From 86d819c2b4170490243435309ff749facc0d80c3 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Mon, 3 Jan 2022 21:47:42 +0100 Subject: [PATCH] Feat: Fin des exercices sur les tableaux --- .../3E_a_partir_de_tableaux.pdf | Bin 0 -> 59880 bytes .../3E_a_partir_de_tableaux.tex | 26 +++++ .../4E_equation_tableau_signe.pdf | Bin 0 -> 47514 bytes .../4E_equation_tableau_signe.tex | 32 ++++++ 2nd/09_Fonctions_tableaux/exercises.tex | 97 +++++++++++++++++- 2nd/09_Fonctions_tableaux/index.rst | 24 +++-- 6 files changed, 171 insertions(+), 8 deletions(-) create mode 100644 2nd/09_Fonctions_tableaux/3E_a_partir_de_tableaux.pdf create mode 100644 2nd/09_Fonctions_tableaux/3E_a_partir_de_tableaux.tex create mode 100644 2nd/09_Fonctions_tableaux/4E_equation_tableau_signe.pdf create mode 100644 2nd/09_Fonctions_tableaux/4E_equation_tableau_signe.tex diff --git a/2nd/09_Fonctions_tableaux/3E_a_partir_de_tableaux.pdf b/2nd/09_Fonctions_tableaux/3E_a_partir_de_tableaux.pdf new file mode 100644 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@@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} +\usepackage{pgfplots} +\pgfplotsset{compat = newest} +\usepgfplotslibrary{external} +\tikzexternalize + +\author{Benjamin Bertrand} +\title{Fonctions tableaux - Exercices} +\date{2021-12-07} + +\DeclareExerciseCollection[step=3]{banque} +\xsimsetup{ + collect, +} + +\pagestyle{empty} + +\begin{document} + +\input{exercises.tex} +\setcounter{exercise}{2} +\printcollection{banque} +\vfill + +\end{document} diff --git a/2nd/09_Fonctions_tableaux/4E_equation_tableau_signe.pdf b/2nd/09_Fonctions_tableaux/4E_equation_tableau_signe.pdf new file mode 100644 index 0000000000000000000000000000000000000000..391a28f328514680ea5c30ac8d161fab09fca9bc GIT binary patch literal 47514 zcmce-bC4*{vMxGUW81cE+qP}n_N?I=+qP}nwr%^Z-@RwYJ15?axbL66JEA+PGqWoC zi_Ff->iU{QURacdftCf5WOi|A6_OdB9^cN;5|W!6l1|yf-UOdcUCz+b#K;+vPRYg4 z`F}}7?Hp|&=>!Gs-0`*O|JpOq|F2UAlI|bP|LVm6Nhf3A>}c`Vg5j^lU;RJVzZQxn 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new file mode 100644 index 0000000..0b7f457 --- /dev/null +++ b/2nd/09_Fonctions_tableaux/4E_equation_tableau_signe.tex @@ -0,0 +1,32 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} +\usepackage{pgfplots} +\pgfplotsset{compat = newest} +\usepgfplotslibrary{external} +\tikzexternalize + +\author{Benjamin Bertrand} +\title{Fonctions tableaux - Exercices} +\date{2021-12-07} + +\DeclareExerciseCollection[step=4]{banque} +\xsimsetup{ + collect, +} + +\pagestyle{empty} + +\begin{document} + +\input{exercises.tex} +\setcounter{exercise}{6} +\printcollection{banque} +\vfill +\printcollection{banque} +\vfill +\printcollection{banque} +\vfill +\printcollection{banque} +\vfill + +\end{document} diff --git a/2nd/09_Fonctions_tableaux/exercises.tex b/2nd/09_Fonctions_tableaux/exercises.tex index b7f2ec2..c31abd7 100644 --- a/2nd/09_Fonctions_tableaux/exercises.tex +++ b/2nd/09_Fonctions_tableaux/exercises.tex @@ -1,4 +1,4 @@ -\begin{exercise}[subtitle={Tableaux pour décrire les fonctions}, step={2}, origin={Création}, topics={Dérivation}, tags={Tableaux de signes, Tableaux de variations}] +\begin{exercise}[subtitle={Tableaux pour décrire les fonctions}, step={2}, origin={Création}, topics={Fonctions}, tags={Tableaux de