)y^\prime-xy=0
\end{equation*}
with the condition: $y(0)=3$.
\vspace{\questionspace}
% -----------------------------------------------------------------
\question Solve the given differential equation:
\begin{equation*}
y^{\prime\prime}-4y=8e^{2x}
\end{equation*}
\vspace{\questionspace}
% -----------------------------------------------------------------
\question Find the velocity $v$ if $v(0)=V$ and determine the maximum distance $x_{max}$ considering the linear motion of a rocket of mass $m$ launched from the earth surface, $M$ and $R$ are the mass and the radius of earth (Figure~\ref{fig:F}). Equation of motion of the rocket is as follows:
\begin{equation*}
m\frac{d^2x}{dt^2} = -G \frac{M \cdot m}{(x+R)^2}
\end{equation*}
where $G$ is the gravitational constant.
\begin{figure}[h]
\centering
\includegraphics[scale=0.90]{F_fig}
\caption{Earth and the rocket}
\label{fig:F}
\end{figure}
\vspace{\questionspace}
% -----------------------------------------------------------------
\end{questions}
\end{document}