index.tex

\documentclass[a4paper]{article}
\usepackage[latin1]{inputenc}
\usepackage[LGR,T1]{fontenc}
\usepackage[greek,frenchb]{babel}
\usepackage{array,multicol,multirow,enumerate}
\usepackage{graphicx,pst-all,pst-eucl}
\usepackage{amsmath,amsfonts,amsthm,geometry}
\usepackage{fancyhdr}
\setlength{\parindent}{0mm}
\def\d{$\diamond \,$}
\def\*{\times}
\def\Euro{\textgreek{\euro}\ }
\def\m@th{\mathsurround=0pt}
\def\trou#1{
    \setbox0=\hbox{\textbf{#1}} \dp0=0pt \m@th
    \underline{\hbox{\hskip\wd0}}
}
\newcommand{\machine}[4]{
        \begin{pspicture}
        \rput(0,0){\rnode{A}{#1}}
        \rput(3,0.11){\rnode{B}{#2}}
        \psset{nodesep=5pt}
        \ncarc[arcangleA=25,arcangleB=25]{->}{A}{B}\mput*{\ovalnode{m}{#3}}
        \ncarc[arcangleA=25,arcangleB=25]{->}{B}{A}\mput*{\ovalnode{d}{#4}}
        \end{pspicture}
        \hskip 3.1cm}
\newcommand{\cylindre}[5]{
\pstGeonode[PointSymbol=*,PointName=#2](0,0){#1}
\pstGeonode[PointSymbol=none,PointName=none](10,0){Aamoi}
\pstGeonode[PointSymbol=none,PointName=none](#4,#3){HG}
\pstGeonode[PointSymbol=none,PointName=none](-#4,#3){HD}
\pstGeonode[PointSymbol=none,PointName=none](#4,0){BG}
\pstGeonode[PointSymbol=none,PointName=none](-#4,0){BD}
\pstLineAB{HG}{BG}
\pstLineAB{HD}{BD}
 
\psplot[linestyle=dashed]{-#4}{#4}{#4 2 exp x 2 exp sub .5 exp #5 mul}
\psplot{-#4}{#4}{#4 2 exp x 2 exp sub .5 exp -#5 mul}
\psplot{-#4}{#4}{#4 2 exp x 2 exp sub .5 exp #5 mul #3 add}
\psplot{-#4}{#4}{#4 2 exp x 2 exp sub .5 exp -#5 mul #3 add}
}
 
\newcommand{\cone}[7]{
\pstGeonode[PointSymbol=*,PointName=#2](0,0){#1}
\pstGeonode[PointSymbol=none,PointName=none](10,0){Aamoi}
\pstGeonode[PointSymbol=none,PointName=none](0,#3){Hsommet}
\pstMiddleAB[PointSymbol=none,PointName=none]{#1}{Hsommet}{Milieuu}
\pstInterCC[PointSymbol=none,PointName=none,RadiusA=\pstDistVal{#6}]{#1}{}{Milieuu}{Hsommet}{Ibidon}{Jbidon}
\pstProjection[PointSymbol=none,PointName=none]{#1}{Aamoi}{Jbidon}{Jbidon'}
\pstProjection[PointSymbol=none,PointName=none]{#1}{Aamoi}{Ibidon}{Ibidon'}
 
\psplot[linestyle=dashed]{-#6}{#6}{#6 2 exp x 2 exp sub .5 exp #7 mul}
\psplot{-#6}{#6}{#6 2 exp x 2 exp sub .5 exp -#7 mul}
\pstHomO[HomCoef=#7,PointSymbol=none,PointName=#5]{#1}{Hsommet}{#4}
\pstHomO[HomCoef=#7,PointSymbol=none,PointName=none]{Jbidon'}{Jbidon}{T1}
\pstHomO[HomCoef=#7,PointSymbol=none,PointName=none]{Ibidon'}{Ibidon}{T2}
\pstLineAB{#4}{T1}
\pstLineAB{#4}{T2}
}
 
\newcommand{\rapporteur}{
\SpecialCoor
\pscircle{5}
\multido{\i=0+1}{181}{\psline(5;\i)}
\pscircle[fillcolor=white,fillstyle=solid,linestyle=none]{4.5}
\multido{\i=0+10}{19}{\psline(5;\i)}
\pscircle[fillcolor=white,fillstyle=solid,linestyle=none]{4}
\pscircle[fillcolor=white,fillstyle=solid]{3}
\psframe[fillcolor=white,fillstyle=solid,linestyle=none](5,-5.1)(-5,-1.75)
\pscircle[fillcolor=white,fillstyle=solid]{.5}
\psframe[fillcolor=white,fillstyle=solid](-5,-1.75)(5,0)
\psline[linecolor=white](-.5,0)(.5,0)
\psline[linecolor=white](-3,0)(-4,0)
\psline[linecolor=white](3,0)(4,0)
\pscircle[fillcolor=white,fillstyle=solid]{.05}
\NormalCoor
}
 
\newcommand{\QCM}[4]{
    \begin{tabular}[t]{p{13cm}c}
    #1 & \psset{xunit=1 cm}
    \begin{pspicture}(-0.3,0)(1.5,0.5)
    \pspolygon(0,0)(1.5,0)(1.5,-.5)(0,-.5)
    \psline(.5,0)(.5,-.5) \psline(1,0)(1,-.5)
    \uput[90](0.25,0){A}  \uput[90](0.75,0){B} \uput[90](1.25,0){C}
    \end{pspicture} \\
    A: #2 \qquad B: #3 \qquad C: #4 & \\
    \end{tabular}}
 
