From c344a569eb9ddc2a179266992ddc412ffbc7cb78 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 22 Sep 2022 10:32:00 +0200 Subject: [PATCH] =?UTF-8?q?Feat:=20fin=20de=20la=20s=C3=A9quence=20sur=20l?= =?UTF-8?q?e=20taux=20d'=C3=A9volution?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 2nd/04_evolution/1B_evolution.pdf | Bin 0 -> 27978 bytes 2nd/04_evolution/1B_evolution.tex | 92 ++++++++++++++++++++++++++++++ 2nd/04_evolution/2B_evolution.pdf | Bin 0 -> 25470 bytes 2nd/04_evolution/2B_evolution.tex | 79 +++++++++++++++++++++++++ 2nd/04_evolution/index.rst | 42 +++++++++++++- 5 files changed, 210 insertions(+), 3 deletions(-) create mode 100644 2nd/04_evolution/1B_evolution.pdf create mode 100644 2nd/04_evolution/1B_evolution.tex create mode 100644 2nd/04_evolution/2B_evolution.pdf create mode 100644 2nd/04_evolution/2B_evolution.tex diff --git a/2nd/04_evolution/1B_evolution.pdf b/2nd/04_evolution/1B_evolution.pdf new file mode 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zy{_L&U#!s~W*Va$fxhiM3y#_3hR}Xo7(iXxH^9uJ)cTyR-3bqjGMMG6^r!npeFkiM-2DBzc?pn YLq}(K@F^1!z{SA|woaoGSCl~fKY2UW&j0`b literal 0 HcmV?d00001 diff --git a/2nd/04_evolution/1B_evolution.tex b/2nd/04_evolution/1B_evolution.tex new file mode 100644 index 0000000..82eea48 --- /dev/null +++ b/2nd/04_evolution/1B_evolution.tex @@ -0,0 +1,92 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Évolution - Cours} +\date{Septembre 2022} + +\pagestyle{empty} + +\begin{document} + +\maketitle + +\section{Evolutions} + +Quand une quantité change, on peut décrire son évolution de deux manières + +\begin{definition}[Evolutions] + Soit une grandeur qui passe de $v_i$(valeur initiale) à $v_f$(valeur finale). + + \begin{multicols}{2} + Évolution absolue + \begin{center} + \begin{tikzpicture}[ + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + ] + %Nodes + \node[roundnode] (leftterme) at (0, 0) {\makebox[0.5cm]{$v_i$}}; + \node[roundnode] (rightterm) at (4, 0) {\makebox[0.5cm]{$v_f$}}; + + %Lines + \path[->] (leftterme) edge [bend left] node [above] {"+a"} (rightterm); + \end{tikzpicture} + \end{center} + + On ajoute la quantité $a$. + + \columnbreak + + Évolution relative + \begin{center} + \begin{tikzpicture}[ + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + ] + %Nodes + \node[roundnode] (leftterme) at (0, 0) {\makebox[0.5cm]{$v_i$}}; + \node[roundnode] (rightterm) at (4, 0) {\makebox[0.5cm]{$v_f$}}; + + %Lines + \path[->] (leftterme) edge [bend left] node [above] {"+t\%"} node [below] {$\times (1 + t\%)$} (rightterm); + \end{tikzpicture} + \end{center} + + On ajoute t\% ce qui revient à multiplier par $(1 + \frac{t}{100})$. + + On appelle t\% le \textbf{taux d'évolution} + \end{multicols} + ~\\ +\end{definition} + +\paragraph{Exemples:}~ +\begin{itemize} + \item Une usine produit 3millions de tonnes de produit par an en 2020. En 2021, cette quantité a augmenté de 5\%. Elle est donc de + \afaire{\vspace{1.5cm}} + \item Un vélo coûte 250\euro. Des soldes font baisser son prix de 20\%. On peut donc l'acheter + \afaire{\vspace{1.5cm}} +\end{itemize} + + +\begin{definition}[Coéfficient multiplicateur] + Une quantité vaut initialement $v_i$ et est transformée avec un taux d'évolution $t$. + \begin{center} + \begin{tikzpicture}[ + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + ] + %Nodes + \node[roundnode] (leftterme) at (0, 0) {\makebox[0.5cm]{$v_i$}}; + \node[roundnode] (rightterm) at (4, 0) {\makebox[0.5cm]{$v_f$}}; + + %Lines + \path[->] (leftterme) edge [bend left] node [above] {"+t"} node [below] {$\times (1 + t)$} (rightterm); + \end{tikzpicture} + \end{center} + + Alors cette quantité est multipliée par + \[ + CM = (1 + t) + \] + On appelle la quantité $CM$ le \textbf{coefficient multiplicateur.} +\end{definition} + +\end{document} diff --git a/2nd/04_evolution/2B_evolution.pdf b/2nd/04_evolution/2B_evolution.pdf new file mode 100644 index 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calcule par + \[ + a = v_f - v_i + \] + + \columnbreak + + Évolution relative + \begin{center} + \begin{tikzpicture}[ + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + ] + %Nodes + \node[roundnode] (leftterme) at (0, 0) {\makebox[0.5cm]{$v_i$}}; + \node[roundnode] (rightterm) at (4, 0) {\makebox[0.5cm]{$v_f$}}; + + %Lines + \path[->] (leftterme) edge [bend left] node [above] {"+t\%"} (rightterm); + \end{tikzpicture} + \end{center} + + La variation relative ou le taux d'évoluiton se calcule par + \[ + t = \frac{v_f - v_i}{v_i} + \] + + Le coefficient multiplicateur se calcule par + \[ + CM = \frac{v_f}{v_i} + \] + \end{multicols} + ~\\ +\end{propriete} + +\paragraph{Exemples:}~ +Le prix d'une robe est passé de 80\euro à 70\euro. +\begin{itemize} + \item Variation absolue: + \item Taux d'évolution: + \item coefficient multiplicateur +\end{itemize} +\afaire{} + + +\end{document} diff --git a/2nd/04_evolution/index.rst b/2nd/04_evolution/index.rst index cb84e07..4ab23c1 100644 --- a/2nd/04_evolution/index.rst +++ b/2nd/04_evolution/index.rst @@ -2,11 +2,47 @@ evolution ######### :date: 2022-09-19 -:modified: 2022-09-19 +:modified: 2022-09-22 :authors: Benjamin Bertrand :tags: Information chiffrée :category: 2nd :summary: Découverte et manipulation des taux d'évolutions. -Étape 1: -======== +Progression +=========== + +Plan de travail + +.. image:: ./plan_de_travail.pdf + :height: 200px + :alt: Plan de travail + +Les solutions aux exercices techniques + +.. image:: ./solutions.pdf + :height: 200px + :alt: solution + +Étape 1: Calculer une valeur à partir d'une évolution +----------------------------------------------------- + +Bilan: + +.. image:: ./1B_evolution.pdf + :height: 200px + :alt: 1B sur les évolutions + + +Étape 2: Calculer une évolution +------------------------------- + +Bilan: + +.. image:: ./2B_evolution.pdf + :height: 200px + :alt: 2B sur les évolutions + +Étape 3: Tout mélangé +--------------------- + +On mélange des exercices sur les évolutions et les proportions