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RGP5u=HQ`cKb@g}S0ssupbdCT3 literal 0 HcmV?d00001 diff --git a/TST/06_Prolongement_geometrique_vers_exponentiel/2B_representation_graphique.tex b/TST/06_Prolongement_geometrique_vers_exponentiel/2B_representation_graphique.tex new file mode 100644 index 0000000..79eca8b --- /dev/null +++ b/TST/06_Prolongement_geometrique_vers_exponentiel/2B_representation_graphique.tex @@ -0,0 +1,62 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Prolongement géométrique vers exponentiel - Cours} +\date{décembre 2020} +\tribe{TST} + +\pagestyle{empty} + +\begin{document} + +\maketitle + +\setcounter{section}{1} +\section{Fonctions puissances / exponentielles} + +\paragraph{Remarques}: +\\ +\begin{minipage}{0.4\linewidth} + \begin{itemize} + \item $f(x) = 3^x$ + \item $g(x) = 1,5^x$ + \item $h(x) = 0.1^x$ + \item $i(x) = 2^x$ + \item $j(x) = 0.8^x$ + \end{itemize} +\end{minipage} +\begin{minipage}{0.6\linewidth} + \begin{tikzpicture}[yscale=0.8, xscale=1.5] + \tkzInit[xmin=-3,xmax=3,xstep=1, + ymin=0,ymax=5,ystep=1] + \tkzGrid + \tkzAxeXY[up space=0.5,right space=.5] + \tkzFct[domain = -5:2, line width=1pt]{3**x} + \tkzFct[domain = -5:5,color=blue,very thick]{1.5**x} + \tkzFct[domain = -5:5,color=red,very thick]{0.1**x} + \tkzFct[domain = -5:5,color=green,very thick]{2**x} + \tkzFct[domain = -5:5,color=gray,very thick]{0.8**x} + \end{tikzpicture} +\end{minipage} +\afaire{Identifier les fonctions et les représentations graphiques} + +\begin{propriete} + Soit $a$ un nombre réel strictement positif et $f(x) = a^x$ la fonction puissance de base $a$, alors + \[ + f(0) = a^0 = 1 \qquad \qquad f(1) = a^1 = a + \] +\end{propriete} + +\begin{propriete} + Soit $a$ un nombre réel strictement positif et $f(x) = a^x$ la fonction puissance de base $a$, alors + \begin{itemize} + \item Si $a > 1$ alors la fonction $f$ est croissante + \item Si $0 < a < 1$ alors la fonction $f$ est décroissante + \end{itemize} +\end{propriete} + + + + 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/dev/null +++ b/TST/06_Prolongement_geometrique_vers_exponentiel/2E_graphique.tex @@ -0,0 +1,42 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Prolongement géométrique vers exponentiel - Exercices} +\date{octobre 2020} + +\DeclareExerciseCollection{banque} +\xsimsetup{ + step=2, +} + +\begin{document} +\input{exercises.tex} + +Les deux exercices ci-dessous ont pour but de vous faire répondre aux questions suivantes: + +\begin{enumerate} + \item Quels sont les points communs que l'on retrouve parmi les fonctions puissances? + \item Peut-on faire une lien en le nombre qui est à la puissances et le graphique de la fonction? + \item Que se passe-t-il quand on multiplie une fonction puissance avec un nombre? +\end{enumerate} + +Vous pouvez réaliser les exercices dans l'ordre que vous souhaitez, allez de l'un à l'autre mais chaque fois que vous avancez regardez si vous ne pouvez pas apporter des réponses aux questions. + +\printcollection{banque} + +\vfill + +Les deux exercices ci-dessous ont pour but de vous faire répondre aux questions suivantes: + +\begin{enumerate} + \item Quels sont les points communs que l'on retrouve parmi les fonctions puissances? + \item Peut-on faire une lien en le nombre qui est à la puissances et le graphique de la fonction? + \item Que se passe-t-il quand on multiplie une fonction puissance avec un nombre? +\end{enumerate} + +Vous pouvez réaliser les exercices dans l'ordre que vous souhaitez, allez de l'un à l'autre mais chaque fois que vous avancez regardez si vous ne pouvez pas apporter des réponses aux questions. + +\printcollection{banque} + +\end{document} diff --git a/TST/06_Prolongement_geometrique_vers_exponentiel/exercises.tex b/TST/06_Prolongement_geometrique_vers_exponentiel/exercises.tex index fc0c52f..72191bf 100644 --- a/TST/06_Prolongement_geometrique_vers_exponentiel/exercises.tex +++ b/TST/06_Prolongement_geometrique_vers_exponentiel/exercises.tex @@ -25,4 +25,52 @@ \end{enumerate} \end{exercise} +\begin{exercise}[subtitle={Représentation graphique des fonctions puissances}, step={2}, origin={Création}, topics={Prolongement géométrique vers exponentiel}, tags={exponentiel, suite, programmation}] + \begin{enumerate} + \item Pour les 8 fonctions suivantes, calculer les images de -1, 0, 1, 2 et 0.5 puis tracer l'allure des fonctions sur un même graphique en identifiant clairement chaque fonction (on prendra $x$ en -2 et 2). + \begin{multicols}{3} + \begin{enumerate} + \item $f(x) = 0.3^x$ + \item $g(x) = 0.7^x$ + + \item $h(x) = 2^x$ + \item $i(x) = 4^x$ + + \item $j(x) = -2^x$ + \item $k(x) = -0.7^x$ + + \item $l(x) = 3\times 0.7^x$ + \item $m(x) = -3\times 0.7^x$ + \end{enumerate} + \end{multicols} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Lien entre la fonction et le graphique}, step={2}, origin={Création}, topics={Prolongement géométrique vers exponentiel}, tags={exponentiel, suite, programmation}] + \begin{minipage}{0.4\linewidth} + On a représenter graphiquement ci-contre 5 fonctions puissance. Vous devez relier chaque graphique avec une des fonction ci-dessous.. + + \begin{itemize} + \item $f(x) = 3^x$ + \item $g(x) = 1,5^x$ + \item $h(x) = 0.1^x$ + \item $i(x) = 2^x$ + \item $j(x) = 0.8^x$ + \end{itemize} + \end{minipage} + \begin{minipage}{0.6\linewidth} + \begin{tikzpicture}[yscale=0.8, xscale=1.5] + \tkzInit[xmin=-3,xmax=3,xstep=1, + ymin=0,ymax=5,ystep=1] + \tkzGrid + \tkzAxeXY[up space=0.5,right space=.5] + \tkzFct[domain = -5:2, line width=1pt]{3**x} + \tkzFct[domain = -5:5,color=blue,very thick]{1.5**x} + \tkzFct[domain = -5:5,color=red,very thick]{0.1**x} + \tkzFct[domain = -5:5,color=green,very thick]{2**x} + \tkzFct[domain = -5:5,color=gray,very thick]{0.8**x} + \end{tikzpicture} + \end{minipage} +\end{exercise} + \collectexercisesstop{banque} diff --git a/TST/06_Prolongement_geometrique_vers_exponentiel/index.rst b/TST/06_Prolongement_geometrique_vers_exponentiel/index.rst index c828eb9..a9c74e5 100644 --- a/TST/06_Prolongement_geometrique_vers_exponentiel/index.rst +++ b/TST/06_Prolongement_geometrique_vers_exponentiel/index.rst @@ -13,6 +13,10 @@ Prolongement géométrique vers exponentiel Activité intro: Compléter les trous d'une suite géométrique et revenir en arrière. +.. image:: ./1E_prolongement.pdf + :height: 200px + :alt: Prolongement des suites géométriques + Cours: Définition des fonctions exponentielles et règles de calculs .. image:: ./1B_prologement.pdf @@ -26,7 +30,16 @@ Tracer les courbes de fonctions exponentielle. C'est l'occasion d'utiliser la ca On donne 8 fonctions exponentielles et exponentielles multipliées par un réel. Les élèves en groupe tracent un graphique précisément puis donne l'allure des autres en se partageant le travail. Ils cherchent ensuite à établir une règle pour la croissance. -Cours: représentation graphique en fonctions des paramètres +.. image:: ./2E_graphique.pdf + :height: 200px + :alt: Recherche des liens entre fonctions puissances et représentation graphique. + +Bilan: représentation graphique en fonctions des paramètres + +.. image:: ./2B_representation_graphique.pdf + :height: 200px + :alt: Bilan sur la représentation graphique et les variations des fonctions puissance + Étape 3: Manipulations techniques de l'exponentielle ====================================================