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4e/Nombres_Calculs/Equation/Cours/balances.pdf 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{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}
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\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}
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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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