From f4b89a913357141b7eae0f7ed3b36fac6783c259 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 24 Feb 2022 12:04:33 +0100 Subject: [PATCH] =?UTF-8?q?Feat:=20bilan=20sur=20coef=20mult=20et=20=C3=A9?= =?UTF-8?q?vo=20succ?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 2nd/14_Information_Chiffrée_2/exercises.tex | 145 +++++++++++++++++- .../plan_de_travail.pdf | Bin 1902276 -> 1902292 bytes 2nd/14_Information_Chiffrée_2/solutions.pdf | Bin 22307 -> 35120 bytes 3 files changed, 143 insertions(+), 2 deletions(-) diff --git a/2nd/14_Information_Chiffrée_2/exercises.tex b/2nd/14_Information_Chiffrée_2/exercises.tex index ffb4f19..debefe7 100644 --- a/2nd/14_Information_Chiffrée_2/exercises.tex +++ b/2nd/14_Information_Chiffrée_2/exercises.tex @@ -57,7 +57,83 @@ \end{exercise} \begin{solution} - + \section*{Lien entre taux d'évolution et coefficient multiplicateur} + + \begin{propriete} + Soit $t$ le taux d'évolution qui fait évolution $v_i$ vers $v_f$ alors + \[ + v_f = (1+t)v_i + \] + \end{propriete} + \begin{definition} + $1+t$ est appelé \textbf{coefficient multiplicateur}, noté $CM$, associé au taux d'évolution $t$. + + \noindent + On a ainsi + \[ + CM = 1+t \qquad \mbox{ou encore} \qquad t = CM - 1 + \] + et + \[ + v_f = CM \times v_i \qquad \mbox{ ou encore } \qquad CM = \frac{v_f}{v_i} + \] + \end{definition} + \paragraph{Exemples} + \begin{itemize} + \item + \begin{tikzpicture}[ + baseline, + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + ] + %Nodes + \node[roundnode] (leftterme) {\makebox[0.5cm]{120}}; + \node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{...}}; + + %Lines + \path[->] (leftterme.north) edge [bend left] + node [pos=0.5, above] {+25\%} + node [pos=0.5, below] {\times CM = ...} + (centerterm.north) + ; + \end{tikzpicture} + Coefficient multiplicateur: \hfill Valeur finale: \hfill. + \item + \begin{tikzpicture}[ + baseline, + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + ] + %Nodes + \node[roundnode] (leftterme) {\makebox[0.5cm]{55}}; + \node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{...}}; + + %Lines + \path[->] (leftterme.north) edge [bend left] + node [pos=0.5, above] {+...} + node [pos=0.5, below] {\times 0.12} + (centerterm.north) + ; + \end{tikzpicture} + Taux d'évolution: \hfill Valeur finale: \hfill. + \item + \begin{tikzpicture}[ + baseline, + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + ] + %Nodes + \node[roundnode] (leftterme) {\makebox[0.5cm]{34}}; + \node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{123}}; + + %Lines + \path[->] (leftterme.north) edge [bend left] + node [pos=0.5, above] {+...\%} + node [pos=0.5, below] {\times ...} + (centerterm.north) + ; + \end{tikzpicture} + Taux d'évolution: \hfill Valeur finale: \hfill. + \end{itemize} + + \afaire{Compléter les calculs} \end{solution} \begin{exercise}[subtitle={Questions divers}, step={2}, origin={Création}, topics={ Information Chiffrée 2 }, tags={ Information chiffrée }, mode={\faIcon{tools}}] @@ -108,7 +184,7 @@ \end{exercise} \begin{exercise}[subtitle={Évolutions successives - bilan}, step={3}, origin={Création}, topics={ Information Chiffrée 2 }, tags={ Information chiffrée }, mode={\faIcon{users}}] - Expliquer votre/vos méthode(s) pour calculer la taux d'évolution d'une transformation composé de plusieurs évolution. Vous illustrerez votre méthode en calculant le taux d'évolution global composé de + Expliquer votre/vos méthode(s) pour calculer la taux d'évolution d'une transformation composé de plusieurs évolution. Vous illustrerez votre méthode en calculant le taux d'évolution global des trois situations suivantes: \begin{enumerate} \item 5 augmentation de 4\%. \item 100 diminution de 5\%. @@ -118,6 +194,71 @@ \begin{solution} \section*{Taux d'évolution successifs} + + \begin{propriete} + Quand une quantité subit des \textbf{évolution successives} $t_1, t_2, ...