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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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4e/Nombres_Calculs/Cal_litt/Conn/Conn0324.pdf Normal file
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\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
% Title Page
\title{}
\author{}
\date{}
\begin{document}
\begin{multicols}{2}
Nom - Prénom:
\section{Connaissance}
\begin{enumerate}
\item $k$, $a$ et $b$ sont trois nombres alors \\
\begin{eqnarray*}
k(a + b) & = & \cdots\cdots\cdots
\end{eqnarray*}
\item Quand il y a un "-" devant des parenthèses, pour les enlever, il faut \dotfill \\[0.5cm]
. \dotfill
\item Évaluer les expressions suivantes avec $x = 2$
\begin{eqnarray*}
A = 2x - 5 = \cdots \\[2cm]
B = 2x^2 - 1 = \cdots \\[2cm]
C = 2(3x - 5) = \cdots
\end{eqnarray*}
\end{enumerate}
\columnbreak
Nom - Prénom
\section{Connaissance}
\begin{enumerate}
\item $k$, $a$ et $b$ sont trois nombres alors
\begin{eqnarray*}
k(a + b) & = & \cdots\cdots\cdots
\end{eqnarray*}
\item Quand il y a rien entre une lettre et un chiffre, c'est comme s'il y avait \dotfill
%. \dotfill
\item Évaluer les expressions suivantes avec $x = 3$
\begin{eqnarray*}
A = 3x - 5 = \cdots \\[2cm]
B = x^2 - 6 = \cdots \\[2cm]
C = 3(2x - 5) = \cdots
\end{eqnarray*}
\end{enumerate}
\end{multicols}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
% Title Page
\title{}
\author{}
\date{}
\begin{document}
\begin{multicols}{2}
Nom - Prénom:
\section{Connaissance}
\begin{enumerate}
\item Une \textbf{expression littérale} est \dotfill \\[0.5cm]
. \dotfill .
\item Effectuer les calculs suivants en indiquant les étapes sur la feuille (calculatrice interdite) \\
$7+2\times3 = $ \\[1cm]
$2^2 +1 = $ \\[1cm]
$2(2-5) = $ \\[1cm]
\end{enumerate}
Nom - Prénom:
\section{Connaissance}
\begin{enumerate}
\item Pour évaluer une expression littérale, il faut \dotfill \\[0.5cm]
. \dotfill .
\item Effectuer les calculs suivants en indiquant les étapes sur la feuille (calculatrice interdite) \\
$9+4\times2 = $ \\[1cm]
$2^2 - 1 = $ \\[1cm]
$4(2-4) = $ \\
\end{enumerate}
\columnbreak
Nom - Prénom:
\section{Connaissance}
\begin{enumerate}
\item Une \textbf{expression littérale} est \dotfill \\[0.5cm]
. \dotfill .
\item Effectuer les calculs suivants en indiquant les étapes sur la feuille (calculatrice interdite) \\
$2 - 4 \times 2 = $ \\[1cm]
$3^2 + 2 = $ \\[1cm]
$4(2-6) = $ \\[1cm]
\end{enumerate}
Nom - Prénom
\section{Connaissance}
\begin{enumerate}
\item Pour évaluer une expression littérale, il faut \dotfill \\[0.5cm]
. \dotfill .
\item Effectuer les calculs suivants en indiquant les étapes sur la feuille (calculatrice interdite) \\
$7\times 2 + 3 = $ \\[1cm]
$3^2 - 1 = $ \\[1cm]
$3(1-5) = $ \\
\end{enumerate}
\end{multicols}
\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}
% Title Page
\title{Develloper factoriser - Exercices}
\author{}
\date{}
\fancyhead[L]{Quatrième}
\fancyhead[C]{\Thetitle}
\fancyhead[R]{\thepage}
\begin{document}
\thispagestyle{empty}
\begin{Exo}
Compléter les pointillés pour développer les expressions.
\begin{enumerate}
\item$A = (2x + 3)(4 + 7x)$
\begin{center}
\includegraphics[scale=0.2]{./fig/doubleProd}
$A = \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots $
\end{center}
\item$B = (5x + 2)(-4 + x)$
\begin{center}
\includegraphics[scale=0.2]{./fig/doubleProd}
$B = \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots $
\end{center}
\item$C = (2x - 3)(-4 + 7x)$
\begin{center}
\includegraphics[scale=0.2]{./fig/doubleProd}
$C = \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots $
\end{center}
\end{enumerate}
\end{Exo}
\setcounter{exo}{0}
\begin{Exo}
Compléter les pointillés pour développer les expressions.
\begin{enumerate}
\item$A = (2x + 3)(4 + 7x)$
\begin{center}
\includegraphics[scale=0.2]{./fig/doubleProd}
$A = \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots $
\end{center}
\item$B = (5x + 2)(-4 + x)$
\begin{center}
\includegraphics[scale=0.2]{./fig/doubleProd}
$B = \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots $
\end{center}
\item$C = (2x - 3)(-4 + 7x)$
\begin{center}
\includegraphics[scale=0.2]{./fig/doubleProd}
$C = \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots $
\end{center}
\end{enumerate}
\end{Exo}
\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}
% Title Page
\title{Develloper factoriser - Exercices}
\author{}
\date{}
\fancyhead[L]{Quatrième}
\fancyhead[C]{\Thetitle}
\fancyhead[R]{\thepage}
\begin{document}
\thispagestyle{fancy}
\begin{Exo}
Réduire les produits suivants
\begin{eqnarray*}
2x \times 3 = \cdots &\hspace{2cm}& 4 \times 3b = \cdots \\[0.4cm]
3x \times (-3) = \cdots &\hspace{2cm}& 7 \times 2b = \cdots \\[0.4cm]
-2x \times (-5) = \cdots &\hspace{2cm}& 4x \times 3x = \cdots \\[0.4cm]
-5x \times (-x) = \cdots &\hspace{2cm}& 4x^2 \times 3 = \cdots \\
\end{eqnarray*}
\end{Exo}
\begin{Exo}
Réduire les sommes suivantes
\begin{eqnarray*}
2x + 3 + 4x & = & \hspace{2cm} \cdots \hspace{2cm} = \hspace{2cm}\cdots \hspace{2cm}\\[0.4cm]
2 + 3x - 6 & = & \hspace{2cm} \cdots \hspace{2cm} = \hspace{2cm}\cdots \hspace{2cm}\\[0.4cm]
-2x + 3x^2 + 6x & = & \hspace{2cm} \cdots \hspace{2cm} = \hspace{2cm}\cdots \hspace{2cm}\\[0.4cm]
2x^2 + 3x - 4x + 4 & = & \hspace{2cm} \cdots \hspace{2cm} = \hspace{2cm}\cdots \hspace{2cm}\\[0.4cm]
9x^2 + 4x - 4x + 4 & = & \hspace{2cm} \cdots \hspace{2cm} = \hspace{2cm}\cdots \hspace{2cm}\\[0.4cm]
x^2 + 3 - 4x + 4 & = & \hspace{2cm} \cdots \hspace{2cm} = \hspace{2cm}\cdots \hspace{2cm}\\[0.4cm]
3\times2^2x + 1\times 3 - 4\times2x + 4 & = & \hspace{2cm} \cdots \hspace{2cm} = \hspace{2cm}\cdots \hspace{2cm}\\[0.4cm]
x^2 + 3 - 4x + 4 & = & \hspace{2cm} \cdots \hspace{2cm} = \hspace{2cm}\cdots \hspace{2cm}\\[0.4cm]
\end{eqnarray*}
\end{Exo}
\vspace{3cm}
\begin{Exo}
Développer les expressions suivantes (on ne demande pas de réduire)
\begin{eqnarray*}
(2x + 3)(4x + 1) &=& \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots \\[0.4cm]
(x + 6)(2x + 3) &=& \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots \\[0.4cm]
(3x - 3)(x + 1) &=& \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots \\[0.4cm]
(3x - 5)(x - 5) &=& \\[0.4cm]
(2x^2 + x)(3 - 3x) &=&
\end{eqnarray*}
\end{Exo}
\begin{Exo}
Développer, réduire et mettre sous la forme $ax^2 + bx + c$.
\begin{eqnarray*}
(2x + 3)(4x + 1) &=& \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots \\[0.4cm]
&=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.4cm]
&=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.4cm]
&=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.4cm]
&=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.6cm]
(x + 4)(2x - 1) &=& \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots \\[0.4cm]
&=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.4cm]
&=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.4cm]
&=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.4cm]
&=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm}
\end{eqnarray*}
\end{Exo}
\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}
% Title Page
\title{Develloper factoriser - Exercices}
\author{}
\date{}
\fancyhead[L]{Quatrième}
\fancyhead[C]{\Thetitle}
\fancyhead[R]{\thepage}
\begin{document}
\thispagestyle{empty}
\begin{Exo}
Développer les expressions suivantes (on ne demande pas de réduire)
\begin{eqnarray*}
A = (6x - 2)(6x + 1) \hspace{1cm}
B = (2x + 3)^2 \hspace{1cm}
C = (2x - 3)^2
\end{eqnarray*}
\end{Exo}
\begin{Exo}
Développer, réduire et mettre sous la forme $ax^2 + bx + c$.
