From ed5f1ec501a1852a52b919ef8d6068aaaa812b29 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 25 Aug 2020 14:56:59 +0200 Subject: [PATCH] =?UTF-8?q?Feat:=20Exercices=20sur=20les=20=C3=A9tapes=20p?= =?UTF-8?q?our=20l'=C3=A9tude=20de=20variations=20d'une=20fonction?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- TST/01_Derivation/2E_tableaux.pdf | Bin 69734 -> 69734 bytes .../{2B_formules.pdf => 3B_fomules.pdf} | Bin .../{2B_formules.tex => 3B_fomules.tex} | 0 TST/01_Derivation/3E_etapes_decomposees.pdf | Bin 0 -> 66965 bytes TST/01_Derivation/3E_etapes_decomposees.tex | 18 ++++++ TST/01_Derivation/exercises.tex | 52 ++++++++++++++++++ TST/01_Derivation/index.rst | 12 ++-- 7 files changed, 75 insertions(+), 7 deletions(-) rename TST/01_Derivation/{2B_formules.pdf => 3B_fomules.pdf} (100%) rename TST/01_Derivation/{2B_formules.tex => 3B_fomules.tex} (100%) create mode 100644 TST/01_Derivation/3E_etapes_decomposees.pdf create mode 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z&2y4U-j0d&Ccw9;w4ZhBG3J+z3ryl-5hBFkv3_4a7$hrvE=lxBsp? zG?Yxupy?&;OibMgv>6B(8Q689>6I-#P5-kCO|MR%%}BsZ!1zLLxho0Sd5*WiGxFoRfLm;gI$Dl`z|tAQl@zR96Df&ROuw_z?J$U>txT z`#}MOX919pLa;A}zaU1SAx3~AMvx;%uw{CHW_l3Q?X@mTigZt^O!IeM zn@xwuQ?pS=?_;x-XU9{snWx`7V011z}%w7Ei%a~s2__b82L8NUP%1^j=1 c7lZ!)0E6ZOApigX literal 0 HcmV?d00001 diff --git a/TST/01_Derivation/3E_etapes_decomposees.tex b/TST/01_Derivation/3E_etapes_decomposees.tex new file mode 100644 index 0000000..e77dad5 --- /dev/null +++ b/TST/01_Derivation/3E_etapes_decomposees.tex @@ -0,0 +1,18 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Dérivation - Cours} +\date{août 2020} + +\DeclareExerciseCollection{banque} +\xsimsetup{ + step=3, +} + +\begin{document} + +\input{exercises.tex} +\printcollection{banque} + +\end{document} diff --git a/TST/01_Derivation/exercises.tex b/TST/01_Derivation/exercises.tex index c54acc6..c147d18 100644 --- a/TST/01_Derivation/exercises.tex +++ b/TST/01_Derivation/exercises.tex @@ -94,4 +94,56 @@ \end{tikzpicture} \end{enumerate} \end{exercise} + +\begin{exercise}[subtitle={$f$ -> $f'$}, step={3}, origin={Création}, topics={Dérivation}, tags={Technique}] + Dériver les fonctions suivantes + \begin{multicols}{3} + \begin{enumerate} + \item $f(x) = x^3 + x$ + \item $g(x) = 4x^3 - 2x + 4$ + \item $h(x) = 10x + 4 - 2x^2$ + + \item $i(x) = -0.3x^3 - 2x + 2$ + \item $j(x) = -5x^3 - 2x + x + 3$ + \item $k(x) = \dfrac{5}{6}x^3 - 2x + \dfrac{1}{2}$ + + \item $i(x) = \dfrac{1}{4}x^2 - \dfrac{4}{9}x^3 + 10$ + \item $j(x) = (0.2x + 2)(0.1x - 10)$ + \item $k(x) = (2x + 1)(x-3)$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={$f'$ -> tableau de signe}, step={3}, origin={Création}, topics={Dérivation}, tags={Technique}] + \begin{enumerate} + \item Résoudre les inéquations suivantes et faire une phrase pour décrire les solutions. + \begin{multicols}{3} + \begin{enumerate} + \item $2x + 4 > 0$ + \item $5x + 15 < 0$ + + \item $-2x + 3 > 0$ + \item $-x - 4 < 0$ + + \item $\dfrac{2}{3}x + 5 \geq 0$ + \item $6x + 15 \leq 5x$ + \end{enumerate} + \end{multicols} + + \item Tracer les tableaux de signes des fonctions suivantes + \begin{multicols}{3} + \begin{enumerate} + \item $f(x) = 2x + 4 $ + \item $g(x) = 5x + 15$ + + \item $h(x) = 3x - 12$ + \item $i(x) = -15x + 10$ + + \item $j(x) = \frac{2}{3}x - 1$ + \item $k(x) = 2 - \frac{6}{5}x$ + \end{enumerate} + \end{multicols} + \end{enumerate} +\end{exercise} + \collectexercisesstop{banque} diff --git a/TST/01_Derivation/index.rst b/TST/01_Derivation/index.rst index 7978425..a4010af 100644 --- a/TST/01_Derivation/index.rst +++ b/TST/01_Derivation/index.rst @@ -40,27 +40,25 @@ Tracer tableaux à partir de graphiques et de formule pure (utilisation de la ca :height: 200px :alt: Tracer des tableaux de signes et de variations à partir de graphiques et inversement. -Étape 3: Technique dérivation -============================= +Étape 3: Étapes décomposées +=========================== Cours: Formules de dérivations -.. image:: 2B_formules.pdf +.. image:: 3B_formules.pdf :height: 200px :alt: Formules de dérivations Les élèves arrivent en classe en ayant auparavant écrit le cours sur les formules de dérivation. -Cette étape est alors assez technique. Il faudra réussir à la dynamiser pour que les élèves ne s'essoufflent pas! +Cette étape va reprendre les étapes de la recherche de variations de façon séparée. Elle est alors assez technique. Il faudra réussir à la dynamiser pour que les élèves ne s'essoufflent pas! -Étape 4: Liens signes dérivé et variations fonctions -==================================================== Plusieurs fonctions à regrouper en famille de dérivation puis tracer les tableaux pour retrouver les liens. Durcissement, forme facto à dev -Étape 5: Dérivation et étude de signes +Étape 4: Dérivation et étude de signes ====================================== Exercices et problèmes