signes, Tableaux de variations}] \begin{minipage}{0.5\textwidth} Ci-contre, le graphique d'une fonction. @@ -23,7 +23,7 @@ \end{minipage} \end{exercise} -\begin{exercise}[subtitle={Faire des tableaux}, step={2}, origin={Création}, topics={Dérivation}, tags={Tableaux de signes, Tableaux de variations}] +\begin{exercise}[subtitle={Faire des tableaux}, step={2}, origin={Création}, topics={Fonctions}, tags={Tableaux de signes, Tableaux de variations}] Pour toutes les fonctions ci-dessous, tracer le tableau de signes puis le tableau de variations. \begin{multicols}{2} @@ -58,3 +58,96 @@ \end{enumerate} \end{multicols} \end{exercise} + +\begin{exercise}[subtitle={Tracer un graphique à partir de tableaux}, step={3}, origin={Création}, topics={Fonctions}, tags={Tableaux de signes, Tableaux de variations}] + Tracer des graphiques qui correspondent aux tableaux suivants + + \begin{multicols}{2} + \begin{enumerate} + \item + \begin{tikzpicture}[baseline=(a.north)] + \tkzTabInit[lgt=1,espcl=2]{$ x $/1, $ f(x) $/2}{-3, 1, 0, 5 } + \tkzTabVar{ +/4, -/3, +/0, -/-1} + \end{tikzpicture} + \item + \begin{tikzpicture}[baseline=(a.north)] + \tkzTabInit[lgt=2,espcl=1]{$ t $/1,$ z(t) $/1}{-5, -1, 3, 4, 5} + \tkzTabLine{, +, z, -, z, +, z, - , } + \end{tikzpicture} + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Vrai/Faux}, step={3}, origin={Création}, topics={Fonctions}, tags={Tableaux de signes, Tableaux de variations}] + Ci-dessous, le tableau de signes de la fonction $f$ et le tableau de variations de $g$. + + \begin{minipage}{0.4\linewidth} + \begin{tikzpicture}[baseline=(a.north)] + \tkzTabInit[lgt=2,espcl=1]{$ t $/1,$ f(t) $/1}{-5, -3, 1, 2, 5} + \tkzTabLine{, -, z, +, z, -, z, + , } + \end{tikzpicture} + \end{minipage} + \begin{minipage}{0.5\linewidth} + \begin{tikzpicture}[baseline=(a.north)] + \tkzTabInit[lgt=1,espcl=2]{$ x $/1, $ g(x) $/2}{-5, -1, 0, 3, 5 } + \tkzTabVar{ +/1, -/0, +/4, -/-1, +/2} + \end{tikzpicture} + \end{minipage} + + Pour chacune des proportions suivantes dire si elle est vraie, fausse ou si les informations à disposition de sont suffisantes pour répondre à la question. + \begin{tasks}(2) + \task Entre -3 et 1, la fonction $f$ est positive. + \task Entre 0 et 5, la fonction $g$ est décroissante. + \task Sur l'intervalle $\intFF{-1}{0}$, $g$ est croissante. + \task Sur l'intervalle $\intFF{1}{2}$, $f$ est positive. + + \task Sur l'intervalle $\intFF{1}{2}$, $g$ est croissante. + \task Sur l'intervalle $\intFF{-3}{-1}$, $f$ est croissante. + \task $g(1)$ est plus grand que $g(2)$. + \task $g(1)$ est plus grand que $g(4)$. + + \task Le maximum de la fonction $g$ est 4. + \task Le minimum de la fonction $g$ est 0. + \task Les solutions de l'équation $f(x) = 0$ sont $x \in \left\{ -3; 1 \right\}$ + \task Les solutions de l'équation $f(x) \leq 0$ sont $x \in \intFF{-5}{-3}\cup \intFF{1}{2}$ + \end{tasks} +\end{exercise} + +\begin{exercise}[subtitle={Création}, step={3}, origin={Création}, topics={Fonctions}, tags={Tableaux de signes, Tableaux de variations}] + Cet exercice est un exercice création. Vous devez créer un vrai/faux à la manière de l'exercice précédent. + + Vous devez inventer le tableau de signes d'une fonction $f$ et le tableau de variations d'une fonction $g$. Puis vous inventerez 6 propositions