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oUp?x-K?X-sKK%D5?c!?e?CSA>`jOaxKp;C8(w8q1ijqkG2a*LI2><{9 literal 0 HcmV?d00001 diff --git a/Technologique/03_Fonctions_graphiques/2E_lecture_concrets.tex b/Technologique/03_Fonctions_graphiques/2E_lecture_concrets.tex new file mode 100644 index 0000000..5cfa20b --- /dev/null +++ b/Technologique/03_Fonctions_graphiques/2E_lecture_concrets.tex @@ -0,0 +1,26 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} +\usepackage{pgfplots} +\pgfplotsset{compat = newest} +\usepgfplotslibrary{external} +\tikzexternalize + +\author{Benjamin Bertrand} +\title{Fonctions et graphiques - Cours} +\date{Octobre 2021} + +\DeclareExerciseCollection[step=2]{banque} +\xsimsetup{collect} + +\thispagestyle{empty} + + +\begin{document} + +\input{exercises.tex} + + +\printcollection{banque} +\vfill + +\end{document} diff --git a/Technologique/03_Fonctions_graphiques/exercises.tex b/Technologique/03_Fonctions_graphiques/exercises.tex new file mode 100644 index 0000000..dc08fd2 --- /dev/null +++ b/Technologique/03_Fonctions_graphiques/exercises.tex @@ -0,0 +1,72 @@ +\begin{exercise}[subtitle={Concentration médicaments}, step={2}, origin={Sesamaths 83p205}, topics={ Fonctions et graphiques }, tags={ Fonctions, Graphiques }] + On a mesuré en continue pendant 4h, la concentration $C$ d'un médicament dans le sang d'un patient. On a représenté les données dans le graphique ci-dessous. + + \noindent + \begin{minipage}{0.45\linewidth} + \begin{enumerate} + \item Quelles sont les deux grandeurs reliés dans le graphique? + \item Quelle est la concentration de médicaments dans le sang au bout de 2h? + \item A quel(s) moment(s) la concentration a-t-elle été de 0.5mg/L? + \item A quelle moment la concentration du médicament a-t-elle été maximal? Quelle était alors cette concentration? + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.5\linewidth} + \includegraphics[scale=0.4]{./fig/concentration} + \end{minipage} + \begin{enumerate} + \setcounter{enumi}{4} + \item Définir le moment où la concentration a été supérieur à 1mg/L. + \item Combien de temps la concentration a été supérieur à 0.25mg/L? + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Fabricants de machins}, step={2}, origin={Nathan 2ST 1P119}, topics={ Fonctions et graphiques }, tags={ Fonctions, Graphiques }] + Une entreprise fabrique des \textit{machins}. Chaque jour, elle peut en produire entre 0 et 80 tonnes. + + Le coût de fabrication et les recettes, en euros, de $x$ tonnes est modélisé par la fonction $C(x)$ et $R(x)$ représentées dans le graphique ci-dessous. + + \noindent + \begin{minipage}{0.55\linewidth} + \begin{enumerate} + \item \textbf{Recettes} + \begin{enumerate} + \item Combien rapporte la vente de 50tonnes de \textit{machins}. + \item Quelle quantité doit être vendue pour avoir une recette de \np{50000}? + \end{enumerate} + \item \textbf{Coûts de productions} + \begin{enumerate} + \item Combien coûte la production de 50tonnes de \textit{machins}. + \item Quelle quantité de \textit{machins} peut-on produire pour une coût de fabrication de \np{100000}\euro? + \end{enumerate} + \item \textbf{Les bénéfices} sont la différence entre les recettes et les coûts. + \begin{enumerate} + \item L'entreprise réalise-t-elle des bénéfices en produisant 10tonnes? + \item Déterminer graphiquement les productions où ses bénéfices sont positifs. + \end{enumerate} + \end{enumerate} + \end{minipage} + \begin{minipage}{0.4\linewidth} + \begin{tikzpicture} + \begin{axis}[ + axis lines = left, + y tick label style={/pgf/number format/.cd,% + scaled y ticks = false, + set thousands separator={$ $}, + fixed}, + grid= both, + xlabel = {En tonnes}, + xtick distance=5, + ylabel = {En \euro}, + ytick distance=10000, + every axis y label/.style={at={(current axis.north west)},above=2mm}, + legend pos = north west, + legend entries={$C(x)$, $R(x)$} + ] + \addplot[domain=0:80,samples=100, color=red, very thick]{x^3 - 105*x^2 + 3700*x + 4000 }; + \addplot[domain=0:80,samples=3, color=blue, very thick]{1900*x} node [above] {$R(x)$}; + \end{axis} + \end{tikzpicture} + \end{minipage} +\end{exercise} + diff --git a/Technologique/03_Fonctions_graphiques/fig/concentration.pdf b/Technologique/03_Fonctions_graphiques/fig/concentration.pdf new file mode 100644 index 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variations et résolutions d'équations et inéquations + +Étape 1: Modélisation +===================== + +.. image:: ./1P_salaires.pdf + :height: 200px + :alt: Qui est le mieux payé? + +Question ouverte à propos de trois salaires. Ils vont pouvoir commencer à chercher à la main les salaires des 3 employés sur plusieurs quantités. Quand ils auront répété suffise ment les mêmes calculs ont pourra les inviter à utiliser le tableur et à tracer les graphiques représentant les 3 évolutions. + +Bilan: La modélisation des 3 salaires avec le tableur, le graphiques et les formules utilisées. + +Étape 2: Cas concrets +===================== + +Exercices contextualisés où les questions reviennent à résoudre des équations et inéquations. +