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import work from year 2016-2017

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Benjamin Bertrand
2017-06-16 09:49:23 +03:00
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\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
% Title Page
\titre{Fonction affines- Exercices}
% \seconde \premiereS \PSTMG \TSTMG
\classe{Troisième }
\date{Mars 2017}
\pagestyle{empty}
\renewcommand{\lexo}{%
\setcounter{exo}{1}
\begin{Exo}[Piscine]
Brahim décide d'aller régulièrement à la piscine pendant un an. Voici les tarifs proposés:
\begin{itemize}
\item Tarif "Abonné": 100\euro par an, nombre illimité d'entrées.
\item Tarif "Adhérant": 40\euro d'adhésion par an puis 1\euro par entrée.
\item Tarif "Libre": 2\euro par entrée.
\end{itemize}
\begin{enumerate}
\item Quel prix paiera-t-il avec \textbf{chaque tarif}, s'il va à la piscine 20 fois en un an?
\item Même question, mais s'il y va 7 fois par mois pendant un an.
\item Expliquer pour chaque tarif, comment exprimer le prix en fonction du nombre d'entrée.
\item Reproduire le tableau ci dessous sur le tableur (on ira jusqu'à 100 entrées)
\includegraphics[scale=0.4]{./fig/tableur_tarif_exo}
\item Que doit-on entrer dans les cases \texttt{B2}, \texttt{C2} et \texttt{D2} puis tirer vers le bas pour calculer le prix pour chaque tarif?
\item Tracer le graphique pour tous ces prix.
\item À partir des graphiques, décrire quand il est intéressant de choisir le tarif 'Adhérent'.
\end{enumerate}
\end{Exo}
}
\begin{document}
\lexo
\vfill
\lexo
\vfill
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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\documentclass[a5paper,10pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
% Title Page
\titre{Fonction affines - Exercices}
% \seconde \premiereS \PSTMG \TSTMG
\classe{Troisième }
\date{Mars 2017}
\pagestyle{empty}
\renewcommand{\lexo}{%
\setcounter{exo}{1}
\begin{Exo}[Abonnement téléphonique]
Abdou se rend chez un opérateur téléphonique pour choisir un abonnement. On lui propose 3 forfaits:
\begin{itemize}
\item Forfait \textbf{Liberté}: 36\euro par mois, textos illimités.
\item Forfait \textbf{Zen}: 20\euro par mois, 5 centimes par textos.
\item Forfait \textbf{Proche}: 20 centimes par textos
\end{itemize}
\begin{enumerate}
\item Abdou estime qu'il envoie 150 textos par mois. Quel forfait doit-il choisir?
\item Une copine, Roubouanti, envoie en moyenne 300 textos par mois et a choisi le forfait \textbf{Liberté}. A-t-elle fait le bon choix?
\item Trouver les fonctions qui transforment le nombre de textos en prix pour les 3 forfaits.
\item Abdou souhaite en savoir plus. Il se demande à partir de combien de textos envoyé, il est plus intéréssant de choisir le forfait \textbf{Liberté}. Aidez le à répondre à sa question.
\end{enumerate}
\end{Exo}
\begin{Exo}[Un peu de géométrie]
On veut comparer l'aire des deux figures ci-dessous en faisant varierla valeur de $x$.
\hspace{-1cm}
\includegraphics[scale=0.5]{./fig/rect_trapeze}
\begin{enumerate}
\item Quelle figure à la plus grande surface quand $x$ vaut 4?
\item Quelle figure à la plus grande surface quand $x$ vaut 1?
\item Pour chaque figure, proposer une fonction permettant de tranformer x en l'aire.
\item Proposer à l'aide du tableur, une façon de savoir à partir de quel valeur de $x$ la première figure a une plus grande aire que la deuxième.
\end{enumerate}
\end{Exo}
\begin{Exo}[Salaires]
Jean, Faïza et Bob fabriquent tous les 3 des jouets mais ne sont pas payé de la même façons.
\begin{itemize}
\item Jean a un salaire fixe de 1500\euro par mois.
\item Faïza a un salaire de 1000\euro augmenté d'une prime de 4\euro par jouet qu'il a frabriqué.
\item Bob a un salaire de 500\euro mais a une prime de 7\euro par jouet.
\end{itemize}
Qui est le mieux payé des 3?
\end{Exo}
}
\begin{document}
\lexo
\vfill
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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Notes autour du chapitre sur les fonctions affines pour les 3e
##############################################################
:date: 2017-03-14
:modified: 2017-03-14
:tags: Fonctions
:category: 3e
:authors: Bertrand Benjamin
:summary: Notes sur le chapitre autour des fonctions affines pour les 3e.
Le chapitre sur les fonctions linéaires n'était pas bien passé à cause d'un gros soucis de sens des opérations.
On va continuer à travailler dans ce sens, avec beaucoup de modélisation. Tant pis si l'aspect formel des fonctions n'est pas trop travaillé. Il faudra le reprendre à la dernière période.
Étape 1
--------
Retour sur la notion de fonction linéaire en créant des formules à partir d'un tableau ou d'un graphique.
`Longueur, poids et prix d'un fil de fer <./tbl_graph_vers_fonction_lin.pdf>`_
On fera ressortir le vocabulaire de proportionnalité, de fonction linéaire et de représentation graphique.
Étape 2
--------
On introduit la notion de fonction affine à côté de la fonction linéaire.
`Tarifs d'une piscine <./comparaison_tarifs.pdf>`_
On donne la définition de fonction affine, sa représentation graphique.
Étape 3
-------
Activité similaire à l'étape 1 mais on mélange des fonctions affines et linaires.
Étape 4
-------
(étape peut être à reporter à la prochaine période) Manipulation théorique de fonction linéaire et affine.

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\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
% Title Page
\titre{Tableau et graphique vers une formule- Exercices}
% \seconde \premiereS \PSTMG \TSTMG
\classe{Troisième }
\date{Mars 2017}
\pagestyle{empty}
\renewcommand{\lexo}{%
\setcounter{exo}{0}
\begin{Exo}[Longueur, poids et prix]
Ci-dessous, un tableau reliant la longueur et le poids d'un fil de fer et un graphique reliant la longueur et le prix du même fil de fer.
\hspace{-1cm}
\begin{minipage}{0.45\textwidth}
\begin{tabular}{|p{3cm}|*{3}{p{1cm}|}}
\hline
Longueur (en m) & 50 & 100 & 200 \\
\hline
Poids (en kg) & 0,7 & 1,4 & 2,8 \\
\hline
\end{tabular}
\end{minipage}
\begin{minipage}{0.6\textwidth}
\includegraphics[scale=0.7]{./fig/fil_fer_long_prix}
\end{minipage}
\begin{enumerate}
\item Combien pèse 62m de ce fil de fer? 284m? Expliquer comment transformer n'importe quel longueur de fil de fer en son poids.
\item Trouver une formule qui donne le poids de fil de fer en fonction de la longueur.
\item Combien coûte 75m de fil de fer? 300m? Expliquer comment vous avez fait.
\item Peut-on écrire une formule qui donne le prix en fonction de la longueur de fil de fer?
\item (dure) Peut-on exprimer (trouver une formule) le prix de fil de fer en fonction de son poids?
\end{enumerate}
\end{Exo}
}
\begin{document}
\lexo
\vfill
\lexo
\vfill
\end{document}
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