\begin{eqnarray*}
A = (2 + 7x)(2x - 7x) &=& \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots \\[0.4cm]
\mbox{Simplification des } "\times" &=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.4cm]
\mbox{On range }&=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.4cm]
\mbox{Simplification des } "+"&=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.4cm]
\mbox{Ordre demandé}&=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.6cm]
\end{eqnarray*}
Ici on a alors
\begin{eqnarray*}
a = \parbox{1cm}{\dotfill} \qquad b = \parbox{1cm}{\dotfill}\qquad c = \parbox{1cm}{\dotfill}
\end{eqnarray*}
En reprennant les mêmes étapes qu'au dessus, développer, réduire et mettre sous la forme $ax^2 + bx + c$ les expressions suivantes
\begin{eqnarray*}
B & = & (2x + 5)(4 + 4x) \\
C & = & (4x - 1)^2 \\
C & = & (-2x - 3)^2 \\
\end{eqnarray*}
\end{Exo}
\vfill\eject
\setcounter{exo}{0}
\begin{Exo}
Développer les expressions suivantes (on ne demande pas de réduire)
\begin{eqnarray*}
A = (6x - 2)(6x + 1) \hspace{1cm}
B = (2x + 3)^2 \hspace{1cm}
C = (2x - 3)^2
\end{eqnarray*}
\end{Exo}
\begin{Exo}
Développer, réduire et mettre sous la forme $ax^2 + bx + c$.
\begin{eqnarray*}
A = (2 + 7x)(2x - 7x) &=& \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots + \cdots \times \cdots \\[0.4cm]
\mbox{Simplification des } "\times" &=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.4cm]
\mbox{On range }&=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.4cm]
\mbox{Simplification des } "+"&=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.4cm]
\mbox{Ordre demandé}&=& \hspace{2cm} + \hspace{2cm} + \hspace{2cm} \\[0.6cm]
\end{eqnarray*}
Ici on a alors
\begin{eqnarray*}
a = \parbox{1cm}{\dotfill} \qquad b = \parbox{1cm}{\dotfill}\qquad c = \parbox{1cm}{\dotfill}
\end{eqnarray*}
En reprennant les mêmes étapes qu'au dessus, développer, réduire et mettre sous la forme $ax^2 + bx + c$ les expressions suivantes
\begin{eqnarray*}
B & = & (2x + 5)(4 + 4x) \\
C & = & (4x - 1)^2 \\
C & = & (-2x - 3)^2 \\
\end{eqnarray*}
\end{Exo}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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Notes sur des exercices autour de la double distributivité
##########################################################
:date: 2014-07-01
:modified: 2014-07-01
:tags: Nombres Calculs,Exo
:category: 4e
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers double_prod_exo_2.tex <double_prod_exo_2.tex>`_
`Lien vers double_prod_exo_2.pdf <double_prod_exo_2.pdf>`_
`Lien vers double_prod_exo.tex <double_prod_exo.tex>`_
`Lien vers double_prod_exo_3.tex <double_prod_exo_3.tex>`_
`Lien vers double_prod_exo_3.pdf <double_prod_exo_3.pdf>`_
`Lien vers double_prod_exo.pdf <double_prod_exo.pdf>`_
`Lien vers fig/doubleProd_num.pdf <fig/doubleProd_num.pdf>`_
`Lien vers fig/doubleProd.pdf <fig/doubleProd.pdf>`_
`Lien vers fig/simpleProd.pdf <fig/simpleProd.pdf>`_

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Notes sur un mot croisé avec des expressions à simplifier
#########################################################
:date: 2014-07-01
:modified: 2014-07-01
:tags: Nombres Calculs, Exo
:category: 4e
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers mots_croise.pdf <mots_croise.pdf>`_
`Lien vers mots_croise.tex <mots_croise.tex>`_
`Lien vers fig/grille.pdf <fig/grille.pdf>`_

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\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classCours}
\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
% Title Page
\titre{Mots croisés et mathématiciens}
% \quatreC \quatreD \troisB \troisPro
\classe{\quatreC}
\date{27 mars 2014}
%\fancyhead[L]{<++classes++> : \Thetitle}
\begin{document}
\maketitle
On donne les expressions suivantes
\begin{eqnarray*}
A = 2(13x + 6)& \hspace{2cm} & B = 3x(5x + 1) + 1 \\
C = (x - 1)(11x + 19)& \hspace{2cm} & D = (x + 1)(23x - 5) \\
E = (2x + 5)^2 & \hspace{2cm} & F = 3(7x + 5) - 8 + 13x^2 \\
F = (3x - 4)^2 &&
\end{eqnarray*}
En suivant l'exemple suivant, remplir le mot croisé suivant pour découvrir le nom des grands mathématiciens.
\large\textbf{Exemple}
\normalsize
\noindent\fbox{\parbox{\linewidth-2\fboxrule-2\fboxsep}{
L'expression est $Z = (2x + 1)(3x + 4)$
\begin{itemize}
\item On développe, réduit et on met l'expression sous la forme $ax^2 + bx + c$.
\begin{eqnarray*}
Z = (2x + 1)(3x-4) = (\cdots) = 6x^2 -5x - 4
\end{eqnarray*}
\item On identifie les coefficients
\begin{eqnarray*}
Za = 6 \hspace{2cm} Zb = -5 \hspace{2cm} Zc = -4
\end{eqnarray*}
\item On fait correspondre le chiffre à la lettre dans l'alphabet
\begin{itemize}
\item $Za = 6 \quad \longrightarrow$ 6e lettre de l'alphabet: F \\
\item $Zb = -5 \quad \longrightarrow$ 5e lettre de l'alphabet: E \\
\item $Zc = -4 \quad \longrightarrow$ 4e lettre de l'alphabet: D \\
\end{itemize}
\item On remplace dans la grille $Za$, $Zb$ et $Zc$ par la lettre correspondante.
\end{itemize}
}}
\vspace{1cm}
\large\textbf{Réponses}
\normalsize
Indiquer le nom des mathématiciens trouvés ainsi que l'époque à laquelle ils ont vécu.
