From b03c41a0e723497f253e9a0b56cdcd90d960c050 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Mon, 20 Feb 2023 15:17:29 +0100 Subject: [PATCH] =?UTF-8?q?Feat(2nd):=20premi=C3=A8re=20version=20du=20dev?= =?UTF-8?q?oir=20pour=20les=202nd?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 2nd/Evaluations/DS_2023-02-24/exercises.tex | 84 ++++++++++++++++++++ 2nd/Evaluations/DS_2023-02-24/sujet.pdf | Bin 0 -> 32723 bytes 2nd/Evaluations/DS_2023-02-24/sujet.tex | 28 +++++++ 3 files changed, 112 insertions(+) create mode 100644 2nd/Evaluations/DS_2023-02-24/exercises.tex create mode 100644 2nd/Evaluations/DS_2023-02-24/sujet.pdf create mode 100644 2nd/Evaluations/DS_2023-02-24/sujet.tex diff --git a/2nd/Evaluations/DS_2023-02-24/exercises.tex b/2nd/Evaluations/DS_2023-02-24/exercises.tex new file mode 100644 index 0000000..c272c0a --- /dev/null +++ b/2nd/Evaluations/DS_2023-02-24/exercises.tex @@ -0,0 +1,84 @@ +\begin{exercise}[subtitle={Factorisation et signe}, step={1}, origin={Création}, topics={ Calcul littéral }, tags={ Coordonnées de points }, points=7] + Les questions suivantes sont indépendantes les unes des autres. Il ne faut pas hésitez à sauter celles qui vous posent problèmes. + \begin{enumerate} + \item Factoriser les expressions suivantes + \begin{tasks}(3) + \task $f(x) = 16x^2 - 24x + 9$ + \task $g(x) = 121x^2 - 4$ + \task $h(x) = 10x^2 - 1$ + \end{tasks} + \item Tracer le tableau de signe des expressions suivantes + \begin{tasks}(3) + \task $o(x) = 5x - 10$ + \task $m(x) = (4x-1)(2x + 12)$ + \task $n(x) = 49x^2 + 14x + 1$ + \end{tasks} + \item Résoudre l'inéquation suivante + \[ + 64x^2 - 1 \leq 0 + \] + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Vrai-Faux}, step={1}, origin={Création}, topics={Tableau de fonctions}, tags={ Coordonnées de points }, points=7] + Ci-dessous, le tableau de signes de la fonction $f$ et le tableau de variations de $g$. + + \begin{minipage}{0.4\linewidth} + \begin{tikzpicture}[baseline=(a.north)] + \tkzTabInit[lgt=2,espcl=1]{$ x $/1,$ f(x) $/1}{-10, -5, 1, 3, 5} + \tkzTabLine{, -, z, +, z, -, z, - , } + \end{tikzpicture} + \end{minipage} + \begin{minipage}{0.5\linewidth} + \begin{tikzpicture}[baseline=(a.north)] + \tkzTabInit[lgt=1,espcl=2]{$ x $/1, $ g(x) $/2}{-5, -2, 0, 5, 10 } + \tkzTabVar{ +/4, -/0, +/1, -/-5, +/3} + \end{tikzpicture} + \end{minipage} + + \begin{enumerate} + \item Pour chacune des propositions suivantes dire si elle est vraie, fausse ou si les informations à disposition sont suffisantes pour répondre à la question. Vous essayerai le plus possible d'expliquer vos réponses. + \begin{tasks}(2) + \task Entre -3 et 1, la fonction $f$ est positive. + \task Entre 0 et 5, la fonction $g$ est