From bd9745ca7f4721b848c01dd41b11130bb366aab9 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Mon, 30 Jan 2023 14:50:43 +0100 Subject: [PATCH] =?UTF-8?q?Feat(1ST):=20d=C3=A9but=20de=20DS4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 1ST/Evaluations/DS_2023-02-01/exercises.tex | 47 ++++++++++++++++++++ 1ST/Evaluations/DS_2023-02-01/sujet.pdf | Bin 0 -> 27866 bytes 1ST/Evaluations/DS_2023-02-01/sujet.tex | 28 ++++++++++++ 3 files changed, 75 insertions(+) create mode 100644 1ST/Evaluations/DS_2023-02-01/exercises.tex create mode 100644 1ST/Evaluations/DS_2023-02-01/sujet.pdf create mode 100644 1ST/Evaluations/DS_2023-02-01/sujet.tex diff --git a/1ST/Evaluations/DS_2023-02-01/exercises.tex b/1ST/Evaluations/DS_2023-02-01/exercises.tex new file mode 100644 index 0000000..016ffc6 --- /dev/null +++ b/1ST/Evaluations/DS_2023-02-01/exercises.tex @@ -0,0 +1,47 @@ +\begin{exercise}[subtitle={Technique}, points=6] +\end{exercise} + +\begin{exercise}[subtitle={Le virus!}, points=6] + On s'intéresse à la propagation d'une maladie dans une ville de 130000 habitants. La fonction $f$ définie sur l'intervalle $\intFF{0}{40}$ par + \begin{align*} + f(x) &= -30x^2 + 1260x + 4000 + \end{align*} + modélise le nombre de personnes touchées par la maladie au bout de $x$ jours de suivi de la propagation. + \begin{enumerate} + \item \textit{On donne en annexe la courbe représentative de la fonction $f$. Répondre aux questions ci-dessous par lecture graphique. Les résultats seront justifés en commentant le travail réalisé sur le graphique et en y laissant les traits de construction.} + \begin{enumerate} + % 1 + \item Déterminer le nombre de personnes touchées par la maladie au bout de 15 jours de suivi de la propagation. + \item Le conseil municipal a décidé de fermer les crèches de la ville lorsque plus de 10\% de la population est touchée par la maladie. Justifier qu'à partir de 13000 personnes contaminée, le conseil municipal ferme les crèches. + \item Pendant combien de jours les crèches ont-elles été fermée? + \end{enumerate} + + \item + \begin{enumerate} + % 1 + \item Déterminer,pour tout réel $x$ de l'intervalle $\intFF{0}{40}$, l'expression de $f'(x)$, où $f'$ désigne la fonction dérivée de la fonction $f$. + % 2 + \item Étudier le signe de $f'(x)$ pour $x$ variant dans l'intervalle $\intFF{0}{40}$. En déduire le tableau de variations de la fonction $f$. + % 1 + \item Au bout de combien de jours de suivi de la propagation le nombre de personnes touchées par la maladie est-il maximal?\\ + Combien y a-t-il alors de personnes touchées? + \end{enumerate} + \end{enumerate} +\end{exercise} + +\begin{annexe} + \begin{tikzpicture}[scale=1.5] + \tkzInit[xmin=0,xmax=40, + ymin=0,ymax=17500, + xstep=5,ystep=2500] + \tkzAxeX[thick, poslabel=right,label=] + \tkzAxeY[thick, poslabel=above,label=] + \tkzDrawX[label={\textit{Nombre de jours}},below= -12pt] + \tkzDrawY[label={\textit{Nombre de personnes touchées}}, below=-10pt] + \tkzGrid + \tkzFct[domain=0:40,color=blue, very thick]{-30*\x*\x + 1260*\x+4000} + \end{tikzpicture} +\end{annexe} + +\begin{exercise}[subtitle={Probailités}, points=6] +\end{exercise} diff --git a/1ST/Evaluations/DS_2023-02-01/sujet.pdf b/1ST/Evaluations/DS_2023-02-01/sujet.pdf new file mode 100644 index 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