\vspace{0.3cm}
\begin{enumerate}
\item \parbox{1cm}{\dotfill} \hspace{5cm} Époque: \parbox{1cm}{\dotfill}
\vspace{0.3cm}
\item \parbox{1cm}{\dotfill} \hspace{5cm} Époque: \parbox{1cm}{\dotfill}
\vspace{0.3cm}
\item \parbox{1cm}{\dotfill} \hspace{5cm} Époque: \parbox{1cm}{\dotfill}
\vspace{0.3cm}
\item \parbox{1cm}{\dotfill} \hspace{5cm} Époque: \parbox{1cm}{\dotfill}
\vspace{0.3cm}
\item \parbox{1cm}{\dotfill} \hspace{5cm} Époque: \parbox{1cm}{\dotfill}
\vspace{0.3cm}
\item \parbox{1cm}{\dotfill} \hspace{5cm} Époque: \parbox{1cm}{\dotfill}
\end{enumerate}
\begin{center}
\hspace*{-2cm}
\includegraphics[scale=0.8]{./fig/grille}
\end{center}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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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{multicol}
\usepackage{eurosym}
\usepackage{enumerate}
\begin{document}
\begin{frame}{L'équation $2x + 40 = 100$}
Deux balles et un boite de 40g pèse autant qu'une boite de 100g. \\ \textbf{Combien pèse une balle?}
\begin{multicols}{2}
\includegraphics[scale=0.2]{./fig/balance1_1}
\vspace{1cm}
\onslide<3->{\includegraphics[scale=0.2]{./fig/balance}}
\vspace{1cm}
\onslide<4->{\includegraphics[scale=0.2]{./fig/balance}}
\columnbreak
\onslide<2->{$2x + 40 = 100$}
\end{multicols}
\end{frame}
\begin{frame}{L'équation $3x = 2x + 80$}
Trois balles pèse autant que deux balles et une boite de 80g. \\ \textbf{Combien pèse une balle?}
\begin{multicols}{2}
\includegraphics[scale=0.2]{./fig/balance2_1}
\vspace{0.5cm}
\onslide<3->{\includegraphics[scale=0.2]{./fig/balance}}
\vspace{0.5cm}
\onslide<4->{\includegraphics[scale=0.2]{./fig/balance}}
\columnbreak
\onslide<2->{$3x = 2x + 80$}
\end{multicols}
\end{frame}
\begin{frame}{L'équation $3x +10 = x + 80$}
Trois balles et une boite de 1àg pèse autant qu'une balle et une boite de 80g. \\ \textbf{Combien pèse une balle?}
\begin{multicols}{2}
\includegraphics[scale=0.2]{./fig/balance3_1}
\onslide<3->{\includegraphics[scale=0.2]{./fig/balance}}
\onslide<4->{\includegraphics[scale=0.2]{./fig/balance}}
\onslide<5->{\includegraphics[scale=0.2]{./fig/balance}}
\columnbreak
\onslide<2->{$3x + 10 = x + 80$}
\end{multicols}
\end{frame}
\begin{frame}{Éxercices}
Résoudre les équations suivantes
\begin{multicols}{2}
\begin{enumerate}[a)]
\item $4x + 90 = 150$
\item $4x = x + 11$
\item $6x + 9 = 4x + 21$
\item $3x - 90 = 30$
\item $6x = 2x -16$
\item $-2x + 10 = 1$
\end{enumerate}
\end{multicols}
\end{frame}
\end{document}

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Notes sur un support de cours pour introduire les équations
###########################################################
:date: 2014-07-01
:modified: 2014-07-01
:tags: Nombres Calculs,Cours
:category: 4e
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers balances.tex <balances.tex>`_
`Lien vers balances.pdf <balances.pdf>`_
`Lien vers fig/balance3_1.pdf <fig/balance3_1.pdf>`_
`Lien vers fig/balance1_2.pdf <fig/balance1_2.pdf>`_
`Lien vers fig/balance.pdf <fig/balance.pdf>`_
`Lien vers fig/balance2_2.pdf <fig/balance2_2.pdf>`_
`Lien vers fig/balance2_1.pdf <fig/balance2_1.pdf>`_
`Lien vers fig/balance3_3.pdf <fig/balance3_3.pdf>`_
`Lien vers fig/balance3_2.pdf <fig/balance3_2.pdf>`_
`Lien vers fig/balance3_4.pdf <fig/balance3_4.pdf>`_
`Lien vers fig/balance1_1.pdf <fig/balance1_1.pdf>`_
`Lien vers fig/grille_balance.pdf <fig/grille_balance.pdf>`_
`Lien vers fig/balance1_3.pdf <fig/balance1_3.pdf>`_

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\documentclass[a4paper,10pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
% Title Page
\title{Pourcentage - Exercices}
\author{}
\date{}
\fancyhead[L]{Quatrième}
\fancyhead[C]{\Thetitle}
\fancyhead[R]{\thepage}
\begin{document}
\thispagestyle{empty}
\begin{Exo}
Dans un magasine, le prix de certains meubles ont été effacé.
\begin{center}
\includegraphics[scale=0.3]{./fig/meubles}
\end{center}
Heureusement, la page des compositions de meubles nous permettent de retrouver les prix manquants.
\begin{enumerate}
\item \includegraphics[scale=0.2]{./fig/compo1} coûte 100\euro. Combien coûte un grand meuble gris?
\item \includegraphics[scale=0.2]{./fig/compo2} coûte 150\euro. Combien coûte un meuble noir?
\item \includegraphics[scale=0.2]{./fig/compo3} coûte 140\euro. Combien coûte un meuble triangulaire?
\end{enumerate}
\end{Exo}
\begin{Exo}
Chez un joaillier, on sait que les perles rondes coûtent 30\euro. Il propose les colliers suivant:
\includegraphics[scale=0.2]{./fig/collier1}\hspace{1cm}
\includegraphics[scale=0.2]{./fig/collier2}\hspace{1cm}
\includegraphics[scale=0.2]{./fig/collier3}
\begin{enumerate}
\item Quel est le prix d'une perle carré?
\item Quel est le prix d'une perle triangulaire?
\item Quel est le prix d'une perle en étoile?
\item Le joaillier montre ces deux colliers et nous dit qu'ils ont le même prix.
\begin{center}
\includegraphics[scale=0.2]{./fig/collier4}
\end{center}
Quel est le prix du pendentif?
\end{enumerate}
\end{Exo}
\begin{Exo}
Tom, Paul et Isabelle sont allé acheter des bonbons.
\begin{itemize}
\item Tom a acheté 5 carambars qui lui ont coûté 1,40\euro.
\item Paul a acheté 10 bonbons à la fraise et 1 carambar. Il a payé 2\euro.
\item Isabelle a acheté 2 bonbons à la menthe et 3 carambars. Elle a payé elle aussi 2\euro.
\end{itemize}
\begin{enumerate}
\item Combien coûte un carambar?
\item Combien coûte un bonbon à la fraise?
\item Si j'achète 2 carambars et 10 bonbons à la menthe, combien vais-je payer?
\item Ils retournent le lendemain au magasin. Cette fois ci, Tom a acheté 4 carambars et 2 bonbons au caramel tandis que Isabelle a acheté 4 bonbons au caramel et 2 carambar. Ils ont payé la même chose. Combien coûte un bonbon au caramel?
\end{enumerate}
\end{Exo}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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Notes sur des exercices de décourte des équations
#################################################
:date: 2014-07-01
:modified: 2014-07-01
:tags: Nombres Calculs, Exo
:category: 4e
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers equation.tex <equation.tex>`_
`Lien vers equation.pdf <equation.pdf>`_
`Lien vers fig/compo2.pdf <fig/compo2.pdf>`_
`Lien vers fig/collier1.pdf <fig/collier1.pdf>`_
`Lien vers fig/collier2.pdf <fig/collier2.pdf>`_
`Lien vers fig/meubles.pdf <fig/meubles.pdf>`_
`Lien vers fig/collier3.pdf <fig/collier3.pdf>`_
`Lien vers fig/collier4.pdf <fig/collier4.pdf>`_
`Lien vers fig/compo1.pdf <fig/compo1.pdf>`_
`Lien vers fig/compo3.pdf <fig/compo3.pdf>`_

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\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
\usepackage{multicol}
% Title Page
\title{Identités remarquables et équations- Exercices}
\author{}
\date{}
\fancyhead[L]{Troisième}
\fancyhead[C]{\Thetitle}
\fancyhead[R]{\thepage}
\begin{document}
\thispagestyle{empty}
\begin{Exo}
\exo{Équations de degrés 1}
\begin{center}
\framebox{\parbox{0.4\textwidth}{
Résoudre l'équation $3x + 5 = 0$.
\begin{eqnarray*}
3x + 5 = 0 & \hspace{1cm} & \mbox{On ajoute l'opposé de 5} \\
3x + 5 \mathbf{+ (-5)} = \mathbf{-5} && \\
3x = -5 & \hspace{1cm} & \mbox{On multiplie par l'inverse de 3} \\
\mathbf{\frac{1}{3} \times }3x = \mathbf{ \frac{1}{3} \times }(-5) && \\
x = \frac{-5}{3}
\end{eqnarray*}
La solution est $x = \frac{-5}{3}$.
}}
\end{center}
\begin{enumerate}
\item Résoudre l'équation $4x + 7 = 0$.
\begin{eqnarray*}
4x + 7 = 0 & \hspace{0.5cm} & \mbox{On ajoute l'opposé de \parbox{1cm}{\dotfill}} \\[0.5cm]
4x + 7 + \parbox{1.5cm}{\dotfill}= \parbox{1.5cm}{\dotfill}&& \\[0.5cm]
4x = \parbox{1cm}{\dotfill}& \hspace{0.5cm} & \mbox{On multiplie par l'inverse de \parbox{1cm}{\dotfill}} \\[0.5cm]
\parbox{1.5cm}{\dotfill} \times 4x = \parbox{1.5cm}{\dotfill} \times \parbox{1cm}{\dotfill} && \\[0.5cm]
x = \frac{\parbox{1cm}{\dotfill}}{\parbox{1cm}{\dotfill}}
\end{eqnarray*}
La solution est \parbox{2cm}{\dotfill}.
\item Résoudre les équations suivantes
\begin{multicols}{2}
\begin{enumerate}
\item $2x + 1 = 0$
\item $6x + 12 = 0$
\item $3x - 3 = 0$
\item $8x - 4 = 0$
\columnbreak
\item $-6x - 3 = 0$
\item $9 + 3x = 0$
\item $5 + 3x = 0$
\item $\frac{2}{3}x + 3 = 0$
\end{enumerate}
\end{multicols}
\end{enumerate}
\end{Exo}
\eject
\setcounter{exo}{0}
\begin{Exo}
\exo{Équations de degrés 1}
\begin{center}
\framebox{\parbox{0.4\textwidth}{
Résoudre l'équation $3x + 5 = 0$.
\begin{eqnarray*}
3x + 5 = 0 & \hspace{1cm} & \mbox{On ajoute l'opposé de 5} \\
3x + 5 \mathbf{+ (-5)} = \mathbf{-5} && \\
3x = -5 & \hspace{1cm} & \mbox{On multiplie par l'inverse de 3} \\
\mathbf{\frac{1}{3} \times }3x = \mathbf{ \frac{1}{3} \times }(-5) && \\
x = \frac{-5}{3}
\end{eqnarray*}
La solution est $x = \frac{-5}{3}$.
