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Import work from year 2013-2014

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Benjamin Bertrand
2017-06-16 09:46:40 +03:00
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3e/Nombres_Calculs/Equation/decouverte/corr_meuble_t.pdf Normal file
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\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
%\usepackage{multicol}
\usepackage{tikz}
\usepackage{enumerate}
\usepackage{fancybox}
% Title Page
\title{Système d'équations - Exercices}
\author{}
\date{}
\fancyhead[L]{Troisième}
\fancyhead[C]{\Thetitle}
\fancyhead[R]{\thepage}
\begin{document}
\thispagestyle{fancy}
\begin{enumerate}
\item
\begin{eqnarray*}
\left\{
\begin{array}{lcl}
2x + 4y &=& -2\\
4x + 5y &=& 5
\end{array}
\right.
\end{eqnarray*}
On veut égaliser lei nombre de $x$. Pour cela on multiplie la première équation par 2
\begin{eqnarray*}
\left\{
\begin{array}{lcl}
4x + 8y &=& -4\\
4x + 5y &=& 5
\end{array}
\right.
\end{eqnarray*}
On fait la différence entre ces deux équations.
\begin{eqnarray*}
0x + 3y & = & -9 \\
y &=& \frac{-9}{3} = -3
\end{eqnarray*}
On remplace $y$ par -3 dans la première équation
\begin{eqnarray*}
2x + 4\times (-3) & = & -2 \\
2x - 12 &=& -2 \\
2x &=& -2 + 12 = 10 \\
x &=& \frac{10}{2} = 5
\end{eqnarray*}
Les solutions du système d'équations sont $x=5$ et $y=-3$.
\eject
\item
\begin{eqnarray*}
\left\{
\begin{array}{lcl}
3x + 2y &=& 75 \hspace{1cm} \times 5\\
5x + 5y &=& 90 \hspace{1cm} \times 3
\end{array}
\right.
\end{eqnarray*}
On veut égaliser le nombre de $x$ dans la première et la deuxième équation. Pour cela on multiplie la première équation par 5 et la deuxième par 3.
\begin{eqnarray*}
\left\{
\begin{array}{lcl}
15x + 10y &=& 375 \\
15x + 15y &=& 270
\end{array}
\right.
\end{eqnarray*}
On fait la différence entre les deux équations
\begin{eqnarray*}
0x - 5y & = & 105\\
y &=& \frac{105}{-5} = -21
\end{eqnarray*}
On remplace $y$ par -21 dans la première équation.
\begin{eqnarray*}
3x + 2\times(-21) & = & 75\\
3x + (-42) &=& 75 \\
3x &=& 75 + 42 = 117\\
x &=& \frac{117}{3} = 39
\end{eqnarray*}
Les solutions du système d'équations sont $x=39$ et $y=-21$.
\eject
\item
\begin{eqnarray*}
\left\{
\begin{array}{lcl}
6x + 3y &=& 114 \hspace{1cm} \times 3 \\
4x + 9y &=& 307
\end{array}
\right.
\end{eqnarray*}
On veut égaliser le nombre de $y$ dans la première et la deuxième équation. Pour cela on multiplie la première équation par 3
\begin{eqnarray*}
\left\{
\begin{array}{lcl}
18x + 9y &=& 342 \\
4x + 9y &=& 307
\end{array}
\right.
\end{eqnarray*}
On fait la différence entre les deux équations
\begin{eqnarray*}
14x + 0y &=& 35\\
x&=& \frac{35}{14} = 2,5
\end{eqnarray*}
On remplace $x$ par 2,5 dans la première équation.
\begin{eqnarray*}
6\times2.5 + 3y &=&114 \\
15 + 3y &=& 114 \\
3y &=& 114 -15 = 99 \\
y&=& \frac{99}{3} = 33
\end{eqnarray*}
Les solutions du système d'équations sont $x=2,5$ et $y=33$.
\eject
\item
\begin{eqnarray*}
\left\{
\begin{array}{lcl}
6x + 44y &=& 755 \hspace{1cm} \times 5 \\
30x - 7y &=& 143
\end{array}
\right.
\end{eqnarray*}
On veut égaliser le nombre de $x$ dans la première et la deuxième équation. Pour cela on multiplie la première équation par 5
\begin{eqnarray*}
\left\{
\begin{array}{lcl}
30x + 220 y &=& 3775 \\
30x - 7y &=& 143
\end{array}
\right.
\end{eqnarray*}
On fait la différence entre les deux équations
\begin{eqnarray*}
0x + 227y &=& 3632\\
y&=& \frac{3632}{227} = 16
\end{eqnarray*}
On remplace $y$ par 16 dans la première équation.
\begin{eqnarray*}
6x + 44\times16 &=& 755 \\
6x + 704 &=& 755 \\
6x &=& 755-704 = 51 \\
x&=& \frac{51}{6} = 8,5
\end{eqnarray*}
Les solutions du système d'équations sont $x=8,5$ et $y=16$.
\eject
\end{enumerate}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
%\usepackage{multicol}
\usepackage{tikz}
\usepackage{fancybox}
% Title Page
\title{Système d'équations - Exercices}
\author{}
\date{}
\fancyhead[L]{Troisième}
\fancyhead[C]{\Thetitle}
\fancyhead[R]{\thepage}
\begin{document}
\thispagestyle{fancy}
\begin{Exo}
Deux compositions de meubles sont exposées dans un magasin.
\includegraphics[scale=0.3]{./fig/meubles}
Les prix possibles des meubles sont 25\euro\;, 50\euro\;, 75\euro\; et 100\euro.
\begin{minipage}{0.25\textwidth}
Quel est le prix de cette composition?
\end{minipage}
\begin{minipage}{0.15\textwidth}
\includegraphics[scale=0.2]{./fig/meubles2}
\end{minipage}
\end{Exo}
\begin{Exo}
Un joaillier vend des colliers dont le prix dépend uniquement des perles posées dessus. Voici trois colliers qu'il a en vitrine:
\begin{center}
\includegraphics[scale=0.4]{./fig/coliers}
\end{center}
Quel est le prix du troisième collier?
\end{Exo}
\eject
\begin{Exo}
Pour les motifs du carrelage d'une salle de bain, l'artisan propose deux motifs différents:
\begin{center}
\includegraphics[scale=0.3]{./fig/triangles}
\end{center}
Les triangles gris n'ont pas le même prix que les triangles blancs. \textbf{Quel est le prix d'un triangle blanc? Et celui d'un triangle noir?}
\end{Exo}
\begin{Exo}
Charles et Sarah ont acheté des bonbons.
\begin{itemize}
\item Charles a acheté 4 \textit{paquets de chewing gums} et 4 \textit{oursons}, il a payé 10\euro.
\item Sarah a acheté 2 \textit{paquets de chewing gum} et 6 \textit{oursons}, elle a payé 7\euro.
\end{itemize}
\textbf{Combien coûte un ourson? Et le paquets de chewing gums?}
\end{Exo}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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Notes sur des exercices pour commencer les équations
####################################################
:date: 2014-07-01
:modified: 2014-07-01
:tags: Nombres Calculs, Équations
:category: 3e
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers corr_meuble_t.pdf <corr_meuble_t.pdf>`_
`Lien vers meubles.pdf <meubles.pdf>`_
`Lien vers meubles_t.tex <meubles_t.tex>`_
`Lien vers meubles.tex <meubles.tex>`_
`Lien vers meubles_b.tex <meubles_b.tex>`_
`Lien vers exo_decouv.tex <exo_decouv.tex>`_
`Lien vers exo_decouv.pdf <exo_decouv.pdf>`_
`Lien vers corr_meuble_t.tex <corr_meuble_t.tex>`_
`Lien vers meubles_b.pdf <meubles_b.pdf>`_
`Lien vers meubles_t.pdf <meubles_t.pdf>`_
`Lien vers fig/coliers.pdf <fig/coliers.pdf>`_
`Lien vers fig/meubles_b1.pdf <fig/meubles_b1.pdf>`_
`Lien vers fig/meubles_b2.pdf <fig/meubles_b2.pdf>`_
`Lien vers fig/meubles.pdf <fig/meubles.pdf>`_
`Lien vers fig/triangles.pdf <fig/triangles.pdf>`_
`Lien vers fig/meubles2.pdf <fig/meubles2.pdf>`_
`Lien vers fig/coliers2.pdf <fig/coliers2.pdf>`_
`Lien vers fig/meubles_t.pdf <fig/meubles_t.pdf>`_

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\documentclass[a4paper,10pt]{beamer}
\usepackage[utf8]{inputenc}
\usepackage[french]{babel}
\usepackage{graphicx}
\usepackage{thumbpdf}
\usepackage{wasysym}
\usepackage{ucs}
\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
\usepackage{verbatim}
\usepackage{subfig}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{enumerate}
\usepackage{eurosym}
\begin{document}
\begin{frame}{Prix d'une cuisine}
Deux compositions de meubles sont exposées dans un magasin.
