From 69f263084b55503b7b7145f9fd9f49183972c5cc Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 23 Aug 2022 16:55:48 +0200 Subject: [PATCH] =?UTF-8?q?Feat:=20ajoute=20la=20premi=C3=A8re=20=C3=A9tap?= =?UTF-8?q?e=20sur=20les=20fonctions?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../1B_fonction.pdf | Bin 0 -> 21957 bytes .../1B_fonction.tex | 33 +++++++ .../1B_representations.pdf | Bin 0 -> 29116 bytes .../1B_representations.tex | 82 ++++++++++++++++++ .../1B_tableur.pdf | Bin 0 -> 39632 bytes .../1B_tableur.tex | 32 +++++++ .../exercises.tex | 14 +++ .../fig/salaire_tableur.png | Bin 0 -> 30797 bytes .../index.rst | 64 ++++++++++++++ .../plan_de_travail.pdf | Bin 0 -> 20808 bytes .../plan_de_travail.tex | 44 ++++++++++ .../salaires.ods | Bin 0 -> 30376 bytes 12 files changed, 269 insertions(+) create mode 100644 1ST/02_Generalites_sur_les_fonctions/1B_fonction.pdf create mode 100755 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+\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} +%\usepackage{pgfplots} +\usetikzlibrary {datavisualization.formats.functions} + +\author{Bertrand Benjamin} +\title{Généralités sur les fonctions - Cours} +\date{Septembre 2022} + +\pagestyle{empty} + + +\usepackage{luacode} + +\begin{luacode*} + function f_table () + for t=-1, 1, 1 do + local x=2*t-5 + sf =[[%d & %d \\]] + tex.print(string.format(sf, t, x)) + end + end +\end{luacode*} +\newcommand{\ftable}{\luadirect{f_table()}} + +\begin{document} + +\maketitle + +\setcounter{section}{1} +\section{Les représentation de fonctions} + +On utilise essentiellement trois façons de représenter des fonctions + +\raggedcolumns +\begin{multicols}{3} + \textbf{Une formule} + + \[ + f(x) = 2x - 5 + \] + + \columnbreak + \textbf{Un tableau de valeurs} + + \begin{center} + \begin{tabular}{|c|c|} + \hline + $x$ & $f(x)$ \\ + \hline + \ftable + \hline + \end{tabular} + \end{center} + + \columnbreak + \textbf{Un graphique} + + \begin{tikzpicture} + \datavisualization [ + school book axes, + visualize as smooth line, + x axis={length=3cm, label}, + y axis={length=3cm, label={$f(x)$}, ticks={step=2}}, + all axes={grid}, + ] + data [format=function] { + var x : interval [-1:4] samples 2; + func y = \value x*2 - 5; + }; + \end{tikzpicture} +\end{multicols} + +\afaire{Identifier image et antécédents dans ces trois représentations. Quel est l'ensemble de définition de la fonction $f$?} + +\paragraph{D'autres représentations} + +\afaire{Trouver deux autres représentations en tableau des fonctions} + + + +\end{document} diff --git a/1ST/02_Generalites_sur_les_fonctions/1B_tableur.pdf b/1ST/02_Generalites_sur_les_fonctions/1B_tableur.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2809162d871f07ed08465576ae7490ce340e7290 GIT binary patch literal 39632 zcmc$`2Rzn)+deKWQ4&!`qM{<%Bti(KqG7M>l|8aYks>SE2}#Jx$c~oC9?4E+WD`Q> z@3_?S+~50o?%(s=zt`)3-~a3N{g$|VuFvN^&ht2q^Elru3R2P>+{gJzS!!Eff2?S4 zeD|J|kBN)PQrDDJM1+a+s*{xg6Q_#2uBm~Z9TVpjdtJNr??_wPm@{z_{#<_tHxs9X zgry^sI)0UliJR;9|C&sk7j*1wObFlS{{55nKk@y`2DX;=HhKoOO#JxPWn9YSx}AXy z{=TkbXCP&uXQ_|RJ#S!PWM|C8&Cet%%Jd&EQd>J4108cx$Ih0W^$JJozYr5`UD+^2 zYG9%N=O_4zaQ}k1^1tsnPW;QBL+Ic79NdH%{MSqfH(?R{`(}ij=U?|E|K7F5{jXbG zJcQ}~_st0pVF~QNzxPQ9Ve((}Bm)25Cm}56f6bHd{WW&|Pa&R1koPY!{%;|^ z=W4d;JFe|LE7Xf#3y0*w_njbCZe|}>s!}>h?R@3P%GyA`hRwD%W(A(j2M>weJv_Wa 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+\newcommand\lecours{ +\setcounter{section}{2} +\section{Évaluer des fonctions avec le tableur} + +\begin{center} + \includegraphics[scale=0.3]{./fig/salaire_tableur.png} +\end{center} +\vfill +} + +\begin{document} + +\lecours +\lecours +\lecours +\lecours +\lecours + + + +\end{document} diff --git a/1ST/02_Generalites_sur_les_fonctions/exercises.tex b/1ST/02_Generalites_sur_les_fonctions/exercises.tex new file mode 100644 index 0000000..169a069 --- /dev/null +++ b/1ST/02_Generalites_sur_les_fonctions/exercises.tex @@ -0,0 +1,14 @@ +\begin{exercise}[subtitle={Salaires}, step={1}, origin={Ma tête}, topics={ Généralités sur les fonctions }, tags={ Analyse, Fonctions }] + Jean, Faïza, Bob et Rachelle travaillent dans une usine de production de jouets mais ne sont pas payé de la même façon. Ils veulent comparer leur revenus. + \begin{itemize} + \item Jean n'a pas de salaire fixe mais a une prime de 9\euro par jouets. + \item Faïza a un salaire fixe de 1500\euro par mois. + \item Bob touche 1000\euro par mois plus une prime de 4\euro par jouet qu'il a fabriqué. + \item Rachelle a un salaire fixe de 500\euro par mois, elle touche 1\euro par jouet fabriqué et elle a une super prime égale à 2 centimes fois le carré du nombre de jouets fabriqués. + \end{itemize} + Qui est le mieux payé? +\end{exercise} + +\begin{solution} + <++> +\end{solution} diff --git a/1ST/02_Generalites_sur_les_fonctions/fig/salaire_tableur.png b/1ST/02_Generalites_sur_les_fonctions/fig/salaire_tableur.png new file mode 100644 index 0000000000000000000000000000000000000000..b69ef54fbe997a1540564c141d45c90abc52602e GIT binary patch literal 30797 zcmc$`2RPS#-#0ETQ4&!