}}
\end{center}
\begin{enumerate}
\item Résoudre l'équation $4x + 7 = 0$.
\begin{eqnarray*}
4x + 7 = 0 & \hspace{0.5cm} & \mbox{On ajoute l'opposé de \parbox{1cm}{\dotfill}} \\[0.5cm]
4x + 7 + \parbox{1.5cm}{\dotfill}= \parbox{1.5cm}{\dotfill}&& \\[0.5cm]
4x = \parbox{1cm}{\dotfill}& \hspace{0.5cm} & \mbox{On multiplie par l'inverse de \parbox{1cm}{\dotfill}} \\[0.5cm]
\parbox{1.5cm}{\dotfill} \times 4x = \parbox{1.5cm}{\dotfill} \times \parbox{1cm}{\dotfill} && \\[0.5cm]
x = \frac{\parbox{1cm}{\dotfill}}{\parbox{1cm}{\dotfill}}
\end{eqnarray*}
La solution est \parbox{2cm}{\dotfill}.
\item Résoudre les équations suivantes
\begin{multicols}{2}
\begin{enumerate}
\item $2x + 1 = 0$
\item $6x + 12 = 0$
\item $3x - 3 = 0$
\item $8x - 4 = 0$
\columnbreak
\item $-6x - 3 = 0$
\item $9 + 3x = 0$
\item $5 + 3x = 0$
\item $\frac{2}{3}x + 3 = 0$
\end{enumerate}
\end{multicols}
\end{enumerate}
\end{Exo}
\eject
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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\documentclass[a4paper,10pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
\usepackage{enumitem}
\usepackage{multicol}
% Title Page
\title{Équations- Exercices}
\author{}
\date{}
\fancyhead[L]{Quatrième}
\fancyhead[C]{\Thetitle}
\fancyhead[R]{\thepage}
\begin{document}
\thispagestyle{empty}
\begin{Exo}
Répondre aux 5 problèmes suivants.
\begin{enumerate}
\item Un libraire vend des livres au prix unique de 12\euro. À la fin de la journée, il a gagné 1020\euro.\\
Combien de livre le libraire a-t-il vendu?
\item Lisa pèse 5 gâteaux identiques. La balance indique 556grammes. \\
Combien pèse un gâteaux?
\item Chloé mesure 1,54m. Elle a grandi de 7cm depuis l'été dernier. \\
Combien mesurait-elle l'été dernier?
\item Paul est au 36e étage. Il veut aller à l'étage 14.\\
De combien d'étages Paul doit-il monter?
\item Bastien achète un blouson à 99\euro\;, comme il lui reste de l'argent, il achète 2 T-shirts. Il dépense en tout 127\euro.\\
Combien coûte un T-shirt?
\end{enumerate}
\end{Exo}
\begin{Exo}
Répondre au 5 problèmes suivants % (on pourra remplacer "$x$" par "bonbon" si on est bloqué)
\begin{enumerate}
\item Si 12 "$x$" vaut 1020. Combien vaut un "$x$"?
\item Si "$5x$" vaut 556. Combien vaut un "$x$"?
\item Quand on ajoute 7 à "$x$", on obtient 154. Combien vaut "$x$"?
\item Quand on ajoute 99 à 2 "$x$", on obtient 127. Combien vaut "$x$"?
\end{enumerate}
\end{Exo}
\begin{Exo}
Écrire les égalités en français (de la même façon que dans l'exercice 2) puis trouver la valeur de $x$ qui convient.
\begin{multicols}{2}
\begin{enumerate}[label=\hspace{1cm}\arabic* )]
\item $12x = 1020$ \\[0.2cm]
\item $x + 7 = 154$\\[0.2cm]
\item $10x = 1300$\\[0.2cm]
\item $5x = 56$\\[0.2cm]
\item $10 = 3x$\\[0.2cm]
\item $x + 12 = 19$
\item $x + 7 = 145$ \\[0.2cm]
\item $36 + x = 14$\\[0.2cm]
\item $x + 50 = 12$\\[0.2cm]
\item $x + 1200 = 1300$\\[0.2cm]
\item $99 + 2x = 127$ \\[0.2cm]
\item $2x + 1 = 3$
\end{enumerate}
\end{multicols}
\end{Exo}
\eject
\setcounter{exo}{0}
\begin{Exo}
Répondre aux 5 problèmes suivants.
\begin{enumerate}
\item Un libraire vend des livres au prix unique de 12\euro. À la fin de la journée, il a gagné 1020\euro.\\
Combien de livre le libraire a-t-il vendu?
\item Lisa pèse 5 gâteaux identiques. La balance indique 556grammes. \\
Combien pèse un gâteaux?
\item Chloé mesure 1,54m. Elle a grandi de 7cm depuis l'été dernier. \\
Combien mesurait-elle l'été dernier?
\item Paul est au 36e étage. Il veut aller à l'étage 14.\\
De combien d'étages Paul doit-il monter?
\item Bastien achète un blouson à 99\euro\;, comme il lui reste de l'argent, il achète 2 T-shirts. Il dépense en tout 127\euro.\\
Combien coûte un T-shirt?
\end{enumerate}
\end{Exo}
\begin{Exo}
Répondre au 5 problèmes suivants % (on pourra remplacer "$x$" par "bonbon" si on est bloqué)
\begin{enumerate}
\item Si 12 "$x$" vaut 1020. Combien vaut un "$x$"?
\item Si "$5x$" vaut 556. Combien vaut un "$x$"?
\item Quand on ajoute 7 à "$x$", on obtient 154. Combien vaut "$x$"?
\item Quand on ajoute 99 à 2 "$x$", on obtient 127. Combien vaut "$x$"?
\end{enumerate}
\end{Exo}
\begin{Exo}
Écrire les égalités en français (de la même façon que dans l'exercice 2) puis trouver la valeur de $x$ qui convient.
\begin{multicols}{2}
\begin{enumerate}[label=\hspace{1cm}\arabic* )]
\item $12x = 1020$ \\[0.2cm]
\item $x + 7 = 154$\\[0.2cm]
\item $10x = 1300$\\[0.2cm]
\item $5x = 56$\\[0.2cm]
\item $10 = 3x$\\[0.2cm]
\item $x + 12 = 19$
\item $x + 7 = 145$ \\[0.2cm]
\item $36 + x = 14$\\[0.2cm]
\item $x + 50 = 12$\\[0.2cm]
\item $x + 1200 = 1300$\\[0.2cm]
\item $99 + 2x = 127$ \\[0.2cm]
\item $2x + 1 = 3$
\end{enumerate}
\end{multicols}
\end{Exo}
\eject
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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Notes sur des exercices autour des équations
############################################
:date: 2014-07-01
:modified: 2014-07-01
:tags: Nombres Calculs,Exo
:category: 4e
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers exo_formel_1.pdf <exo_formel_1.pdf>`_
`Lien vers exo_formel_1.tex <exo_formel_1.tex>`_
`Lien vers exo_pratique.pdf <exo_pratique.pdf>`_
`Lien vers exo_pratique.tex <exo_pratique.tex>`_

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Notes sur le liens entre les équations et les programmes de calculs
###################################################################
:date: 2014-07-01
:modified: 2014-07-01
:tags: Nombres Calculs, Exo
:category: 4e
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers programme.pdf <programme.pdf>`_
`Lien vers programme.tex <programme.tex>`_

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\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
\usepackage{multicol}
% Title Page
\title{Identités remarquables et équations- Exercices}
\author{}
\date{}
\fancyhead[L]{Troisième}
\fancyhead[C]{\Thetitle}
\fancyhead[R]{\thepage}
\begin{document}
\thispagestyle{empty}
\begin{Exo}
Voici deux programmes de calcul:
\fbox{\colorbox{base2}{
\begin{minipage}[h]{0.2\textwidth}
\textbf{Programme A} \\ Choisir un nombre \\ Multiplier 6 \\ Ajouter par 3
\end{minipage}
}
}
\fbox{\colorbox{base2}{
\begin{minipage}[h]{0.2\textwidth}
\textbf{Programme B} \\ Choisir un nombre \\ Multiplier pas 4 \\ Enlever 20
\end{minipage}
}
}
\begin{enumerate}
\item Appliquer, en expliquant les étapes, le programme A à 3 et à 10.