vraies ou fausses. Enfin vous proposerez un correction de votre exercice. +\end{exercise} + +\begin{exercise}[subtitle={Tableaux de signes}, step={4}, origin={Création}, topics={Fonctions}, tags={Tableaux de signes, Tableaux de variations}] + Tracer le tableau de signes des fonctions suivantes sans tracer le graphique. Une fois le tableau de signes terminé, vous vérifierez votre tableau avec la calculatrice. + + \begin{tasks}(3) + \task $f(x) = 2x$ + \task $g(x) = 5x$ + \task $h(x) = x + 2$ + + \task $i(x) = x - 5$ + \task $j(x) = x - 1$ + \task $k(x) = 2x + 4$ + + \task $l(x) = 6x - 12$ + \task $m(x) = -2x + 6$ + \task $n(x) = -5x - 10$ + \end{tasks} +\end{exercise} + + +\begin{exercise}[subtitle={Tableaux de signes et produit}, step={4}, origin={Création}, topics={Fonctions}, tags={Tableaux de signes, Tableaux de variations}] + Tracer le tableau de signes des fonctions suivantes sans tracer le graphique. Une fois le tableau de signes terminé, vous vérifierez votre tableau avec la calculatrice. + + \begin{tasks}(3) + \task $f(x) = (x + 1)(x - 1)$ + \task $g(x) = (x - 2)(x - 5)$ + \task $h(x) = 2x (x - 1)$ + + \task $i(x) = (2x + 6)(3x - 12)$ + \task $j(x) = (x - 1)(-5x + 10)$ + \task $j(x) = (x + 1)(-x + 2)$ + \end{tasks} +\end{exercise} diff --git a/2nd/09_Fonctions_tableaux/index.rst b/2nd/09_Fonctions_tableaux/index.rst index 4845ac1..82f762a 100644 --- a/2nd/09_Fonctions_tableaux/index.rst +++ b/2nd/09_Fonctions_tableaux/index.rst @@ -24,29 +24,41 @@ Pendant ce temps, l'observateur note les éléments de descriptions qui lui ont On espère que sorte la notion de signe d'une fonction et de variations. Ce qui nous permettra d'introduire la notion de tableau de signes et de variations. + +Étape 2: Tracer des tableaux +============================ + Bilan: Des exemples de tableaux de signe et de variations .. image:: ./1B_tableaux.pdf :height: 200px :alt: - -Étape 2: Tracer des tableaux -============================ +Après avoir compléter en cours magistral les tableaux, les élèves essayent de refaire le même travail en groupe sur l'exercice 1 de la fiche ci-dessous. Cet exercice sera ensuite rédigé dans le cahier de groupe en expliquant l'intérêt des questions 3 et 4. .. image:: ./2E_tracer_tableau.pdf :height: 200px :alt: - -A partir de graphique et de fonctions (à tracer avec la calculatrice) les élèves doivent tracer les tableaux. +Bilan: des réponses et des erreurs intéressantes. Étape 3: Raisonner sur des tableaux =================================== -On donne des tableaux les élèves doivent dans un premier temps tracer des graphiques qui peuvent correspondre. On pourra ajouter un exercice d'analyse d'un tableau pour trouver des extremums. +On donne des tableaux les élèves doivent dans un premier temps tracer des graphiques qui peuvent correspondre. Ils enchainent ensuite sur un vrai/faux puis terminent avec un exercice de création d'exercice type vrai/faux. + +.. image:: ./3E_a_partir_de_tableaux.pdf + :height: 200px + :alt: analyser un tableau Étape 4: tableau de signe et inéquations ======================================== +Exercices techniques pour tracer un tableau de signe grace à la résolution d'équations. + +.. image:: ./4E_equation_tableau_signe.pdf + :height: 200px + :alt: résolution d'inéquations + +