$, elle subit alors une \texbf{évolution globale}. + + Les taux d'évolution \textbf{ne peuvent pas} s'ajouter. + + \bigskip + + Il faut multiplier les \textbf{coefficient multiplicateur} entre eux. + + \begin{center} + \begin{tikzpicture}[ + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + node distance=2cm and 2cm + ] + %Nodes + \node[roundnode] (termA) {\makebox[0.5cm]{}}; + \node[roundnode] (termB) [right=of termA] {\makebox[0.5cm]{}}; + \node[roundnode] (termC) [right=of termB] {\makebox[0.5cm]{}}; + \node[roundnode] (termD) [right=of termC] {\makebox[0.5cm]{}}; + \node (termE) [right=of termD] {\makebox[0.5cm]{...}}; + \node[roundnode] (termF) [right=of termE] {\makebox[0.5cm]{}}; + + %Lines + \path[->] (termA.north) edge [bend left=50] node [above] {$+t_1$} node [below] {$\times CM_1$} (termB.north) ; + \path[->] (termB.north) edge [bend left=50] node [above] {$+t_2$} node [below] {$\times CM_2$} (termC.north) ; + \path[->] (termC.north) edge [bend left=50] node [above] {$+t_3$} node [below] {$\times CM_3$} (termD.north) ; + + \path[->] (termA.south) edge [bend right=10] node [above] {Taux d'évolution global} node [below] {$\times CM_1 \times CM_2 \times CM_3 \times ...$} (termF.south); + \end{tikzpicture} + \end{center} + \end{propriete} + + \paragraph{Exemples:} + \begin{itemize} + \item Une quantité a subit 5 augmentations de 10\%. + \begin{center} + \begin{tikzpicture}[ + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + node distance=2cm and 2cm + ] + %Nodes + \node[roundnode] (termA) {\makebox[0.5cm]{}}; + \node[roundnode] (termB) [right=of termA] {\makebox[0.5cm]{}}; + \node[roundnode] (termC) [right=of termB] {\makebox[0.5cm]{}}; + \node[roundnode] (termD) [right=of termC] {\makebox[0.5cm]{}}; + \node[roundnode] (termE) [right=of termD] {\makebox[0.5cm]{}}; + \node[roundnode] (termF) [right=of termE] {\makebox[0.5cm]{}}; + + %Lines + \path[->] (termA.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termB.north) ; + \path[->] (termB.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termC.north) ; + \path[->] (termC.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termD.north) ; + \path[->] (termD.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termE.north) ; + \path[->] (termE.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termF.north) ; + + \path[->] (termA.south) edge [bend right=10] node [above] {Taux d'évolution global} node [below] {$\times ... \times ... \times ... \times ... \times ... = \times ...$} (termF.south); + \end{tikzpicture} + \end{center} + Le coefficient global est donc de $CM = ...$ + + On en déduit le \textbf{taux d'évolution global} $t = ...$ + \item Une quantité a subit une augmentation de 5\% puis un diminution de 10\% et enfin une autre augmentation de 5\%. Calculons le taux d'évolution global. + \end{itemize} + \afaire{Compléter les exemples} \end{solution} \begin{exercise}[subtitle={Techniques}, step={3}, origin={Création}, topics={ Information Chiffrée 2 }, tags={ Information chiffrée }, mode={\faIcon{tools}}] diff --git a/2nd/14_Information_Chiffrée_2/plan_de_travail.pdf b/2nd/14_Information_Chiffrée_2/plan_de_travail.pdf index 1f26573186a4018bc495e1187c561a5c2342c50b..ac70667d0816a2ef7c0f42652bbcb92792495f46 100644 GIT binary patch delta 2143 zcmV-l2%z`GjdawFbby2bgaU*Egam{Iga(8Mgb0KQgbIWUgbaiYgbsucgb;)ggc5`k zgcO7ogcgJsgcyVwgc^h!v>Y{?0yH$2AgCM^mrI)*4u6Vz0t*A<*bb0e+r0%jrD!kR zLwo7pFZCQrmdCTsy4hl3%vcg1B0rH7y?pv(;?t)c&rb%@ahy0)QUN`zK!wxaG&`R8 z<kyRe=rHlQ0mEY!5paR`DOa@#JSL%E4LR&@6x{`Jtci+ z|J>^^ynp{mNKS8H_FtbrlL#1#0OGBr>1Ajg$VgqIr6qke0_yS%I~q^XmQK&RzZL-q zBtVh?WB_vd_Oko(m1cgU&u5}SXQzL{+85fdV^T?a|8x3v_w$?EQ=(;D_ItICY-s4i z$#6${dYh_f&oFkTr_2UbGOh>~&(==E$qAlW9Dn-`Bi^(3jKdFSZ70W^7FxFZXTnX! 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