From 9069dc55ee276486e406ee4e02485c71b629e68a Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 3 Feb 2022 10:20:36 +0100 Subject: [PATCH] Feat: sujet DS6 pour les 2nd --- 2nd/Evaluations/DS_2022-02-07/exercises.tex | 107 ++++++++++++++++++++ 2nd/Evaluations/DS_2022-02-07/sujet.pdf | Bin 0 -> 37033 bytes 2nd/Evaluations/DS_2022-02-07/sujet.tex | 33 ++++++ 3 files changed, 140 insertions(+) create mode 100644 2nd/Evaluations/DS_2022-02-07/exercises.tex create mode 100644 2nd/Evaluations/DS_2022-02-07/sujet.pdf create mode 100644 2nd/Evaluations/DS_2022-02-07/sujet.tex diff --git a/2nd/Evaluations/DS_2022-02-07/exercises.tex b/2nd/Evaluations/DS_2022-02-07/exercises.tex new file mode 100644 index 0000000..b44b082 --- /dev/null +++ b/2nd/Evaluations/DS_2022-02-07/exercises.tex @@ -0,0 +1,107 @@ +\begin{exercise}[subtitle={Géométrie}, step={1}, origin={Création}, topics={ Géométrie repérée }, tags={ Coordonnées de points }, points=7] + % Géométrie repérée + \noindent + \begin{minipage}{0.45\linewidth} + \begin{enumerate} + \item Quelles sont les coordonnées du point $D$? + \item Placer les points dans le repère orthonormée ci-contre. + \[ + A(-3; 0) \qquad B(-1; 4) \qquad C(3;2) + \] + \item Calculer les distances $AB$, $BC$ et $AC$. + \item En déduire la nature du triangle $ABC$. + \item Calculer les coordonnées du point $E$ milieu du segment $[AC]$. + \item Démontrer que les diagonales du quadrilatère $ABCD$ se coupent en leur milieu. + \item Démontrer à partir des résultats des questions précédentes qua $ABCD$ est un carré. + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.5\linewidth} + \begin{tikzpicture} + \repere{-5}{5}{-5}{5} + \draw (1, -2) node {x} node [ below left ] {$D$}; + \end{tikzpicture} + \end{minipage} +\end{exercise} + + +\begin{exercise}[subtitle={Nombre d'écrans}, step={1}, origin={Création}, topics={ Statistiques }, tags={ Moyenne, médiane }, points=7] + % Statistiques + On a réalisé deux études statistiques portant sur le nombre d'écrans dans les foyers de deux villes. Les résultats sont reportés ci-dessous. + + \medskip + \begin{minipage}{0.45\linewidth} + Données brutes récoltées dans la ville de Bonvoyant + + \begin{center} + 0; 4; 2; 4; 3; 1: 5: 3; 4; 5; 3; 4; 5; 5 + \end{center} + \end{minipage} + \hfill + \begin{minipage}{0.45\linewidth} + Données regroupées récoltées dans la ville de Viedehors + + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + Nombre d'écrans & 0 & 2 & 3 & 5 & 20 \\ + \hline + Effectif & 5 & 12 & 10 & 8 & 2\\ + \hline + \end{tabular} + \end{center} + \end{minipage} + \begin{enumerate} + \item Décrire ces études statistiques (caractère, individus et populations). + \item Calculer la proportion de foyers ayant deux ou moins écrans dans la ville de Viedehors. + \item Pour chaque villes calculer les indicateurs suivants: + \begin{multicols}{2} + \begin{itemize} + \item Effectif total + \item Étendu + \item Moyenne + \item Médiane + \end{itemize} + \end{multicols} + \item Comparer ces deux études statistiques. + + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Tableau et fonctions}, step={1}, origin={Création}, topics={ Tableaus de fonctions }, tags={ Tableau de signes, tableau de variation, inéquations }, points=7] + % Tableau de fonctions + Les questions de cet exerces sont indépendantes, elles peuvent être traitées sans avoir traité les questions précédentes. + \begin{enumerate} + \item On définit $f$ la fonction représentée ci-dessous. + + \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{(-5, -4) (-4, 0) (-3, 2) (0, -1) (1, 1) (3, -1) (4, 1) (5, 4)}; + \draw (4,3) node[above right] {$\mathcal{C}_f$}; + \end{tikzpicture} + \end{center} + \begin{enumerate} + \item Tracer le tableau de signes de la fonction $f$ + \item Tracer le tableau de variations de la fonction $f$ + \item Résoudre \textbf{graphiquement} l'équation et l'inéquations suivantes + \begin{multicols}{2} + \begin{enumerate} + \item $f(x) = 1$ + \item $f(x) \geq -2$ + \end{enumerate} + \end{multicols} + \end{enumerate} + + \item Tracer le tableau de signe des fonctions suivantes en passant par la résolution d'une inéquation + \begin{multicols}{2} + \begin{enumerate} + \item $f(x) = 5x - 25$ + \item $g(x) = 10 + 2x$ + \end{enumerate} + \end{multicols} + \end{enumerate} +\end{exercise} diff --git a/2nd/Evaluations/DS_2022-02-07/sujet.pdf b/2nd/Evaluations/DS_2022-02-07/sujet.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6b3483de96bb5a20c94c10e5b51e16db57f7834c GIT binary patch literal 37033 zcmce-1CVXavZ&j(jn%eo+qP}n#%kNP-K%YPueNR5)?5F+=bXLoJNun?<3{W~Bjy-0 zYK&1;IWi+>ewA4y^1`At474mzBom8$3qvb2gTqkF`1JU8hL%v=-1v0L9`+{qbn0@3 zmL^8d_;gAxhR%O$5w&x)!KeG{__sS4@aY5v?cDLT{ya*L&p`jbzB>4HG6v3$7Js!f z{I4s2JN{``G;y+XaWpb>0Q?j12Fk?N_&=`v`SsWQ+5YtW?~{Z5UnU2~ zzf}%~zcl!-Q3%6dM)2>`2m|B4PLhAGZ87}ojEnIvb^rTx!uXd7{A;X>k?G$n$zN{r 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literal 0 HcmV?d00001 diff --git a/2nd/Evaluations/DS_2022-02-07/sujet.tex b/2nd/Evaluations/DS_2022-02-07/sujet.tex new file mode 100644 index 0000000..167eeb0 --- /dev/null +++ b/2nd/Evaluations/DS_2022-02-07/sujet.tex @@ -0,0 +1,33 @@ +\documentclass[a4paper,12pt]{article} +\usepackage{myXsim} + +% Title Page +\title{ DS6 \hfill } +\tribe{2nd} +\date{2022-02-07} +\duree{1h} + +\DeclareExerciseCollection[step=1]{banque} +\xsimsetup{collect} + + +\begin{document} +\maketitle + +\bigskip + +Le barème est donné à titre indicatif, il pourra être modifié. + +\bigskip +{\huge Nom Prénom: } +\bigskip + +\input{exercises.tex} +\printcollection{banque} +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: +