# Mailinglist Archive: opensuse-edu (43 mails)

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##### Re: LaTeX
• From: Roger Whittaker <roger@xxxxxxxxxx>
• Date: Tue, 4 Apr 2000 13:02:52 +0000 (UTC)
• Message-id: <Pine.LNX.4.10.10004041354540.21467-302000@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>
Here are the examples.
A standard install will almost certainly have TeX and LaTeX installed.
To check, just type
latex
at the prompt. If it's there you'll get

This is TeX, Version 3.14159 (Web2C 7.3.1)
**

or similar.

When you do latex to a LaTeX source (.tex) file, it makes it into a .dvi
file. The DVI viewer can view that. You can further process it with
dvips to make a postscript file (.ps) and if you want with ps2pdf to make
a .pdf file (acrobat reader format)

Play with the examples I sent. I have better ones, but they're at home (I
don't do much `A'-level maths teaching here at SuSE...)

I hope you dont mind, but I'll forward this to the list also.

On Tue, 4 Apr 2000, Peter Rutherford wrote:

> Dear Roger
>
> I am re-sending the following reply to your message about LaTeX; my first effort was "bounced" back to me!
>
> Re. LaTeX
>
> I would love to see such examples and look forward to receiving them.
>
> I have performed a "standard" installation on my old 486. Will LaTeX be
> there as a matter of routine and, if so, how do I get to it?
>
> Is the DVI viewer in the KDE related to TeX in some way?
>
> Thanks
>
> Peter
>

--
Roger Whittaker
SuSE Linux Ltd
The Kinetic Centre
Theobald Street
Borehamwood
Herts
WD6 4PJ
----------------------
020 8387 1482
----------------------
roger@xxxxxxxxxxxxxxxx
----------------------
\documentclass[10 pt, a4paper, fleqn]{article} % fleqn aligns equations left
\setlength{\textwidth}{14.66 cm} % width of actual text
\setlength{\textheight}{24 cm} % height of actual text
\setlength{\oddsidemargin}{0.46 cm} % left margin minus one inch
% In practice this seems to give equal margins with just about the right text width.
\setlength{\topmargin}{0 cm}
\pagestyle{empty} % avoids page numbers
\setlength{\mathindent}{0 cm} % no indent for maths
\setlength{\parindent}{0 cm} % no indent for paragraphs
\setlength{\parskip}{11pt plus 1pt minus 1pt} % gap between paragraphs
\setlength{\marginparwidth}{0.8 cm} % width of margin paragraph
\usepackage{times}
\begin{document}