`q@p63krGm&6fJvYuk5`kqsU4&Aqg23vPVny&L)+SO~@Yq z*H7p5T<3K^*Z;n+=Qy6@cpUd}U)9Oa_xl;|&uhIu53fs0>>{NjB_bl)by@P_O(LQ# 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a/1ST/02_Generalites_sur_les_fonctions/index.rst b/1ST/02_Generalites_sur_les_fonctions/index.rst new file mode 100644 index 0000000..34112cd --- /dev/null +++ b/1ST/02_Generalites_sur_les_fonctions/index.rst @@ -0,0 +1,64 @@ +Généralités sur les fonctions +############################# + +:date: 2022-08-23 +:modified: 2022-08-23 +:authors: Benjamin Bertrand +:tags: Analyse, Fonctions +:category: 1ST +:summary: Etude graphiques des fonctions. + +Programme +========= + +Dans ce chapitre, on se concentre sur la manipulation de la représentation graphique des fonctions. + +Contenus +--------- + +Les fonctions comme modèles mathématiques d’évolutions continues: + +- différents modes de représentation d’une fonction: expression littérale, représentation graphique ; +- notations y = ƒ(x) et x ↦ ƒ(x); +- Tableau de signes et de variation + +Capacités attendues + +- Modéliser la dépendance entre deux grandeurs à l’aide d’une fonction. +- Résoudre graphiquement une équation du type ƒ(x) = k ou une inéquation de la forme f(x)k. + +Progression +=========== + +Étape 1: Questions de salaire +----------------------------- + +Seul puis en groupe les élèves planchent sur le problème des salaires. La question est mal posée. On ne peut pas y répondre avant de définir ce qui signifie "mieux payé". C'est la première question que l'on va traiter en plénière, la nouvelle question remplacera celle là. + +A nouveau un travail individuel pour que tout le monde commence à écrire quelque chose sur l'activité. Seulement à ce moment là, on autorisera le travail de groupe. Régulièrement, on arrêtera la séance pour donner la parole aux groupes qui ont des idées ou des difficultés. + +Quand la notion de fonction émerge, on s'appliquera à s'assurer que tout le monde sache calculer des images à partir d'une formule. On prendra le soin de valoriser ceux qui savent utiliser leur calculatrice et à leur donner la parole pour qu'ils viennent expliquer leur technique. + +Ce travail sera conclu par une séance informatique où les élèves traceront les graphiques représentant et apporteront une réponse graphique à la question. + +Bilans: + +- Fonction comme transformation entre deux grandeurs, images et antécédents + +.. image:: ./1B_fonction.pdf + :height: 200px + :alt: Bilan sur la définition des fonctions + +- Différents modes de représentation d'une fonction (formule, tableaux de valeur, graphique, tableau de signes et tableau de variations) + +.. image:: ./1B_representations.pdf + :height: 200px + :alt: Bilan sur les représentations de fonctions + +- Utilisation du tableur pour calculer des valeurs + +.. image:: ./1B_tableur.pdf + :height: 200px + :alt: Bilan sur l'utilisation du tableur + +- Résolution graphique d'équations et inéquations diff --git 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+\DeclareExerciseCollection{banque} +\xsimsetup{ +} + + +\begin{document} +\maketitle + +% Résumé + +\bigskip + +Savoir-faire de la séquence +\begin{itemize} + \item +\end{itemize} + +\bigskip + +Ordre des étapes à respecter + + +\section{} + +\listsectionexercises + + +\pagebreak + +\input{exercises.tex} +\printcollection{banque} + + +\end{document} diff --git a/1ST/02_Generalites_sur_les_fonctions/salaires.ods b/1ST/02_Generalites_sur_les_fonctions/salaires.ods new file mode 100644 index 0000000000000000000000000000000000000000..3ec2539fa6650d18b5e5fed7512bf0ae68879918 GIT binary patch literal 30376 zcmagF1yozj*Dj80fwpLoQlrHw#R`<-6!##(p=fXjZbge*p-6ElBqV5%;83JEg#;^B zoM0{P|MdNR-@Wg;-~F$fwN7&8>@zc&J!kfQ_A~ovs^AmQ;NXzp;P5!p10oznV|a0J zaQ+_HOE^yUPS&2juGSW=u8#Ir7M}Jl&U{|Z?|EG;JnTJqU0ki5-@90WovfWbc|Ba+ ztu5Yr*jZb9YW~wE2?@zRZDO1GUmqsynTDlzJE zu#LL+$1hUZ)AVIPL6Xz9{l3xE zTtl^gppS=(Pxm@%`Gpvg{jDX{gVFe_nZdSSO$!;L6Q|S2?5Hi0*_dNJQGq&G>WiuH 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