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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:
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