From d315b2142a24412d07b6df3fe9b5685fb838db07 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Wed, 15 Mar 2023 11:32:33 +0100 Subject: [PATCH] Feat(2nd): DS5 --- 2nd/Evaluations/DS_2023-03-17/exercises.tex | 68 ++++++++++++++++++++ 2nd/Evaluations/DS_2023-03-17/sujet.pdf | Bin 0 -> 29459 bytes 2nd/Evaluations/DS_2023-03-17/sujet.tex | 28 ++++++++ 3 files changed, 96 insertions(+) create mode 100644 2nd/Evaluations/DS_2023-03-17/exercises.tex create mode 100644 2nd/Evaluations/DS_2023-03-17/sujet.pdf create mode 100644 2nd/Evaluations/DS_2023-03-17/sujet.tex diff --git a/2nd/Evaluations/DS_2023-03-17/exercises.tex b/2nd/Evaluations/DS_2023-03-17/exercises.tex new file mode 100644 index 0000000..c509f1d --- /dev/null +++ b/2nd/Evaluations/DS_2023-03-17/exercises.tex @@ -0,0 +1,68 @@ +\begin{exercise}[subtitle={Augmentation de salaire}, step={1}, origin={Sesamath 66p302}, topics={ Statistiques }, tags={ médiane, moyenne, quartiles }, points={7}] + Une entreprise, où le salaire mensuel moyen est de \np{2381}\euro, propose une augmentation généralisée du salaire de ses employés, selon deux modalités possibles: + \begin{itemize} + \item modalité 1: tous les salaires augmentent de 10\%. + \item modalité 2: tous les salaires augmentent de 200\euro. + \end{itemize} + \begin{enumerate} + \item L'entreprise réalise un votre auprès de ses employés pour savoir quelle modalité choisir. À votre avis, quelle modalité va être choisie par les employés? + \end{enumerate} + On recueille les salaires de tous les employés de cette entreprise + \begin{center} + 1510, 1925, 5125, 1510, 1450, 1450, 1450, 1450, 1925, 1510\\ + 2340, 1925, 5125, 5125, 1925, 2340, 1450, 1450, 5125, 1510 + \end{center} + \begin{enumerate} + \setcounter{enumi}{1} + \item Décrire cette série Statistique. + \item Quel est l'effectif total de la série ? Son étendue ? + \item Calculer la médiane, les quartiles $Q_1$ et $Q_3$ et l'écart interquartile de cette série des salaires dans l'entreprise. + \item De manière "Très surprenante", le résultat du vote montre que les employés préfèrent la modalité 2. Expliquer pourquoi. + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Spécialité de première}, step={1}, origin={Ma tete}, topics={ Probabilité }, tags={Probabilité, Ensembles}, points={6}] + On choisit au hasard un élève parmi les 160 élèves de première générale. Dans ces élèves, il y a + \begin{itemize} + \item 120 élèves qui ont choisit spé mathématiques + \item 45 élèves qui ont choisit spé HLP + \item 25 qui n'ont ni choisi spé math ni spé HLP + \end{itemize} + \begin{enumerate} + \item Modéliser la situation par un diagramme de Venn (vous détaillerez les calculs). + \item Calculer les probabilités des évènements suivants + \begin{tasks}(2) + \task l'élève a choisit spé math + \task l'éleve a choisit spé math mais pas spé HLP + \end{tasks} + \item On note les évènements de la manière suivante + \begin{itemize} + \item M: "l'élève a choisi spé math" + \item H: "l'élève a choisi spé HLP" + \end{itemize} + Pour chaque évènement ci-dessous, les décrire en une phrase puis calculer la probabilité. + \begin{tasks}(4) + \task $M \cap H$ + \task $M \cup H$ + \task $\overline{H}$ + \task $\overline{M} \cup H$ + \end{tasks} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Géométrie}, step={1}, origin={Ma tete}, topics={ Probabilité }, tags={Probabilité, Ensembles}, points={7}] + Dans un plan muni d'un repère orthonormé, on a placé les points + \begin{eqnarray*} + T(-2;-2) \qquad R(0;2) \qquad I(2;1) + \end{eqnarray*} + \begin{enumerate} + \item Tracer le repère, placer les points et compléter au fil des questions suivantes. + \item Calculer les longueurs des trois côtés du triangle $TRI$. + \item Démontrer que le triangle $TRI$ est un triangle rectangle. Est-il isocèle? + \item On place le point $A$ au milieu du segment $[TI]$. Calculer les coordonnées de $A$. + \item Est-ce que le point $R$ est sur le cercle de centre $A$ et passant pas le point $I$? + \item Où doit-on placer le point $B$ pour que $A$ soit le milieu de $[BR]$? + \item Quelle est alors la nature du quadrilatère $TRIB$? + \end{enumerate} + +\end{exercise} diff --git a/2nd/Evaluations/DS_2023-03-17/sujet.pdf b/2nd/Evaluations/DS_2023-03-17/sujet.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3655fe7312b0b585f143f8025719978f6fa436ee GIT binary patch literal 29459 zcmce+1CS@pwy)i`F>TwnZQHhOThq2}+x_op+vc=wPj`RsKKHwKzY%B0i5oX!?}{iy zR#j%LSif4C>&YZj6cwjqqGy94n_31e4X@1&jli%HG7>r%Tf^}35;CZIIhqkNXet<6 zo0+&0GN`y2yZ%>+xP!ADA;Uk8|MdhDA%n26gD0WRU#~I}GBN(IU5}7K&dAl->L2Ay z|Le|w9sep|i`M77=F@DQEUTfFM7CZ(+>rP5=Kpe_j3K`#Juq`9Eg|=fBMk zuK%bVO#krUzsDg={}91{&Ld3B|2|9pv)W?%_lb-7AMXCo`Gol&68QJ1i<#v=Yso*t zur!MOhMMb|Lq->SO|-b?y>+JwW|jbyNv)C`C>JFccN|!h3Lt+hBWx@ zD1TS~&x^EXQH>_rzB+yXx6j+tk%OhiM4V~^sm0W5X=hW~s9rk((FzucJe4`)MJCi$ 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