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+\author{Benjamin Bertrand} +\title{Fonctions et graphiques - Cours} +\date{Septembre 2021} + +\DeclareExerciseCollection[step=4]{banque} +\xsimsetup{collect} + + +\begin{document} + +\input{exercises.tex} +\printcollection{banque} +\vfill + +\end{document} diff --git a/2nd/03_Fonctions_et_graphiques/5P_salaires.pdf b/2nd/03_Fonctions_et_graphiques/5P_salaires.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f6e4447bb53ac67637bcc03e51aec3919db8f3c5 GIT binary patch literal 27879 zcmce-1FR@b*Cx96Ioq~v+qP}nwr$%s&$eybwr%U4_y6ZhW^yN)xi|T~PP$X8YIUWb zs#D`0 z9c`T*42>P}=>MrwfS{E!wlQ@w!=q=$`ybceZp^Kmj2-Z3MXdCljD?I1ZHOwMEdMqT ztp7O>Z2vA04F9?1#PDxhP7MFd@qfl982*{`e~V!=u>Z$EF#hAT{w*LF8UAx1{#m*I z9uWV344aXKfrgEd8IO^fhKZ5!|6{md{I}UR%Rf{7FVpx}G@@r>`|oh{e~v~=s*;Wy zEO6Zys=Fu_B?5OOcIQ$h(xzSwRhnCY1+(QG9%>2cC0|clz_obf4f5K|HdpA7g9f=f zJbVz(@!-z~LRo(hRKPEA$O6nuTUS!bHSEi=IGHYe9KM83c{SS_seaUq*Y*fGiMOJ} z*=O!!U&PJ$+W67vyvCB6H`zy+Si4Oori^AtWLww5B=F95sXwCgM|0e(wcr4!FXSM> 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dépasser le prof. +Bilan: Modélisation de la transformation d'une grandeur en une autre avec un fonction dont on peut trouver une formule. + Étape 3: Situation où l'on utilise les graphiques ================================================= @@ -48,16 +50,27 @@ A partir de graphiques issus des autres matières, on pose des questions aux él Lors de la correction, l'enseignant prendra soin de traduire les questions en language mathématiques et poussera les élèves petit à petit à utiliser ce language. +Bilan: pas de bilan + Étape 4: Exercices techniques ============================= Identique à l'étape précédentes mais avec des graphiques purement mathématiques. Les questions seront elles aussi posées de façon mathématiques. +Bilan: résumé les méthodes de résolutions d'équations et inéquations avec des graphiques + Étape 5: Tableur ================ A partir d'une situation déjà modélisée (ou à modéliser) on utilise le tableur pour tracer les fonctions et répondre à des questions. +.. image:: ./5P_salaires.pdf + :height: 200px + :alt: Qui est le mieux payé? + + +Bilan: étirer une formule sur un tableur + Notes, references et pistes ===========================

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b/2nd/03_Fonctions_et_graphiques/5P_salaires.tex new file mode 100644 index 0000000..4c01270 --- /dev/null +++ b/2nd/03_Fonctions_et_graphiques/5P_salaires.tex @@ -0,0 +1,29 @@ +\documentclass[12pt,xcolor=table]{classPres} + +\title{Comparaison de salaires} +\date{Septembre 2021} + + +\begin{document} + +\begin{frame}{Salaires} + Jean, Faïza et Bob fabriquent tous les 3 des jouets mais ne sont pas payé de la même façons et veulent comparer leurs revenus. + \begin{itemize} + \item Bob n'a pas de salaire fixe mais a une prime de 9\euro par jouet. + \item Jean a un salaire fixe de 1500\euro par mois. + \item Faïza a un salaire de 1000\euro plus une prime de 4\euro par jouet qu'il a fabriqué. + \end{itemize} + + \vfill + \begin{center} + Qui est le mieux payé? + \end{center} + \vfill +\end{frame} +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: + diff --git a/2nd/03_Fonctions_et_graphiques/exercises.tex b/2nd/03_Fonctions_et_graphiques/exercises.tex index 6e6c9a8..65316d3 100644 --- a/2nd/03_Fonctions_et_graphiques/exercises.tex +++ b/2nd/03_Fonctions_et_graphiques/exercises.tex @@ -29,6 +29,139 @@ \end{tikzpicture} \item Écrire 4 