\newcommand{\smallbox}{
    \begin{pspicture}(.5,.5)
    \pspolygon(0,0)(.25,0)(.25,.25)(0,.25)
    \end{pspicture}}
 
\renewcommand{\vec}[1]
{\mathord{\setbox0\hbox{$#1$} \mathop{\smash{#1}\setbox1\copy0\ht1 0.8\ht0
\vphantom{\copy1}\mskip0.8\thinmuskip}
\limits^{\hbox to\wd0{$\mskip0.8\thinmuskip$\rightarrowfill}}\mskip-0.8\thinmuskip}}
 
\newcommand{\system}[2]{
\left\{
\begin{array}{l}
#1\\
#2
\end{array}
\right.
}
 
\newcolumntype{I}{!{\vrule width 1.5pt}}
\newlength\savedwidth
\newcommand\whline{\noalign{\global\savedwidth\arrayrulewidth\global\arrayrulewidth
1.5pt} \hline \noalign{\global\arrayrulewidth\savedwidth}}
% Marges
\geometry{ hmargin=1.5cm, vmargin=1.5cm }
% Exo
\newcounter{nexo}
\setcounter{nexo}{0}
\newcommand{\exo}{
    \stepcounter{nexo}
    {\textbf{$\triangleright$ Exercice \arabic{nexo} :}}
}
% Questions
\newenvironment{questions}{\begin{enumerate}[1 $\, \diamond$]}{\end{enumerate}}
 
    \lhead{\textsf{Collège Château Forbin} - \textit{Mathématiques}}
    \chead{}
    \rhead{\textit{Année} 2005/2006}
    \pagestyle{fancy}
  \renewcommand{\headrulewidth}{0.5pt}
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Début du document %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
\begin{document}
{\noindent \textbf{NOM :} \hfill \textit{lundi $16$ janvier
$2006$}}
 
\vskip 0.3cm
 
{\noindent \textbf{Prénom :} \hfill \textbf{Classe : 5\ieme 5}}
\begin{center}
    {\large \textbf{Contrôle de cours \textit{n}°$3$}}\\
    \textit{durée : $20$ minutes}
\end{center}
 
\vskip 0.3cm \hrule\vspace{\baselineskip}
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DEBUT DES EXERCICES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
\vskip 1.5cm
 
\exo (2 points) - Compléter les phrases suivantes :
 
\vskip 0.5cm
 
\begin{enumerate}[(a)]
    \item Dans l'écriture $\dfrac{a}{b}$, $a$ est le
    \trou{numérateur} et $b$ est le \trou{dénominateur} du
    quotient de \trou{~~a~~} par \trou{~~b~~}. \vskip 0.5cm
    \item L'écriture fractionnaire du quotient de $3$ par $4$ est
    : \dotfill \vskip 0.5cm
    \item Le numérateur du quotient $\dfrac{25}{9}$ est :
    \dotfill
    \item Le dénominateur du quotient $\dfrac{70}{5,6}$ est
    :\dotfill
 
\end{enumerate}
 
\vskip 1.5cm
 
\exo (3 points) - Calculer les nombres suivants en donnant le
résultat sous la forme d'une fraction.
\begin{multicols}{2}
\begin{enumerate}[(a)]
    \item $\dfrac{2}{3}\*\dfrac{3}{4}=$\dotfill \vskip 0.5cm
    \item $\dfrac{7}{2}\*\dfrac{5}{2}=$\dotfill \vskip 0.5cm
    \item $\dfrac{2}{3}\*\dfrac{9}{2}=$\dotfill \vskip 0.5cm
    \item $\dfrac{8}{7}\*\dfrac{3}{2}=$\dotfill \vskip 0.5cm
    \item $\dfrac{0,5}{7}\*\dfrac{10}{100}=$\dotfill \vskip 0.5cm
    \item $\dfrac{21}{3}\*\dfrac{3}{5}=$\dotfill
\end{enumerate}
\end{multicols}
 
\vskip 1.5cm
 
\exo (5 points) - Simplifier au maximum puis calculer les nombres
suivants en donnant le résultat sous la forme d'une fraction :
 
\vskip 1.5cm
 
\begin{enumerate}[(a)]
    \item $\dfrac{2}{3}\*\dfrac{3}{4}\*\dfrac{7}{14}=$\dotfill \vskip 0.5cm
    \item $\dfrac{8}{3}\*\dfrac{6}{16}\*\dfrac{10}{5}=$\dotfill \vskip 0.5cm
    \item $\dfrac{81}{28}\*\dfrac{14}{27}\*\dfrac{5}{10}=$\dotfill \vskip 0.5cm
    \item $\dfrac{10}{14}\*\dfrac{7}{5}\*\dfrac{3}{10}\*\dfrac{10}{30}=$\dotfill \vskip 0.5cm
    \item $\dfrac{1}{2}\*\dfrac{2}{3}\*\dfrac{3}{4}\*\dfrac{4}{5}=$\dotfill
\end{enumerate}
 
 
 
\end{document}