From 784d5b2d2a4c6a93c1afce963b0250bfe0db2d18 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 17 Jan 2023 10:58:23 +0100 Subject: [PATCH] Feat(2nd): DS3 --- 2nd/Evaluations/DS_2023-01-18/exercises.tex | 182 ++++++++++++++++++ .../DS_2023-01-18/scripts/indice_imc.py | 6 + .../scripts/interpretation_imc.py | 8 + 2nd/Evaluations/DS_2023-01-18/sujet.pdf | Bin 0 -> 49823 bytes 2nd/Evaluations/DS_2023-01-18/sujet.tex | 28 +++ 5 files changed, 224 insertions(+) create mode 100644 2nd/Evaluations/DS_2023-01-18/exercises.tex create mode 100644 2nd/Evaluations/DS_2023-01-18/scripts/indice_imc.py create mode 100644 2nd/Evaluations/DS_2023-01-18/scripts/interpretation_imc.py create mode 100644 2nd/Evaluations/DS_2023-01-18/sujet.pdf create mode 100644 2nd/Evaluations/DS_2023-01-18/sujet.tex diff --git a/2nd/Evaluations/DS_2023-01-18/exercises.tex b/2nd/Evaluations/DS_2023-01-18/exercises.tex new file mode 100644 index 0000000..fb1053d --- /dev/null +++ b/2nd/Evaluations/DS_2023-01-18/exercises.tex @@ -0,0 +1,182 @@ +\begin{exercise}[subtitle={Probabilités}, step={1}, origin={Ma tête}, points=7, topics={ }, tags={ Probabilités }] + Dans cet exercice les parties sont indépendantes, elles peuvent être traités séparément. + + \begin{enumerate}[label={\textbf{Partie \Alph*:}}] + \item \textbf{répartition géographique} + + On a relevé le sexe des enfants nés en février dans 3 communes différentes et on a noté les résultats. + + On considère l'expérience aléatoire qui consiste à tirer au hasard un enfant né en février dans une de ces trois communes. + + \hspace{-1cm} + \begin{minipage}{0.4\linewidth} + \begin{center} + \begin{tabular}{|c|c|c|c|} + \hline + Communes & Garçons & Filles & Total \\ + \hline + Villeouf & 432 & 456 & 888\\ + \hline + Betedeville & 11 & 10 & 21\\ + \hline + Sacrévillage & 54 & 70 & 124\\ + \hline + Total & 497 & 536 & 1033\\ + \hline + \end{tabular} + \end{center} + \end{minipage} + \hfill + \begin{minipage}{0.6\linewidth} + \begin{tasks}[label={\Alph*=}] + \task $\left\{ \mbox{ l'enfant est une fille} \right\}$ + \task $\left\{ \mbox{ l'enfant est né à Betedeville} \right\}$ + \task $\left\{ \mbox{ l'enfant est un garçon et il est né à Villeouf}\right\}$ + %\task $\left\{ \mbox{ l'enfant est une fille ou il est né à Sacrévillage} \right\}$ + \end{tasks} + \end{minipage} + \item \textbf{fonder une famille} + + M.Dupont et Mme Dupont souhaitent avoir 3 enfants. Ils se sont renseignés, chaque enfants a autant de chance d'être un garçon qu'une fille. + + On associe ce souhait d'avoir 3 enfants à une expérience aléatoire où l'on s'intéressera au sexe des enfants. + \begin{enumerate} + \item En utilisant un arbre de probabilité, déterminer l'univers de cette expérience aléatoire. + \item Quelle est la loi de probabilité de cette expérience aléatoire ? Est-ce une situation d'équiprobabilité? + \item Quelle est la probabilité pour que le couple ait 2 filles puis un garçon? + \item Quelle est la probabilité pour que le couple ait 2 filles ? + % \item Quelle est la probabilité que leur deuxième enfant soit un garçon? + \item Quelle est la probabilité pour que les deux ainés (les deux enfants nés en premier) soient du même sexe ? + \item Quelle est la