croissante. + + \task Sur l'intervalle $\intFF{-1}{0}$, $g$ est croissante. + \task Sur l'intervalle $\intFF{-3}{-1}$, $f$ est positive. + + \task Sur l'intervalle $\intFF{1}{2}$, $g$ est croissante. + \task Les solutions de l'équation $f(x) = 0$ sont $x \in \left\{ -3; 1 \right\}$ + + \task $g(1)$ est plus grand que $g(2)$. + \task $f(0)$ est plus grand que $f(4)$. + + \task Le maximum de la fonction $g$ est 4. + \task Le maximum de la fonction $f$ est 5. + \end{tasks} + \item Tracer un graphique possible de la fonction $f$ et un graphique possible de la fonction $g$. + \end{enumerate} +\end{exercise} + +\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 orthonormé ci-contre. + \[ + A(-3; 0) \qquad B(-1; 4) \qquad C(3;2) + \] + \item Calculer les coordonnées du point $E$ milieu du segment $[AC]$. + \item Démontrer que les diagonales du quadrilatère $ABCD$ se coupent en leur milieu. Que peut-on en déduire sur la nature du quadrilatère $ABCD$? + \item Démontrer que $AB = \sqrt{20}$ et que $AC = \sqrt{40}$. + \item On admet que $BC = \sqrt{20}$ (vous n'avez pas à le calculer). Que peut-on dire du triangle $ABC$. + \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} diff --git a/2nd/Evaluations/DS_2023-02-24/sujet.pdf b/2nd/Evaluations/DS_2023-02-24/sujet.pdf new file mode 100644 index 0000000000000000000000000000000000000000..58e3897a86bfc9ea64832bb8ea002ecbaf5666e8 GIT binary patch literal 32723 zcmce-1CS_9wk_PYZQHhO+s0|zwyo3d)3$Bfwr#ur@4N4RZzkeS+<5UKW-6i(Sy`F2 zW3S5ExmIpc1rae?Mmkm~(#fU1#i7;N!C@#C0tNy*qhC-wJOuPA9`>dL^cwO;zf6st z3FwtwjGX_gM9j|7hJgO>Lij@9p%F^1|)bX#gwV|`Ah^eui$zT1-nA(~g4{#l-xdwdC(%^50|$ z+ke)Qzrpwg;JnK_vLX^{WN5PzjJ6^p|T*FB@W2pvsyuJ1o5u)&N> z(6aW5c9=XkMyN;7c6mWx=2up(wX{{&FpYIr*ik_dQ8+4JC`Hr#*?xPp0nX>kq>wWa z!d%6&8-}bjaU|c_;d7$D!`JEab2}Bq8l^DFHSu)+Jphcf>sKo=6uc7k6su{I_JW^= zzim&)a-x)t7qb5f{dhL=vcpPaVU;|97!6`MZoX^yfyQ+A`Mnp%RBkUr)u2(54pR5| 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zg_(=^OMG3`%FFCaq@9bHN%KFH*;&8T+5gdGx3_os`ucwgvP;{U+kdV7GjsdW29_54 z^5kRY$F$TRtK8o1UDzoCjrLsI@6^|utjX&OhqD>d}5`aXN(W|88MCx zHqlgA8lNH`5vBbMsM?u-{G!|HnEfe=pNl137&nB-fs%{#K0+Lce}mmi42#{*96@aa zUVtr%vzOXSUhEKMrbhpGdYLAS(U3a8hglm=QE4&|K~%5uU8C&^z;0`_R{myi|6K#g zXKRq~q3W61=3|U;%eST=u(-+I^um61Bj-|*tB+=CroU~Y#Z)op1?o7IiuC{elRLW@ YIk|XzJvqPvzNY`IuoM*HiW0E@1B{UjlK=n! literal 0 HcmV?d00001 diff --git a/2nd/Evaluations/DS_2023-02-24/sujet.tex b/2nd/Evaluations/DS_2023-02-24/sujet.tex new file mode 100644 index 0000000..a6fc3ad --- /dev/null +++ b/2nd/Evaluations/DS_2023-02-24/sujet.tex @@ -0,0 +1,28 @@ +\documentclass[a4paper,12pt]{article} +\usepackage{myXsim} + +% Title Page +\title{ DS 4 \hfill } +\tribe{2nd} +\date{24 février 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: