Feat: fin de la séquence sur le taux d'évolution
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2nd/04_evolution/1B_evolution.pdf
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2nd/04_evolution/1B_evolution.pdf
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2nd/04_evolution/1B_evolution.tex
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2nd/04_evolution/1B_evolution.tex
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\author{Benjamin Bertrand}
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\title{Évolution - Cours}
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\date{Septembre 2022}
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\pagestyle{empty}
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\begin{document}
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\maketitle
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\section{Evolutions}
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Quand une quantité change, on peut décrire son évolution de deux manières
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\begin{definition}[Evolutions]
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Soit une grandeur qui passe de $v_i$(valeur initiale) à $v_f$(valeur finale).
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\begin{multicols}{2}
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Évolution absolue
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\begin{center}
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\begin{tikzpicture}[
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roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
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]
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%Nodes
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\node[roundnode] (leftterme) at (0, 0) {\makebox[0.5cm]{$v_i$}};
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\node[roundnode] (rightterm) at (4, 0) {\makebox[0.5cm]{$v_f$}};
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%Lines
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\path[->] (leftterme) edge [bend left] node [above] {"+a"} (rightterm);
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\end{tikzpicture}
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\end{center}
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On ajoute la quantité $a$.
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\columnbreak
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Évolution relative
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\begin{center}
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\begin{tikzpicture}[
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roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
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]
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%Nodes
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\node[roundnode] (leftterme) at (0, 0) {\makebox[0.5cm]{$v_i$}};
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\node[roundnode] (rightterm) at (4, 0) {\makebox[0.5cm]{$v_f$}};
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%Lines
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\path[->] (leftterme) edge [bend left] node [above] {"+t\%"} node [below] {$\times (1 + t\%)$} (rightterm);
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\end{tikzpicture}
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\end{center}
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On ajoute t\% ce qui revient à multiplier par $(1 + \frac{t}{100})$.
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On appelle t\% le \textbf{taux d'évolution}
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\end{multicols}
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~\\
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\end{definition}
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\paragraph{Exemples:}~
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\begin{itemize}
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\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
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\afaire{\vspace{1.5cm}}
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\item Un vélo coûte 250\euro. Des soldes font baisser son prix de 20\%. On peut donc l'acheter
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\afaire{\vspace{1.5cm}}
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\end{itemize}
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\begin{definition}[Coéfficient multiplicateur]
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Une quantité vaut initialement $v_i$ et est transformée avec un taux d'évolution $t$.
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\begin{center}
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\begin{tikzpicture}[
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roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
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]
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%Nodes
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\node[roundnode] (leftterme) at (0, 0) {\makebox[0.5cm]{$v_i$}};
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\node[roundnode] (rightterm) at (4, 0) {\makebox[0.5cm]{$v_f$}};
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%Lines
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\path[->] (leftterme) edge [bend left] node [above] {"+t"} node [below] {$\times (1 + t)$} (rightterm);
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\end{tikzpicture}
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\end{center}
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Alors cette quantité est multipliée par
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\[
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CM = (1 + t)
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\]
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On appelle la quantité $CM$ le \textbf{coefficient multiplicateur.}
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\end{definition}
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\end{document}
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2nd/04_evolution/2B_evolution.pdf
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2nd/04_evolution/2B_evolution.pdf
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2nd/04_evolution/2B_evolution.tex
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2nd/04_evolution/2B_evolution.tex
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\author{Benjamin Bertrand}
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\title{Évolution - Cours}
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\date{Septembre 2022}
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\pagestyle{empty}
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\begin{document}
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\maketitle
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\setcounter{section}{1}
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\section{Calculer une évolution}
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\begin{propriete}[Evolutions]
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Soit une grandeur qui passe de $v_i$(valeur initiale) à $v_f$(valeur finale).
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\begin{multicols}{2}
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Évolution absolue
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\begin{center}
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\begin{tikzpicture}[
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roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
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]
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%Nodes
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\node[roundnode] (leftterme) at (0, 0) {\makebox[0.5cm]{$v_i$}};
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\node[roundnode] (rightterm) at (4, 0) {\makebox[0.5cm]{$v_f$}};
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%Lines
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\path[->] (leftterme) edge [bend left] node [above] {"+a"} (rightterm);
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\end{tikzpicture}
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\end{center}
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La variation absolue se calcule par
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\[
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a = v_f - v_i
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\]
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\columnbreak
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Évolution relative
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\begin{center}
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\begin{tikzpicture}[
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roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
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]
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%Nodes
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\node[roundnode] (leftterme) at (0, 0) {\makebox[0.5cm]{$v_i$}};
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\node[roundnode] (rightterm) at (4, 0) {\makebox[0.5cm]{$v_f$}};
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%Lines
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\path[->] (leftterme) edge [bend left] node [above] {"+t\%"} (rightterm);
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\end{tikzpicture}
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\end{center}
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La variation relative ou le taux d'évoluiton se calcule par
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\[
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t = \frac{v_f - v_i}{v_i}
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\]
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Le coefficient multiplicateur se calcule par
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\[
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CM = \frac{v_f}{v_i}
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\]
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\end{multicols}
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~\\
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\end{propriete}
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\paragraph{Exemples:}~
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Le prix d'une robe est passé de 80\euro à 70\euro.
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\begin{itemize}
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\item Variation absolue:
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\item Taux d'évolution:
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\item coefficient multiplicateur
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\end{itemize}
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\afaire{}
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\end{document}
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@ -2,11 +2,47 @@ evolution
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#########
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:date: 2022-09-19
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:modified: 2022-09-19
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:modified: 2022-09-22
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:authors: Benjamin Bertrand
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:tags: Information chiffrée
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:category: 2nd
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:summary: Découverte et manipulation des taux d'évolutions.
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Étape 1:
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========
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Progression
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===========
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Plan de travail
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.. image:: ./plan_de_travail.pdf
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:height: 200px
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:alt: Plan de travail
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Les solutions aux exercices techniques
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.. image:: ./solutions.pdf
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:height: 200px
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:alt: solution
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Étape 1: Calculer une valeur à partir d'une évolution
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-----------------------------------------------------
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Bilan:
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.. image:: ./1B_evolution.pdf
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:height: 200px
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:alt: 1B sur les évolutions
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Étape 2: Calculer une évolution
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-------------------------------
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Bilan:
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.. image:: ./2B_evolution.pdf
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:height: 200px
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:alt: 2B sur les évolutions
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Étape 3: Tout mélangé
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---------------------
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On mélange des exercices sur les évolutions et les proportions
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