probabilité pour d'avoir une seule fille? + \end{enumerate} + \end{enumerate} +\end{exercise} + +\begin{solution} + \begin{enumerate}[label={\textbf{Partie \Alph*:}}] + \item + Probabilités + \[ + P(A) = \frac{536}{1033} \qquad P(B) = \frac{21}{1033} \qquad P(C)= \frac{432}{1033} + \] + \item + \begin{enumerate} + \item En notant $F$ une fille et $G$ un garçon. L'univers est + \[ + \Omega = \left\{ FFF, FFG, FGF, FGG, GFF, GFG, GGF, GGG \right\} + \] + \item Loi de probabilités + \begin{center} + \begin{tabular}{|c|*{8}{c|}} + \hline + Issues & FFF & FFG & FGF & FGG & GFF & GFG & GGF & GGG \\ + \hline + Probabilités & $\frac{1}{8}$ & $\frac{1}{8}$ & $\frac{1}{8}$ & $\frac{1}{8}$ & $\frac{1}{8}$ & $\frac{1}{8}$ & $\frac{1}{8}$ & $\frac{1}{8}$ \\ + \hline + \end{tabular} + Comme il y a autant de chance d'avoir une fille ou un garçon, c'est une situation d'équiprobabilité. + \end{center} + \item La probabilités d'avoir deux filles est de $\frac{3}{8}$ + \item La probabilité d'avoir les deux ainés du même sexe est de $\frac{4}{8} = \frac{1}{2}$ + \end{enumerate} + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Tableaux}, step={1}, origin={Création?}, topics={Fonctions}, tags={Tableau de signes, Tableau de variations}, points=5] + \begin{enumerate} + \item Tracer le tableau de signes puis le tableau de variation de la fonction suivante + \begin{center} + \begin{tikzpicture}[yscale=0.5] + \tkzInit[xmin=-5,xmax=5,xstep=1, + ymin=-5,ymax=4,ystep=1] + \tkzGrid + \tkzAxeXY + \draw[very thick, color=red] plot [smooth,tension=0.5, mark=*] coordinates{(-4, -4) (-3.5, -3) (-3, 0) (-2, 1) (-1, 0) (0, -3) (1, -1) (2, -3) (2.5,0) (3, 2) (4, 3)}; + \draw (4,3) node[above right] {$\mathcal{C}_f$}; + \end{tikzpicture} + \end{center} + \item En utilisant la calculatrice tracer le \textbf{tableau de signes} de la fonction + \[ + g(x) = x^3 + x^2 - 2x + \] + \end{enumerate} +\end{exercise} + + +\begin{exercise}[subtitle={Cducosto}, step={1}, origin={Création?}, topics={Fonctions}, tags={Tableau de signes, Tableau de variations, inéquations}, points=5] + L'entreprise Cducosto produit des outils de bricolages, en particulier, des marteaux. Voici les tableaux décrivant le signe et les variations des bénéfices (notés $B(x)$) en fonction du nombre de marteaux qu'elle produit et vend. + + \begin{center} + \begin{tikzpicture} + \tkzTabInit[]{$x$/1,Signes de $B(x)$/2}{0, 30, 120, 150} + \tkzTabLine{, -, z, +, z, -,} + \end{tikzpicture} + + \begin{tikzpicture}[baseline=(a.north)] + \tkzTabInit[]{$ x $/1, Variations de $ B(x) $/2}{0, 75, 150} + \tkzTabVar{ -/-175, +/100, -/-175} + \end{tikzpicture} + \end{center} + + \begin{enumerate} + \item Tracer le graphique d'une fonction qui aurait le même tableau de signes que la fonction $B(x)$. + \item Tracer le graphique d'une fonction qui aurait le même tableau de variations que la fonction $B(x)$. + \item Si l'entreprise produit 10 marteaux, fait-elle des bénéfices? + \item Sur quel intervalle doit-elle produire pour que ses bénéfices soient positifs? + \item Quelle quantité de marteaux doit-elle produire pour faire un maximum de bénéfices? + \end{enumerate} +\end{exercise} + +\begin{solution} + \begin{enumerate} + \item Graphique possible + \begin{center} + \begin{tikzpicture}[xscale=1] + \begin{axis}[ + xscale=2, + axis lines = center, + %grid = both, + xlabel = {Quantité}, + %xtick={0, 20, ..., 150}, + xtick distance=10, + ylabel = {Bénéfices}, + ytick distance=50, + ymax=150, + grid=major + ] + \addplot[domain=0:150,samples=40, color=red, very thick]{-0.05*x*x + 7.5*x - 180}; + \end{axis} + \end{tikzpicture} + \end{center} + \item Si l'entreprise produit 10 marteaux, on est entre 0 et 30 marteaux donc les bénéfices sont négatifs. + \item Pour que les bénéfices soient positifs , il faut que la production reste sur l'intervalle $\intFF{30}{120}$ + \item Pour des bénéfices maximaux, il faut produire 75 marteaux d'après le tableau de variations. + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Programmation}, step={1}, origin={Création}, topics={Programmation}, tags={Python}, points=3] + Dans cet exercice, vous devez compléter les programmes Python au niveau des pointillés. + \begin{enumerate} + \item On souhaite écrire une programme qui calculer l'indice IMC avec la formule $IMC = \dfrac{taille^2}{masse}$. + \begin{center} + \begin{minipage}{0.9\linewidth} + \inputminted[bgcolor=base3,linenos]{python}{./scripts/indice_imc.py} + \end{minipage} + \end{center} + \item A un indice IMC, on associe une interprétation suivant la règle suivante + \begin{center} + \begin{tabular}{|c|c|c|c|} + \hline + Indice IMC & 0 à 18.5 & 18.5 à 25 & plus de 25 \\ + \hline + Interprétation & Insuffisance & Normale & Surpoids\\ + \hline + \end{tabular} + \end{center} + \begin{center} + \begin{minipage}{0.9\linewidth} + \inputminted[bgcolor=base3,linenos]{python}{./scripts/interpretation_imc.py} + \end{minipage} + \end{center} + \end{enumerate} +\end{exercise} diff --git a/2nd/Evaluations/DS_2023-01-18/scripts/indice_imc.py b/2nd/Evaluations/DS_2023-01-18/scripts/indice_imc.py new file mode 100644 index 0000000..87cdb27 --- /dev/null +++ b/2nd/Evaluations/DS_2023-01-18/scripts/indice_imc.py @@ -0,0 +1,6 @@ +taille = int(input("Quelle est votre taille (en m)?")) +taille = int(input("Quelle est votre masse (en kg)?")) + +imc = ..... + +print("Votre indice IMC est de ", imc) diff --git a/2nd/Evaluations/DS_2023-01-18/scripts/interpretation_imc.py b/2nd/Evaluations/DS_2023-01-18/scripts/interpretation_imc.py new file mode 100644 index 0000000..238253a --- /dev/null +++ b/2nd/Evaluations/DS_2023-01-18/scripts/interpretation_imc.py @@ -0,0 +1,8 @@ +imc = float(input("Quel est votre indice IMC?")) + +if ..... : + print("Insuffisance") +........... + print("Normale") +........... + print("Surpoids") diff --git a/2nd/Evaluations/DS_2023-01-18/sujet.pdf b/2nd/Evaluations/DS_2023-01-18/sujet.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1007d2e857b472b36a9ebb0d91501e4e68856273 GIT binary patch literal 49823 zcmce-1#Blxt}i-aX69tV%uEwzX2yS*nVFe6nJ_amGcz+Yb0*3CzH{$=yH96z^z@|N 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2023} +\duree{1h} + +\DeclareExerciseCollection[step=1]{banque} +\xsimsetup{collect} + +\pagestyle{empty} + +\begin{document} +\maketitle + +Le barème est donné à titre indicatif, il pourra être modifié. + +\input{exercises.tex} +\printcollection{banque} +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: