From 3d67cd2fc03323164aa9e2752e4ccd8762666ee9 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Wed, 24 May 2023 18:05:07 +0200 Subject: [PATCH] =?UTF-8?q?Feat(2nd):=20Dernier=20devoir=20de=20l'ann?= =?UTF-8?q?=C3=A9e?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 2nd/Evaluations/DS_2023-05-26/exercises.tex | 96 ++++++++++++++++++++ 2nd/Evaluations/DS_2023-05-26/sujet.pdf | Bin 0 -> 30359 bytes 2nd/Evaluations/DS_2023-05-26/sujet.tex | 27 ++++++ 3 files changed, 123 insertions(+) create mode 100644 2nd/Evaluations/DS_2023-05-26/exercises.tex create mode 100644 2nd/Evaluations/DS_2023-05-26/sujet.pdf create mode 100644 2nd/Evaluations/DS_2023-05-26/sujet.tex diff --git a/2nd/Evaluations/DS_2023-05-26/exercises.tex b/2nd/Evaluations/DS_2023-05-26/exercises.tex new file mode 100644 index 0000000..e2a894c --- /dev/null +++ b/2nd/Evaluations/DS_2023-05-26/exercises.tex @@ -0,0 +1,96 @@ +\begin{exercise}[subtitle={Vecteurs - uniquement spé math et STI2D}, step={1}, origin={Création}, topics={ }, tags={ }, points=6] + \begin{minipage}{0.55\linewidth} + On définit $\vect{z}$ $\vect{w}$ dans le repère ci-contre et $\vect{u} \vectCoord{3}{4}$ et $\vect{v} \vectCoord{-2}{-3}$ par leurs coordonnées. + \begin{enumerate} + \item Déterminer les coordonnées de $\vect{z}$ et $\vect{w}$. + \item Tracer les vecteurs $\vect{u}$ et $\vect{v}$ dans le repère ci-contre. + \item Calculer les coordonnées du vecteur $\vect{a} = \vect{u} + 2\vect{v}$. Puis tracer ce vecteur sur le graphique. + \item Soient $A(0; 2)$, $B(2; 1)$ et $C(20; -8)$ trois points et $M(x;y)$ un point "libre". Quelles doivent être les coordonnées de $M$ pour que l'on ait + \[ + \vect{AM} = \vect{AB} - \vect{BC} + \] + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.4\linewidth} + \begin{tikzpicture}[scale=0.7] + \repereOIJ{-5}{5}{-5}{5} + \draw [->, very thick] (2, 4) -- node [midway, above] {$\vect{x}$} ++(2, -3); + \draw [->, very thick] (0, 0) -- node [midway, above] {$\vect{w}$} ++(-4, 2); + + %\draw [->, very thick] (0, 0) -- node [midway, above] {$\vect{u}$} ++(3, 4); + %\draw [->, very thick] (0, 0) -- node [midway, above] {$\vect{v}$} ++(-2, -3); + \end{tikzpicture} + \end{minipage} +\end{exercise} + +\begin{exercise}[subtitle={Taux d'évolution - uniquement non spé math et STMG}, step={1}, origin={Création}, topics={ }, tags={ }, points=6] + Les questions suivantes sont indépendantes + \begin{enumerate} + \item Compléter le tableau suivant en détaillant les calculs + + \begin{center} + \begin{tabular}{|c|*{3}{c|}} + \hline + Valeur de départ & Valeur d'arrivée & Coefficient multiplicateur & Taux d'évolution \\ + \hline + 110 & & & -18\% \\[10ex] + \hline + & 47 & & +22\% \\[10ex] + \hline + 240 & 180 & & \\[10ex] + \hline + \end{tabular} + \end{center} + + \item Dans une entreprise 1, les salaires ont augmenté de 2\% puis de 3\%. Dans l'entreprise 2, les salaires ont augmenté de 4\% puis de 1\%. + + Dans quelle entreprise, les salaires ont le plus augmenté ? + + \item Les résultats d'une entreprise ont diminué de 15\% en une année. Quel doit être le taux d'évolution du résultat l'année suivante pour qu'il revienne à sa valeur initial? + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Equation de droite}, step={1}, origin={Création}, topics={ }, tags={ }, points=8] + On se donne deux droites. + \[ + (a): y = 2x - 1 \mbox{ et } (b): y = -0.5x + 2 + \] + \begin{enumerate} + + \item Traduire en français l'équation de la droite $(a)$. + \item Déterminer à quelles droites appartiennent ces deux points. + \[ + A(2; 1) \qquad B(0.4; -0.2) + \] + \item Déterminer la valeur de $y$ pour que $M(2; y)$ soit sur la droite $(a)$. + \item Déterminer la valeur de $x$ pour que $N(x; 4)$ soit sur la droite $(b)$. + \item Placer les points $A$, $B$, $M$ et $N$ ainsi que les droites $(a)$ et $(b)$ sur le repère ci-dessous. + \begin{center} + \begin{tikzpicture}[scale=0.7] + \repereOIJ{-5}{5}{-5}{5} + + %\draw [->, very thick] (0, 0) -- node [midway, above] {$\vect{u}$} ++(3, 4); + %\draw [->, very thick] (0, 0) -- node [midway, above] {$\vect{v}$} ++(-2, -3); + \end{tikzpicture} + \end{center} + + \item Soient deux points $C(0; 4)$ et $D(-1; 2)$. + \begin{enumerate} + \item Calculer la pente de la droite $(CD)$. + \item En déduire l'équation de la droite $(CD)$. + \end{enumerate} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Fonctions de référence}, step={1}, origin={Création}, topics={ }, tags={ }, points=6] + Répondre aux questions sans justifier. + \begin{enumerate} + \item Donner la formule de la fonction cube. + \item Tracer l'allure graphique de la fonction inverse. + \item Tracer le tableau de signe de la fonction racine carré. + \item Tracer le tableau de variations de la fonction carré. + \item Donner un exemple de fonction impaire. + \item Quelle(s) fonction(s) de référence a(ont) pour ensemble de définition $\R$? + \end{enumerate} +\end{exercise} diff --git a/2nd/Evaluations/DS_2023-05-26/sujet.pdf b/2nd/Evaluations/DS_2023-05-26/sujet.pdf new file mode 100644 index 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