\item Même chose avec le programme B.
\item Appliquer le programme A à $x$.
\item Même chose avec le programme B.
\item Quel chiffre doit-on choisir au départ pour que le programme A donne 9?
\item Quel chiffre doit-on choisir au départ pour que le programme A donne 21?
\item Quel chiffre doit-on choisir au départ pour que le programme B donne 9?
\end{enumerate}
\end{Exo}
\begin{Exo}
On a l'expression $5x + 6$
\begin{itemize}
\item Écrire un programme qui permet de calculer l'expression.
\item Quelle valeur de $x$ doit-on choisir pour que l'expression soit égale à 36?
\item Quelle valeur de $x$ doit-on choisir pour que l'expression soit égale à 10?
\end{itemize}
\end{Exo}
\eject
\begin{Exo}
\exo{Équations de degrés 1}
\begin{center}
\framebox{\parbox{0.4\textwidth}{
Résoudre l'équation $3x + 5 = 0$.
\begin{eqnarray*}
3x + 5 = 0 & \hspace{1cm} & \mbox{On ajoute l'opposé de 5} \\
3x + 5 \mathbf{+ (-5)} = \mathbf{-5} && \\
3x = -5 & \hspace{1cm} & \mbox{On multiplie par l'inverse de 3} \\
\mathbf{\frac{1}{3} \times }3x = \mathbf{ \frac{1}{3} \times }(-5) && \\
x = \frac{-5}{3} \approx 1,6
\end{eqnarray*}
La solution est $x = \frac{-5}{3} \approx 1,6$.
}}
\end{center}
\begin{enumerate}
\item Résoudre l'équation $4x + 7 = 0$.
\begin{eqnarray*}
4x + 7 = 0 & \hspace{0.5cm} & \mbox{On ajoute l'opposé de \parbox{1cm}{\dotfill}} \\[0.5cm]
4x + 7 + \parbox{1.5cm}{\dotfill}= \parbox{1.5cm}{\dotfill}&& \\[0.5cm]
4x = \parbox{1cm}{\dotfill}& \hspace{0.5cm} & \mbox{On multiplie par l'inverse de \parbox{1cm}{\dotfill}} \\[0.5cm]
\parbox{1.5cm}{\dotfill} \times 4x = \parbox{1.5cm}{\dotfill} \times \parbox{1cm}{\dotfill} && \\[0.5cm]
x = \frac{\parbox{1cm}{\dotfill}}{\parbox{1cm}{\dotfill}} \approx \parbox{1cm}{\dotfill}
\end{eqnarray*}
La solution est \parbox{2cm}{\dotfill}.
\item Résoudre les équations suivantes
\begin{multicols}{2}
\begin{enumerate}
\item $2x + 1 = 0$
\item $6x + 12 = 0$
\item $3x - 3 = 0$
\item $8x - 4 = 0$
\columnbreak
\item $-6x - 3 = 0$
\item $9 + 3x = 0$
\item $5 + 3x = 0$
\item $\frac{2}{3}x + 3 = 0$
\end{enumerate}
\end{multicols}
\end{enumerate}
\end{Exo}
\eject
\end{document}
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\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
% Title Page
\title{}
\author{}
\date{}
\begin{document}
\begin{multicols}{2}
Nom - Prénom:
\section{Connaissance}
\begin{enumerate}
\item Soient $a, b, c$ trois entiers relatifs tels que .. .. .. .. .. \\
Alors
\begin{eqnarray*}
a \times \frac{b}{c} & = & .. .. .. .. ..
\end{eqnarray*}
\item Soient $a, b, c, d$ trois entiers relatifs tels que .. .. .. .. .. \\
Alors
\begin{eqnarray*}
\frac{a}{b} \times \frac{c}{d} & = & .. .. .. .. ..
\end{eqnarray*}
\item Faire ces calculs en donnant une réponse en \textbf{écriture fractionnaire}. Simplifier quand c'est possible.
\begin{eqnarray*}
A & = & \frac{2}{3} + \frac{4}{2}
\end{eqnarray*}
~\\[2cm]
\begin{eqnarray*}
B & = & \frac{3}{4} \times \frac{4}{2}
\end{eqnarray*}
\end{enumerate}
\columnbreak
Nom - Prénom
\section{Connaissance}
\begin{enumerate}
\item Soient $a, b, c$ trois entiers relatifs tels que .. .. .. .. .. \\
Alors
\begin{eqnarray*}
a \times \frac{b}{c} & = & .. .. .. .. ..
\end{eqnarray*}
\item Soient $a, b, c, d$ trois entiers relatifs tels que .. .. .. .. .. \\
Alors
\begin{eqnarray*}
\frac{a}{b} : \frac{c}{d} & = & .. .. .. .. ..
\end{eqnarray*}
\item Faire ces calculs en donnant une réponse en \textbf{écriture fractionnaire}. Simplifier quand c'est possible.
\begin{eqnarray*}
A & = & \frac{5}{2} + \frac{4}{3}
\end{eqnarray*}
~\\[2cm]
\begin{eqnarray*}
B & = & \frac{5}{3} \times \frac{4}{2}
\end{eqnarray*}
\end{enumerate}
\end{multicols}
\end{document}
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\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
% Title Page
\title{}
\author{}
\date{}
\begin{document}
\begin{multicols}{2}
Nom - Prénom:
\section{Connaissance}
\begin{enumerate}
\item Soient $a, b, c$ trois entiers relatifs tels que .. .. .. .. .. \\
Alors
\begin{eqnarray*}
a \times \frac{b}{c} & = & .. .. .. .. ..
\end{eqnarray*}
\item Soient $a, b, c, d$ trois entiers relatifs tels que .. .. .. .. .. \\
Alors
\begin{eqnarray*}
\frac{a}{b} \times \frac{c}{d} & = & .. .. .. .. ..
\end{eqnarray*}
\item Diviser par un nombre revient à \dotfill \\
~\\[0.5cm]
.\dotfill
~\\[0.5cm]
\item L'inverse d'un nombre $b$ est \dotfill \\
~\\[0.5cm]
.\dotfill
~\\[0.5cm]
\item Est-ce que $0,5$ et $\frac{-1}{2}$ sont opposés? Justifier
\end{enumerate}
\columnbreak
Nom - Prénom
\section{Connaissance}
\begin{enumerate}
\item Soient $a, b, c$ trois entiers relatifs tels que .. .. .. .. .. \\
Alors
\begin{eqnarray*}
a \times \frac{b}{c} & = & .. .. .. .. ..
\end{eqnarray*}
\item Soient $a, b, c, d$ trois entiers relatifs tels que .. .. .. .. .. \\
Alors
\begin{eqnarray*}
\frac{a}{b} : \frac{c}{d} & = & .. .. .. .. ..
\end{eqnarray*}
\item L'opposé d'un nombre $b$ est \dotfill \\
~\\[0.5cm]
.\dotfill
~\\[0.5cm]
\item L'inverse de $\frac{a}{b}$ est \dotfill
~\\[1cm]
\item Est-ce que $\frac{3}{4}$ et $\frac{2}{1,5}$ sont inverses? Justifier
\end{enumerate}
\end{multicols}
\end{document}
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\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
% Title Page
\title{}
\author{}
\date{}
\begin{document}
\begin{multicols}{2}
Nom - Prénom:
\section{Connaissance}
\begin{enumerate}
\item $a$, $b$ et $k$ désignent des nombres relatifs avec $b \neq 0$ et $b \neq 0$, alors on a
\begin{equation*}
\frac{a}{b} = \frac{\qquad \qquad}{\qquad} = \frac{\qquad \qquad}{\qquad}
\end{equation*}
\vspace{1cm}
\item $a$, $b$, $c$ et $d$ désignent des nombres relatifs avec $b \neq 0$ et $d \neq 0$.
\begin{center}
Si $\frac{a}{b} = \frac{c}{d}$ alors \dotfill
\end{center}
\vspace{1cm}
\item Le quotient de deux nombres de même signe est \\ .\dotfill
\vspace{1cm}
\end{enumerate}
\columnbreak
Nom - Prénom
\section{Connaissance}
\begin{enumerate}
\item $a$, $b$ et $k$ désignent des nombres relatifs avec $b \neq 0$ et $b \neq 0$, alors on a
\begin{equation*}
\frac{a}{b} = \frac{\qquad \qquad}{\qquad} = \frac{\qquad \qquad}{\qquad}
\end{equation*}
\vspace{1cm}
\item $a$, $b$, $c$ et $d$ désignent des nombres relatifs avec $b \neq 0$ et $d \neq 0$.
\begin{center}
Si $a\times d = c \times b$ alors \dotfill
\end{center}
\vspace{1cm}
\item Le quotient de deux nombres de signes différents est \\ .\dotfill
\vspace{1cm}
\end{enumerate}
\end{multicols}
\end{document}
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\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
% Title Page
\title{}
\author{}
\date{}
\begin{document}
\large
\begin{multicols}{2}
Nom - Prénom:
\section{Connaissance}
\begin{enumerate}
\item $a$, $b$ et $k$ désignent des nombres relatifs avec $b \neq 0$ et $b \neq 0$, alors on a
\begin{equation*}
\frac{a}{b} = \frac{\qquad \qquad}{\qquad}
\end{equation*}
\vspace{1cm}
\item $a$, $b$, $c$ et $d$ désignent des nombres relatifs avec $b \neq 0$ et $d \neq 0$.
\vspace{0.5cm}
\begin{center}
Si $\frac{a}{b} = \frac{c}{d}$ alors \dotfill
\end{center}
\vspace{1cm}
\item Le quotient de deux nombres de même signe est
\vspace{0.5cm}
.\dotfill
\vspace{1cm}
\item Pour \textbf{comparer} des fractions, il faut
\vspace{0.5cm}
.\dotfill
\vspace{1cm}
\end{enumerate}
\columnbreak
Nom - Prénom
\section{Connaissance}
\begin{enumerate}
\item $a$, $b$ et $k$ désignent des nombres relatifs avec $b \neq 0$ et $b \neq 0$, alors on a
\begin{equation*}
\frac{a}{b} = \frac{\qquad \qquad}{\qquad}
\end{equation*}
\vspace{1cm}
\item $a$, $b$, $c$ et $d$ désignent des nombres relatifs avec $b \neq 0$ et $d \neq 0$.
\vspace{0.5cm}
\begin{center}
Si $a\times d = c \times b$ alors \dotfill
\end{center}
\vspace{1cm}
\item Le quotient de deux nombres de signes différents est
\vspace{0.5cm}
.\dotfill
\vspace{1cm}
\item Pour \textbf{additionner} des fractions, il faut
\vspace{0.5cm}
.\dotfill
\vspace{1cm}
\end{enumerate}
\end{multicols}
\end{document}
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Notes sur des exercices autour des fractions
############################################
:date: 2014-07-01
:modified: 2014-07-01
:tags: Nombres Calculs, Exo
:category: 4e
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers problemes.pdf <problemes.pdf>`_
`Lien vers problemes.tex <problemes.tex>`_

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\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classCours}
\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
% Title Page
\titre{Problèmes sur les fractions}
% \quatreC \quatreD \troisB \troisPro
\classe{\quatreC}
\date{12 janvier 2014}
%\fancyhead[L]{<++classes++> : \Thetitle}
\begin{document}
\thispagestyle{empty}
\begin{Exo}
Dans une forêt, il y a $\frac{2}{3}$ des arbres qui sont feuillu (avec des feuilles). Parmi ces arbres, il y en a $\frac{1}{2}$ qui sont de chênes.
Quelle est la proportion de chênes dans cette forêt?
\end{Exo}
\begin{Exo}
Marine utilise $\frac{4}{5}$ d'un paquet de farine pour faire un gâteau. La moitié de ce qui reste lui sert à faire des crêpes.
Quelle est la proportion du paquet de farine utilisée pour la confection des crêpes?
\end{Exo}
\begin{Exo}
Sur un parking à vélos, $\frac{4}{11}$ des vélos sont rouges, $\frac{3}{22}$ sont noirs et $\frac{5}{11}$ des vélos restant sont blancs.
\begin{enumerate}
\item Quelle est la fraction des vélos rouge ou noirs?
\item Quelle est la fraction des vélos blancs?
\item Quelle est la fraction des vélos qui ne sont ni rouges, ni noirs, ni blancs?
\end{enumerate}
\end{Exo}
\begin{Exo}
Dans un club sportif, $\frac{1}{2}$ des adhérents ont moins de 30 ans et les $\frac{3}{20}$ des autres ont plus de 40ans.
\begin{enumerate}
\item Quelle est la fraction des adhérents qui ont plus de 40 ans?
\item Quelle est la fraction des adhérents qui ont entre 30 et 40 ans?
\end{enumerate}
\end{Exo}
~\\[0.5cm]
\hline
~\\[0.5cm]
\setcounter{exo}{0}
\begin{Exo}
Dans une forêt, il y a $\frac{2}{3}$ des arbres qui sont feuillu (avec des feuilles). Parmi ces arbres, il y en a $\frac{1}{2}$ qui sont de chênes.
Quelle est la proportion de chênes dans cette forêt?
\end{Exo}
\begin{Exo}
Marine utilise $\frac{4}{5}$ d'un paquet de farine pour faire un gâteau. La moitié de ce qui reste lui sert à faire des crêpes.
Quelle est la proportion du paquet de farine utilisée pour la confection des crêpes?
\end{Exo}
\begin{Exo}
Sur un parking à vélos, $\frac{4}{11}$ des vélos sont rouges, $\frac{3}{22}$ sont noirs et $\frac{5}{11}$ des vélos restant sont blancs.
\begin{enumerate}
\item Quelle est la fraction des vélos rouge ou noirs?
\item Quelle est la fraction des vélos blancs?
\item Quelle est la fraction des vélos qui ne sont ni rouges, ni noirs, ni blancs?
\end{enumerate}
\end{Exo}
\begin{Exo}
Dans un club sportif, $\frac{1}{2}$ des adhérents ont moins de 30 ans et les $\frac{3}{20}$ des autres ont plus de 40ans.
\begin{enumerate}
\item Quelle est la fraction des adhérents qui ont plus de 40 ans?
\item Quelle est la fraction des adhérents qui ont entre 30 et 40 ans?
\end{enumerate}
\end{Exo}
\end{document}
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Notes sur une activité de découverte des puissances
###################################################
:date: 2014-07-01
:modified: 2014-07-01
:tags: Nombres Calculs, Exo
:category: 4e
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers redecouverte_puiss.tex <redecouverte_puiss.tex>`_
`Lien vers redecouverte_puiss.pdf <redecouverte_puiss.pdf>`_
`Lien vers puissance10.pdf <puissance10.pdf>`_

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\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
\usepackage{multicol}
% Title Page
\title{Puissances - Exercices}
\author{}
\date{}
\fancyhead[L]{Quatrième}
\fancyhead[C]{\Thetitle}
\fancyhead[R]{\thepage}
\begin{document}
\thispagestyle{fancy}
\begin{Exo}
Un laboratoire fait des recherches sur le développement d'une population de cellules. Ils observent que le nombre de cellules est multiplié par 3 toutes les heures. En vous aidant du tableau déterminer le nombre de cellules qu'il y aura au bout de 24h s'il y a une seule cellule au début.
\begin{center}
\begin{tabular}{|c|*{13}{c|}}
\hline
Heure & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline
Cellules & & & & & & & & & & & & &\\
\hline
\end{tabular}
\begin{tabular}{|c|*{12}{c|}}
\hline
Heure & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 \\
\hline
Cellules & & & & & & & & & & & &\\
\hline
\end{tabular}
\end{center}
On rappelle que l'on peut réduire des écritures en utilisant les puissances. Par exemple,
\begin{eqnarray*}
2^4 & = & 2 \times 2 \times 2 \times 2
\end{eqnarray*}
En utilisant cette écriture, réécrire le nombre de cellules au bout de 24h puis de 48h.
\end{Exo}
\begin{Exo}
\begin{multicols}{2}
\begin{enumerate}
\item Réécrire avec des multiplications les puissances suivantes
\begin{eqnarray*}
2^5 & = \parbox{1cm}{\dotfill} \\
6^7 & = \parbox{1cm}{\dotfill} \\
3,1^5 & = \parbox{1cm}{\dotfill} \\
2^{10} & = \parbox{1cm}{\dotfill} \\
5^1 & = \parbox{1cm}{\dotfill} \\
2^0 & = \parbox{1cm}{\dotfill}
\end{eqnarray*}
\columnbreak
\item Réécrire avec des puissances
\begin{eqnarray*}
4 \times 4 \times 4 & = 4^{\parbox{0.5cm}{\dotfill}} \\
3 \times 3 \times 3 \times 3 \times 3 & = 3^{\parbox{0.5cm}{\dotfill}} \\
7 \times 7 & = 7^{\parbox{0.5cm}{\dotfill}} \\
10\times 10 \times 10 \times 10 \times 10 & = \parbox{1cm}{\dotfill} \\
5 & = \parbox{1cm}{\dotfill} \\
5 \times 5 \times 5 \times 1& = \parbox{1cm}{\dotfill}
\end{eqnarray*}
\end{enumerate}
\end{multicols}
\end{Exo}
\eject
\begin{Exo}
Compléter le tableau sans utiliser la calculatrice.
\hspace{-0.8cm}
\begin{tabular}{|c|c|c|c|}
\hline
Expression & Avec les puissances & Avec des produits & Valeur décimale \\
\hline
6 puissance 2 & $6^2$ & $6 \times 6$ & 36 \\
\hline
3 puissance 4 & & & \\
\hline
2 puissance 5 & & & \\
\hline
& $(-2)^3$ & & \\
\hline
& & $(-4) \times (-4) \times (-4)$ & \\
\hline
& & & 1000\\
\hline
\end{tabular}
\end{Exo}
\begin{Exo}
\begin{enumerate}
\item
En passant par l'écriture avec les $\times$, mettre les multiplications suivantes sous la forme $a^n$
\begin{eqnarray*}
2^3\times2^4 =& 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 &= 2^7\\
3^4 \times 3^5 =& \parbox{5cm}{\dotfill} & = 3^{\parbox{1cm}{\dotfill}} \\
6^2 \times 6^3 =& \parbox{5cm}{\dotfill} & = 6^{\parbox{1cm}{\dotfill}} \\
9 \times 9^6 =& \parbox{5cm}{\dotfill} & = 9^{\parbox{1cm}{\dotfill}} \\
5^4 \times 5^3 =& \parbox{5cm}{\dotfill} & = 5^{\parbox{1cm}{\dotfill}} \\
2^7 \times 2^0 =& \parbox{5cm}{\dotfill} & = 2^{\parbox{1cm}{\dotfill}} \\
\end{eqnarray*}
\item
Donner une idée pour compléter la formule suivante
\begin{eqnarray*}
a^n \times a^m & = & a^{\parbox{1cm}{\dotfill}}
\end{eqnarray*}
\end{enumerate}
\end{Exo}
\end{document}
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Notes sur une fiche d'exercices autour des puissances
#####################################################
:date: 2014-07-01
:modified: 2014-07-01
:tags: Nombres Calculs, Exo
:category: 4e
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers puissances_1.pdf <puissances_1.pdf>`_
`Lien vers puissances_1.tex <puissances_1.tex>`_

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\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
\usepackage{multicol}
% Title Page
\title{Puissances - Exercices}
\author{}
\date{}
\fancyhead[L]{Quatrième}
\fancyhead[C]{\Thetitle}
\fancyhead[R]{\thepage}
\begin{document}
\thispagestyle{fancy}
\begin{Exo}
\begin{enumerate}
\item
En passant par l'écriture avec les $\times$, mettre les multiplications suivantes sous la forme $a^n$
\begin{eqnarray*}
2^3\times2^4 =& 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 &= 2^7\\
3^4 \times 3^5 =& \parbox{5cm}{\dotfill} & = 3^{\parbox{1cm}{\dotfill}} \\
6^2 \times 6^3 =& \parbox{5cm}{\dotfill} & = 6^{\parbox{1cm}{\dotfill}} \\
9 \times 9^6 =& \parbox{5cm}{\dotfill} & = 9^{\parbox{1cm}{\dotfill}} \\
5^4 \times 5^3 =& \parbox{5cm}{\dotfill} & = 5^{\parbox{1cm}{\dotfill}} \\
2^7 \times 2^0 =& \parbox{5cm}{\dotfill} & = 2^{\parbox{1cm}{\dotfill}} \\
\end{eqnarray*}
\item
Donner une idée pour compléter la formule suivante
\begin{eqnarray*}
a^n \times a^m & = & a^{\parbox{1cm}{\dotfill}}
\end{eqnarray*}
\end{enumerate}
\end{Exo}
\begin{Exo}
Compléter les tableau suivants
\vspace{1cm}
\hspace{-0.5cm}
\begin{tabular}{|c|*{7}{p{1.2cm}|}}
\hline
Puissances & $10^{-3}$ & $10^{-2}$ &$10^{-1}$ &$10^{0}$ &$10^{1}$ &$10^{2}$ &$10^{3}$ \\
\hline
Expression & & & & & & & \\
\hline
Décimale & & & & & & & \\
\hline
\end{tabular}
\vspace{1cm}
\hspace{-0.5cm}
\begin{tabular}{|c|*{7}{p{1.2cm}|}}
\hline
Puissances & $2^{-3}$ & $2^{-2}$ &$2^{-1}$ &$2^{0}$ &$2^{1}$ &$2^{2}$ &$2^{3}$ \\
\hline
Expression & & & & & & & \\
\hline
Décimale & & & & & & & \\
\hline
\end{tabular}
\end{Exo}
\eject
\begin{Exo}
\begin{enumerate}
\item Réécrire avec des multiplications puis mettre sous la forme $a^n$
\vspace{-0.5cm}
\begin{eqnarray*}
\frac{2^5}{2^3} = \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 2^{\parbox{1cm}{\dotfill}} \\[0.5cm]
\frac{10^4}{10^2} = \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 10^{\parbox{1cm}{\dotfill}} \\[0.5cm]
\frac{3^4}{3^5} = \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 3^{\parbox{1cm}{\dotfill}}
\end{eqnarray*}
\begin{eqnarray*}
\frac{2^4}{2^5} = \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 2^{\parbox{1cm}{\dotfill}} \\[0.5cm]
\end{eqnarray*}
\vspace{-1.5cm}
\item Donner une idée pour compléter la formule suivante
\begin{eqnarray*}
\frac{a^n}{a^m} & = & a^{\parbox{1cm}{\dotfill}}
\end{eqnarray*}
\end{enumerate}
\end{Exo}
\begin{Exo}
Mettre les expressions suivantes sous la forme $a^n$ en passant la l'écriture avec les multiplications.
\begin{multicols}{3}
\begin{eqnarray*}
\frac{3^5}{3^5} \\[0.5cm]
\frac{5^2 \times 5^3}{5^2} \\[0.5cm]
\frac{7^3}{ 7^2 \times 7} \\[0.5cm]
\end{eqnarray*}
\columnbreak
\begin{eqnarray*}
\frac{2^5 \times 2^7}{2^5} \\[0.5cm]
\frac{2^7 \times 2^2}{2^9} \\[0.5cm]
\frac{2^5 \times 2^{-2}}{ 2^4 \times 2^5} \\[0.5cm]
\end{eqnarray*}
\columnbreak
\begin{eqnarray*}
\frac{10^4 \times 10^8}{10^2} \\[0.5cm]
\frac{10^{-8} \times 10^7}{10^{15}} \\[0.5cm]
\frac{10^6}{ 10^3 \times 10^5} \\[0.5cm]
\end{eqnarray*}
\end{multicols}
\end{Exo}
\end{document}
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Notes sur une fiche d'exercices autour de la notation scientifique
##################################################################
:date: 2014-07-01
:modified: 2014-07-01
:tags: Nombres Calculs, Exo
:category: 4e
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers scientifique_corr.pdf <scientifique_corr.pdf>`_
`Lien vers scientifique.tex <scientifique.tex>`_
`Lien vers scientifique_corr.tex <scientifique_corr.tex>`_
`Lien vers scientifique.pdf <scientifique.pdf>`_

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\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
\usepackage{multicol}
%\usepackage{enumitem}
% Title Page
\title{Puissances - Exercices}
\author{}
\date{}
\fancyhead[L]{Troisième}
\fancyhead[C]{\Thetitle}
\fancyhead[R]{\thepage}
\begin{document}
\thispagestyle{fancy}
\begin{Exo}
Passer les écritures suivantes en écriture décimale (sans multiplications)
\begin{enumerate}
\begin{multicols}
\item $123,4567 \times 10^3$
\item $3,56 \times 10^4$
\item $58,345 \times 10^2$
\item $0,0472 \times 10^6$
\columnbreak
\item $3,56 \times 10^{-4}$
\item $234,45 \times 10^{-1}$
\item $2345 \times 10^{-6}$
\item $4,56 \times 10^{-3}$
\end{multicols}
\end{enumerate}
\end{Exo}
\begin{Exo}
Relie chaque nombre à gauche à son écriture scientifique à droite.
\begin{tabular}{rp{2cm}l}
23,456 $\bullet$ && $\bullet$$2,3456 \times 10^{0}$ \\
234,56 $\bullet$ && $\bullet$$2,3456 \times 10^{2}$\\
2,3456 $\bullet$ && $\bullet$$2,3456 \times 10^{1}$\\
0,0023456 $\bullet$ && $\bullet$$2,3456 \times 10^{-3}$
\end{tabular}
\end{Exo}
\begin{Exo}
Voici les caractéristiques de plusieurs planètes du système solaire.
\begin{tabular}{|c|c|c|}
\hline
Planète & Rayon moyen (km) & Masse(kg) \\
\hline
Mercure & 2439,7 & $3,302\times 10^{23}$ \\
\hline
Terre & 6 371 & $5,9736 \times 10^{24}$ \\
\hline
Mars & 3390 & $6,4185 \times 10^{23}$ \\
\hline
Jupiter & 69 911 & $1,8986 \times 10^{27}$ \\
\hline
Neptune & 24 622 & $1,0243 \times 10^{26}$ \\
\hline
\end{tabular}
\begin{enumerate}
\item Classer ces planètes de la plus petite à la plus grosse.