\section*{S6 PURE MATHEMATICS \hfill 22-10-98} % \hfill gets date right aligned
\bfseries Half-term homework \hfill \underline{Show all working clearly}\\
\normalfont
To be handed in on Monday 2-11-98
\vspace{-0.2 cm}
\newcounter{qno}
% if we don't declare the counter it won't work.
\begin{list}{ \arabic{qno})}{\usecounter {qno} \setlength{\leftmargin}{0 cm}}
% setlength{\leftmargin} gets the question text exactly aligned to the main left margin. Otherwise by default it is indented.
\setlength{\labelwidth}{1 cm}
\setlength{\labelsep}{0.5 cm}
\setlength{\itemsep}{0.2 ex plus 0.2 ex}
\newcommand{\marks}[1]{\marginpar{\hfill {\bfseries \small{#1}}}}
\item The first term of a geometric series is $$2500$$ and the fifth term is $$4$$. Given that the common ratio is positive, calculate\\
a) the seventh term of the series\\
b) the sum to infinity of the series. \marks{[5]}
\item $\mbox{i) Find }\sum_{r=1}^{100}\frac{2r}{3}$
ii) Find the sum to infinity of $$\frac{7}{10}+\frac{7}{100}+\frac{7}{1000}+\ldots$$, giving your answer as a fraction.\\ \vspace{-0.4 cm}
$\mbox{Hence or otherwise, find the value of }\sum_{r=1}^{\infty}\frac{k}{10^r} \mbox{ in terms of } k$ \vspace{-0.8 cm} \marks{[6]} \vspace{0.8 cm}
\item An arithmetic series has first term $$24$$ and common difference $$-3$$.\\
a) Prove that the sum $$S_n$$ of the first $$n$$ terms of this series is given by $$2S_n = 3n(17-n)$$\\
b) Given that $$S_n=105$$ find the possible values of $$n$$. \marks{[8]}
\item The third and sixth terms of a geometric series are $$4$$ and $$-\frac{1}{2}$$ respectively.\\
a) Find the first term of this series.\\
b) Find, to three significant figures, the sum of the first $$10$$ terms of this series. \marks{[7]}
\item $\mbox{Calculate the values of a) }\sum_{r=1}^{100}r \mbox{ , \quad b) }\sum_{r=1}^{50}2r$ \vspace{-0.2 cm}
$\mbox{Hence or otherwise, evaluate the sum } \sum_{r=1}^{50}(2r-1)$ \vspace{ -0.8 cm} \marks{[5]} \vspace{0.8 cm}
\item The points \emph{A}, \emph{B} and \emph{C} have coordinates $$(-3, 4)$$, $$(-1, 9)$$ and $$(7, 8)$$ respectively. \\
a) Calculate the gradient of \emph{AB}.\\
b) Find an equation of the line which passes through \emph{C} and is parallel to \emph{AB}. \marks{[4]}
\item a) Show that the triangle \emph{PQR} with vertices \emph{P}$$(-1, 7)$$, \emph{Q}$$(8, 19)$$ and \emph{R}$$(-8, 31)$$ is right-angled.\\
b) Find an equation of the line \emph{PQ}.\\
c) Calculate the area of $$\Delta$$\emph{PQR}. \marks{[6]}
\item The first four terms of an arithmetic progression are $$2$$, $$a-b$$, $$2a+b+7$$ and $$a-3b$$ respectively, where $$a$$ and $$b$$ are constants. Find $$a$$ and $$b$$ and hence determine the sum of the first $$30$$ terms of the progression. \marks{[5]}
\item A line $$\ell$$ passes through the point \emph{P}$$(3, k)$$, where $$k$$ is a constant, and is parallel to the line joining the points \emph{A}$$(1, 4)$$ and \emph{B}$$(k, 5)$$.\\
a) Find, in terms of $$k$$, an equation of $$\ell$$.\\
b) Show that $$\ell$$ passes through the point whose coordinates are $$(k+2, k+1)$$.\\
c) Given that the angle between the line $$\ell$$ and the positive $$x$$ axis is $$45^\circ$$, find the possible values of $$k$$. \marks{[8]}
\item a) Find, in terms of $$x$$ and $$y$$, the distance between the point \emph{P}$$(x, y)$$ and the point \emph{M}$$(3, 7)$$.\\
b) In the same way, find the distance between \emph{P}$$(x, y)$$ and the point \emph{N}$$(7, 1)$$.\\
c) Use your answers to form and simplify an equation for the path of \emph{P} if it moves so that the distances \emph{PM} and \emph{PN} are equal. \marks{[8]}
\item $$\ell_1$$ is the line $$2x+y=5$$ and $$\ell_2$$ is the line $$x+4y=6$$.\\
a) Calculate the coordinates of the point of intersection of $$\ell_1$$ and $$\ell_2$$.\\
b) Calculate in degrees to one decimal place, the angle between $$\ell_1$$ and $$\ell_2$$.\\
\emph{(A sketch diagram might be useful.)} \marks{[6]}
\end {list}
\end{document}\documentclass[11 pt, a4paper, fleqn]{article} % fleqn aligns equations left
\setlength{\textwidth}{14.66 cm} % width of actual text
\setlength{\textheight}{24 cm} % height of actual text
\setlength{\oddsidemargin}{0.46 cm} % left margin minus one inch
% In practice this seems to give equal margins with just about the right text width.
\setlength{\topmargin}{0 cm}
\pagestyle{empty} % avoids page numbers
\setlength{\mathindent}{0 cm} % no indent for maths
\setlength{\parindent}{0 cm} % no indent for paragraphs
\setlength{\parskip}{10pt plus 1pt minus 1pt} % gap between paragraphs
\setlength{\marginparwidth}{0.8 cm} % width of margin paragraph
\usepackage{times} % nice text fonts
\usepackage{multicol}
%\usepackage{amsmath} % easier equation alignment etc
%\usepackage{amsfonts} % to get extra symbols
%\usepackage{graphicx} if you want to include *.eps pictures
% USE \begin{quest} ... \end{quest} for main questions list.
% USE \begin{subq}... \end{subq} for alphabetically listed subquestions.
\begin{document}
\section*{S6 PURE MATHEMATICS \hfill 2-2-99} % \hfill gets date right aligned
\bfseries Trigonometry \hfill \underline{Show all working clearly}

\normalfont
\newcommand{\marks}[1]{\marginpar{\hfill {\bfseries \small{#1}}}} %defining marks command
\newcounter{qno}% if we don't declare the counter it won't work.
\newenvironment{quest} % main question list environment
{
\begin{list}{\arabic{qno})}
{
\usecounter {qno}
\setlength{\leftmargin}{0 cm} % align to left margin
\setlength{\labelwidth}{1 cm}
\setlength{\labelsep}{0.5 cm}
\setlength{\itemsep}{0.5 ex plus 0.2 ex}
}
}
{\end{list}
} % end of definition
\newcounter{qpart} % if we don't declare the counter it won't work.
\newenvironment{subq} % defining subquestion environment
{
\begin{list}{\alph{qpart}\hfill)} % alphabetic counter
{
\usecounter {qpart}
\setlength{\itemindent}{1.65 em}
\setlength{\labelwidth}{0.8 em}
\setlength{\labelsep}{0.8 em}
\setlength{\leftmargin}{0 em}
\setlength{\itemsep}{0.2 ex plus 0.1 ex} %these lengths look right at the moment
}
}
{\end{list}
} % end of definition
\begin{quest}
\vspace{-0.2 cm}
\item In each case express the trigonometrical ratio in terms of an acute angle.\\
(Examples: $$\sin 200^\circ=-\sin 20^\circ$$, \quad $$\cos 300^\circ=\cos 60^\circ.$$)
\begin{multicols}{4}
\begin{subq}
\item $$\sin 250^\circ$$
\item $$\cos 250^\circ$$
\item $$\tan 250^\circ$$
\item $$\sin 132^\circ$$
\item $$\cos 132^\circ$$
\item $$\tan 132^\circ$$
\item $$\sin (-75^\circ)$$
\item $$\cos (-75^\circ)$$
\item $$\tan (-75^\circ)$$
\item $$\sin 346^\circ$$
\item $$\cos 346^\circ$$
\item $$\tan 346^\circ$$
\end{subq}
\end{multicols}
\marks{[24]}
\item Express the following angles in radians:
\begin{subq}
\begin{multicols}{4}
\item $$300^\circ$$
\item $$60^\circ$$
\item $$120^\circ$$
\item $$315^\circ$$
\item $$225^\circ$$
\item $$30^\circ$$
\item $$600^\circ$$
\item $$15^\circ$$
\item $$330^\circ$$
\item $$720^\circ$$
\item $$135^\circ$$
\item $$270^\circ$$
\end{multicols}
\end{subq}
\marks{[12]}

\item Express the following angles in degrees:
\begin{subq}
\begin{multicols}{4}
\item $$2 \pi$$
\item $$\frac{\pi}{4}$$
\item $$\frac{3 \pi}{4}$$
\item $$\frac{5 \pi}{6}$$
\item $$\frac{7 \pi}{6}$$
\item $$\frac{5 \pi}{3}$$
\item $$\frac{5 \pi}{4}$$
\item $$\frac{3 \pi}{2}$$
\item $$\frac{2 \pi}{3}$$
\item $$\frac{5 \pi}{3}$$
\item $$\frac{2 \pi}{9}$$
\item $$\frac{\pi}{12}$$
\end{multicols}
\end{subq}
\marks{[12]}

\item Find all solutions between $$0^\circ$$ and $$360^\circ$$ of the following equations:
\begin{multicols}{4}
\begin{subq}
\item $$\sin \theta = \frac{1}{2}$$
\item $$\sin \theta = 0$$
\item $$\cos \theta = -\frac{1}{2}$$
\item $$\tan \theta = \sqrt{3}$$
\item $$\sin 2\theta = -\frac {1}{\sqrt{2}}$$
\item $$\cos 3\theta = 0$$
\item $$\sin^2\theta = \frac{3}{4}$$
\item $$\tan \theta = 1$$
\item $$\tan 2\theta = -\sqrt{3}$$
\item $$\sin \theta = -1$$
\item $$\sin 5\theta = \frac{1}{2}$$
\item $$\cos 5\theta = -1$$
\end{subq}
\end{multicols}
\marks{[24]}
\item Draw neat, clearly labelled sketch graphs of the following for $$0^\circ \leq x \leq 360^\circ$$ :
\begin{subq}
\item $$y=\cos 2x$$
\item $$y=5+\sin x$$
\item $$y=\sin(x-45^\circ)$$
\item $$y=1+\cos 3x$$
\end{subq}
\marks{[12]}
\item
\begin{subq}
\item Make a table of values and draw an accurate graph of $$y=\sin^2 x$$.
\item Draw a clear labelled sketch of the graph of $$y=1-\cos 2x$$.
\item Draw an intellegent conclusion.
\end{subq}
\marks{[12]}
\item Prove that for all angles $$\theta$$, $$\sin^2 \theta + \cos^2 \theta = 1$$. \marks{[4]}
\item Given that $$\cos \phi = \frac {5}{13}$$ and $$\phi$$ is acute, find the exact values of $$\sin \phi$$ and $$\tan \phi$$. \marks{[4]}
\item Given that $$\sin \psi = \frac {2}{7}$$ and $$\psi$$ is obtuse, find, as surds the values of $$\cos \psi$$ and $$\tan \psi$$. \marks{[4]}

\end{quest}
\end{document}
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