questions qui pourraient être répondu par la lecture des graphiques que vous venez de tracer. - \end{enumerate} \end{exercise} + +\begin{exercise}[subtitle={Concentration médicaments}, step={3}, 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={3}, 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}{0.5\linewidth} + \begin{enumerate} + \item \textbf{Recettes} + \begin{enumerate} + \item Combien rapporte la vente de 50tonnes de \textit{machins}. + \item Quelle quantité doit être vendu 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}{0.5\linewidth} + \begin{tikzpicture}[xscale=0.5, yscale=0.4] + \tkzInit[xmin=0,xmax=80,xstep=5, + ymin=0,ymax=160000,ystep=10000] + \tkzGrid + \tkzAxeXY + %\tkzFct[domain=0:80,color=red,very thick]{\x**3-105*\x**2+3700*\x+4000}; + \end{tikzpicture} + \end{minipage} +\end{exercise} + +\begin{exercise}[subtitle={Fabricants de machins}, step={3}, origin={Nathan 2ST 1P119}, topics={ Fonctions et graphiques }, tags={ Fonctions, Graphiques }] +\end{exercise} + +\begin{exercise}[subtitle={Lecture graphique}, step={4}, origin={???}, topics={ Fonctions et graphiques }, tags={ Fonctions, Graphiques }] + \begin{minipage}{0.5\textwidth} + \begin{tikzpicture}[yscale=0.4, xscale=0.6] + %\repere{-9}{4}{-5}{4} + \tkzInit[xmin=-9,xmax=4,xstep=1, + ymin=-5,ymax=4,ystep=1] + \tkzGrid + \tkzAxeXY + \draw[very thick, color=red] plot [smooth,tension=0.2] coordinates{% + (-8,0.2) (-6,3) (-2,-4.5) (0,-2) (1,0) (3,1.5) + }; + \draw (3,1) node[above right] {$\mathcal{C}_f$}; + \end{tikzpicture} + \end{minipage} + \begin{minipage}{0.5\textwidth} + \begin{enumerate} + \item Résoudre graphiquement les équations suivantes + \begin{multicols}{2} + \begin{enumerate} + \item $f(x) = 0$ + \item $f(x) = -5$ + \item $f(x) = 3$ + \end{enumerate} + + \end{multicols} + \item Résoudre graphiquement les inéquations suivantes + \begin{multicols}{2} + \begin{enumerate} + \item $f(x) \leq 0$ + \item $f(x) > -2$ + \item $f(x) \geq 1,5 $ + \end{enumerate} + \end{multicols} + \end{enumerate} + \end{minipage} +\end{exercise} + +\begin{exercise}[subtitle={Lecture graphique}, step={4}, origin={???}, topics={ Fonctions et graphiques }, tags={ Fonctions, Graphiques }] + \begin{minipage}{0.5\textwidth} + \begin{tikzpicture}[xscale=0.7, yscale=0.6] + \tkzInit[xmin=-6,xmax=6,xstep=1, + ymin=-3,ymax=3,ystep=1] + \tkzGrid + \tkzAxeXY + \draw (4,2) node[below left] {$\mathcal{C}_g$}; + \tkzFct[domain = -6:6,color=red,very thick]% + {0.05*(x+5)*(x+1)*(x-4)} + \end{tikzpicture} + \end{minipage} + \begin{minipage}{0.5\textwidth} + \begin{enumerate} + \item Résoudre graphiquement les équations suivantes + \begin{multicols}{2} + \begin{enumerate} + \item $g(x) = 1,5$ + \item $g(x) = -2$ + \item $g(x) = 3$ + \end{enumerate} + + \end{multicols} + \item Résoudre graphiquement les inéquations suivantes + \begin{multicols}{2} + \begin{enumerate} + \item $g(x) \geq 0$ + \item $g(x) < -1,5$ + \item $g(x) > 1 $ + \end{enumerate} + \end{multicols} + \end{enumerate} + \end{minipage} +\end{exercise} diff --git a/2nd/03_Fonctions_et_graphiques/fig/concentration.pdf b/2nd/03_Fonctions_et_graphiques/fig/concentration.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3e253bddc8ed39db9f71cbd1c13cf2a8a78c0e6d GIT binary patch literal 246899 zcmZs?18^nJ*DxF>8{4*R+qTUc+qSc@ZQI^xW1Ab>#(w$zRnJ@X-RhdT=XB2;bk7|1 zkSU6a(=pMrL6fyy*1kit5;79n8v~$uc?lV0&Fm~(ED71ZQOeMSgoF&@RyHnXPTyx6 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