\item Classer ces planète en fonction de leur masse.
\item Classe les planètes selon leur masse volumique. La formule pour calculer la masse volumique est ($m$ représente la masse et $r$ le rayon).
\begin{eqnarray*}
\frac{3m}{4\pi\times r^3}
\end{eqnarray*}
\item Peut-on à partir du calcul de la masse volumique faire deux groupes de planètes, les planètes gazeuses et les planètes tellurique?
\end{enumerate}
\end{Exo}
\begin{Exo}
Écrire les nombres suivants sous forme scientifique.
\begin{enumerate}
\item $12345$
\item $456,34$
\item $987,003$
\item $0.0043$
\end{enumerate}
\end{Exo}
\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}
\renewcommand{\arraystretch}{2}
\begin{document}
\begin{frame}{Masse volumique des planètes}
\begin{tabular}{|c|c|c|c|}
\hline
Planète & Rayon moyen (km) & Masse(kg) & Masse volumique ($kg/m^3$)\\
\hline
Mercure & 2439,7 & $3,302\times 10^{23}$ & $ 5,428\times 10^{12}$\\
\hline
Terre & 6 371 & $5,9736 \times 10^{24}$ & $ 5,514\times 10^{12}$\\
\hline
Mars & 3390 & $6,4185 \times 10^{23}$ & $ 3,933\times 10^{12}$\\
\hline
Jupiter & 69 911 & $1,8986 \times 10^{27}$ & $ 1,326\times 10^{12}$\\
\hline
Neptune & 24 622 & $1,0243 \times 10^{26}$ & $ 1,638\times 10^{12}$\\
\hline
\end{tabular}
\end{frame}
\end{document}

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\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
% Title Page
\title{}
\author{}
\date{}
\begin{document}
\begin{multicols}{2}
Nom - Prénom:
\section{Connaissance}
Completer les phrases suivantes
\begin{itemize}
\renewcommand{\labelitemi}{$\star$}
\item Les nombres relatifs sont \dotfill
\vspace{2cm}
\item Si on multiplie deux nombres relatifs de même signe \\ alors \dotfill \\
\end{itemize}
\vspace{3cm}
Nom - Prénom:
\section{Connaissance}
Completer les phrases suivantes
\begin{itemize}
\renewcommand{\labelitemi}{$\star$}
\item Les nombres relatifs sont \dotfill
\vspace{2cm}
\item Si on multiplie deux nombres négatifs ensembles \\ alors le résultat est \dotfill \\
\end{itemize}
\columnbreak
Nom - Prénom:
\section{Connaissance}
Completer les phrases suivantes
\begin{itemize}
\renewcommand{\labelitemi}{$\star$}
\item Les nombres relatifs sont \dotfill
\vspace{2cm}
\item Si on multiplie un nombre négatif avec un nombre positif \\ alors \dotfill \\
\end{itemize}
\vspace{3cm}
Nom - Prénom:
\section{Connaissance}
Completer les phrases suivantes
\begin{itemize}
\renewcommand{\labelitemi}{$\star$}
\item Les nombres relatifs sont \dotfill
\vspace{2cm}
\item Si on multiplie un nombre positif avec un nombre négatif \\ alors \dotfill \\
\end{itemize}
\end{multicols}
\end{document}
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\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
% Title Page
\title{}
\author{}
\date{}
\begin{document}
\begin{multicols}{2}
Nom - Prénom - Classe:
\section{Connaissance}
Compléter les phrases suivantes
\begin{itemize}
\renewcommand{\labelitemi}{$\star$}
\item Les nombres relatifs sont \dotfill\\
\item Si on multiplie deux nombres relatifs de même signe \\ alors \dotfill \\
\item Lors d'une multiplication, si le nombre de chiffres négatifs est impaire alors \dotfill
\end{itemize}
\vspace{2cm}
Nom - Prénom - Classe:
\section{Connaissance}
Compléter les phrases suivantes
\begin{itemize}
\renewcommand{\labelitemi}{$\star$}
\item Les nombres relatifs sont \dotfill \\
\item Si on multiplie deux nombres négatifs ensembles \\ alors le résultat est \dotfill \\
\item Lors d'une multiplication, si le nombre de chiffres négatifs est paire alors \dotfill
\end{itemize}
\columnbreak
Nom - Prénom - Classe:
\section{Connaissance}
Compléter les phrases suivantes
\begin{itemize}
\renewcommand{\labelitemi}{$\star$}
\item Les nombres relatifs sont \dotfill \\
\item Si on multiplie un nombre négatif avec un nombre positif \\ alors \dotfill \\
\item Lors d'une multiplication, si le nombre de chiffres négatifs est impaire alors \dotfill
\end{itemize}
\vspace{2cm}
Nom - Prénom - Classe:
\section{Connaissance}
Compléter les phrases suivantes
\begin{itemize}
\renewcommand{\labelitemi}{$\star$}
\item Les nombres relatifs sont \dotfill \\
\item Si on multiplie un nombre positif avec un nombre négatif \\ alors \dotfill \\
\item Lors d'une multiplication, si le nombre de chiffres négatifs est paire alors \dotfill
\end{itemize}
\end{multicols}
\end{document}
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Notes sur le cours autour de nombre relatif
###########################################
:date: 2014-07-01
:modified: 2014-07-01
:tags: Nombres Calculs,Cours
:category: 4e
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers nbr_relatifs.tex <nbr_relatifs.tex>`_
`Lien vers nbr_relatifs.pdf <nbr_relatifs.pdf>`_

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\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classCours}
\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
% Title Page
\titre{Nombres reltifs}
% \quatreC \quatreD \troisB \troisPro
\classe{Quatrième}
\date{9 septembre 2013}
\begin{document}
\maketitle
\section{Calcul litteral}
\begin{Def}
Une \textbf{expression littérale} est une expression dans laquelle un ou plusieurs chiffres ont été remplacé par des lettres.
\end{Def}
\begin{Ex}
\begin{itemize}
\item $x + 5$ est une expression littérale. Si on remplace $x$ par 5, on obtient: $5 + 5 = 10$.
\item $a(a-3) + 1$ est une expression littérale. Si on remplace $a$ par 2 on obtient $2(2-1) + 1 = 2\times(-1) + 1 = -2 + 2 = -1$. Si on remplace $a$ par $2x$, on obtient...
\end{itemize}
\end{Ex}
\paragraph{Rappel:} le carré
\begin{eqnarray*}
5^2 = 5\times 5 = 25 \\
(-3)^2 = (-3) \times (-3) = 9
\end{eqnarray*}
\begin{Ex}
\begin{itemize}
\item Calculer $(a+b)^2$ et $a^2 + b^2$ avec $a = 2$ et $b = 1$
\item Calculer $(a-b)^2$ et $a^2 - b^2$ avec $a = 2$ et $b = 3$
\end{itemize}
% 9/09/2013
% On s'arrete ici avec les 2 classes. Le remplacement des lettres par des chiffres marche plutôt bien même en ce début d'année. Par contre bien entendu, ils ne savent pas calculer -3x(-3) .. vu que c'est le thème du chapitre!
% Il faudrait peut être faire plus d'exemple où l'on remplace les lettres par des chiffres pour montrer l'interet du calcul littéral.
\paragraph{Que remarque-t-on?} On remarque que $(2 + 1)^2 = ..$ n'est pas égal à $2^2 + 1^2 = ..$.
\end{Ex}
\section{Développer et factoriser}
\subsection{Développer}
\begin{Ex}
Développer les expressions suivantes
\begin{eqnarray*}
3(2x + 1) & = & \\
2x(x - 1) & = & \\
\end{eqnarray*}
\end{Ex}
\begin{Def}
\textbf{Développer} c'est transformer un produit en somme, ou encore enlever des parenthèses.
\end{Def}
\paragraph{Question:} Comment enlever les parenthèses pour $(2x=1)(x+3)$?
\begin{Prop}
$a, b, c, d$ représentent des nombres \note{Bien sûr, on a les flêches pour représenter ça!)}
\begin{eqnarray*}
(a+b)(c+d) & = & ac + ad + bc + bd
\end{eqnarray*}
\end{Prop}
\end{document}
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