\begin{center}
\includegraphics[scale=0.2]{./fig/meubles}
\end{center}
Les prix possibles des meubles sont 25\euro\;, 50\euro\;, 75\euro\; et 100\euro.
\begin{minipage}{0.5\textwidth}
Quel est le prix de cette composition?
\end{minipage}
\begin{minipage}{0.4\textwidth}
\includegraphics[scale=0.2]{./fig/meubles2}
\end{minipage}
\end{frame}
\end{document}

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\documentclass[a4paper,10pt]{beamer}
\usepackage[utf8]{inputenc}
\usepackage[french]{babel}
\usepackage{graphicx}
\usepackage{thumbpdf}
\usepackage{wasysym}
\usepackage{ucs}
\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
\usepackage{verbatim}
\usepackage{subfig}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{enumerate}
\usepackage{eurosym}
\begin{document}
\begin{frame}{Prix d'une cuisine}
\begin{itemize}
\item
Deux compositions de meubles sont exposées dans un magasin.
\begin{center}
\includegraphics[scale=0.2]{./fig/meubles_b1}
\end{center}
En combinant les deux compositions, retrouver le prix d'un petit meuble carré. En déduire le prix d'un grand meuble gris.
\item<2-> Mêmes questions pour les compositions suivantes
\begin{center}
\includegraphics[scale=0.2]{./fig/meubles_b2}
\end{center}
\end{itemize}
\end{frame}
\end{document}

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3e/Nombres_Calculs/Equation/decouverte/meubles_t.tex Normal file
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\documentclass[a4paper,10pt]{beamer}
\usepackage[utf8]{inputenc}
\usepackage[french]{babel}
\usepackage{graphicx}
\usepackage{thumbpdf}
\usepackage{wasysym}
\usepackage{ucs}
\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
\usepackage{verbatim}
\usepackage{subfig}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{enumerate}
\usepackage{eurosym}
\usepackage{multicol}
\begin{document}
\begin{frame}{Méthode par combinaison}
\begin{center}
$ \left\{
\begin{array}{lcl}
3x + 4y &=& 195 \\
4x + 5y &=& 249
\end{array}
\right.$
\end{center}
\vfill
\onslide<2->{
Composition de meubles correspondante
\includegraphics[scale=0.2]{./fig/meubles_t}
\textbf{Comment faire pour avoir le même nombre de meubles $X$?}
}
\vfill
\end{frame}
\begin{frame}{Éxercices}
\begin{multicols}{2}
\begin{enumerate}[a)]
\item $ \left\{
\begin{array}{lcl}
2x + 4y &=& -2\\
4x + 5y &=& 5
\end{array}
\right.$
% x = 5 et y = -3
\vspace{0.5cm}
\onslide<2>{x=5 et y = -3}
\vspace{0.5cm}
\item $ \left\{
\begin{array}{lcl}
3x + 2y &=& 75 \\
5x + 5y &=& 90
\end{array}
\right.$
% x = -3 et y = 21
\vspace{0.5cm}
\onslide<2>{x=-3 et y = 21}
\vspace{0.5cm}
\item $ \left\{
\begin{array}{lcl}
6x + 3y &=& 114 \\
4x + 9y &=& 307
\end{array}
\right.$
%x = 2.5 et y = 33
\vspace{0.5cm}
\onslide<2>{x=2.5 et y = 33}
\vspace{0.5cm}
\item $ \left\{
\begin{array}{lcl}
6 x + 44 y &=& 755 \\
30 x - 7y &=& 143
\end{array}
\right.$
%x = 8.5 et y = 16
\vspace{0.5cm}
\onslide<2>{x=8.5 et y = 16}
\vspace{0.5cm}
\end{enumerate}
\end{multicols}
\end{frame}
\end{document}