From 59606f44de83639fe7d0d852bad511bd2d9b34c2 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 19 May 2022 10:41:49 +0200 Subject: [PATCH] Feat: ajoute DS9 pour les 2nd --- 2nd/Evaluations/DS_2022-05-20/exercises.tex | 181 ++++++++++++++++++++ 2nd/Evaluations/DS_2022-05-20/sujet.pdf | Bin 0 -> 33985 bytes 2nd/Evaluations/DS_2022-05-20/sujet.tex | 28 +++ 2nd/Evaluations/DS_2022-05-20/sujet_2.pdf | Bin 0 -> 33280 bytes 2nd/Evaluations/DS_2022-05-20/sujet_2.tex | 28 +++ 5 files changed, 237 insertions(+) create mode 100644 2nd/Evaluations/DS_2022-05-20/exercises.tex create mode 100644 2nd/Evaluations/DS_2022-05-20/sujet.pdf create mode 100644 2nd/Evaluations/DS_2022-05-20/sujet.tex create mode 100644 2nd/Evaluations/DS_2022-05-20/sujet_2.pdf create mode 100644 2nd/Evaluations/DS_2022-05-20/sujet_2.tex diff --git a/2nd/Evaluations/DS_2022-05-20/exercises.tex b/2nd/Evaluations/DS_2022-05-20/exercises.tex new file mode 100644 index 0000000..971097f --- /dev/null +++ b/2nd/Evaluations/DS_2022-05-20/exercises.tex @@ -0,0 +1,181 @@ +\begin{exercise}[subtitle={Questions flashs}, step={1}, origin={Création}, topics={ }, tags={ }, points=4] + \begin{enumerate} + % Inéquation + \item Résoudre l'inéquation + \[ + 4x + 12 \geq 16 + \] + + % Inéquation + \item Résoudre l'inéquation + \[ + -3x - 6 > 15 + \] + + % Info chiffrée + \item Après avoir augmenté le prix d'un article de 30\%, le vendeur décide de la baisser de 30\%. Quelle évolution aura subi le prix de cet article après ces deux évolutions? + + % Info chiffrée + \item Un prix passe de 300\euro à 230\euro. Le commerçant veut revenir au prix initial. Quel pourcentage de baisse doit-il appliquer? + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Questions flashs}, step={2}, origin={Création}, topics={ }, tags={ }, points=4] + \begin{enumerate} + % Inéquation + \item Résoudre l'inéquation + \[ + 5x + 12 < 16 + \] + + % Inéquation + \item Résoudre l'inéquation + \[ + 2x - 6 \geq 16 + \] + + % Info chiffrée + \item Après avoir augmenté le prix d'un article de 40\%, le vendeur décide de la baisser de 40\%. Quelle évolution aura subi le prix de cet article après ces deux évolutions? + + % Info chiffrée + \item Un prix passe de 259\euro à 300\euro. Le commerçant veut revenir au prix initial. Quel pourcentage de baisse doit-il appliquer? + \end{enumerate} +\end{exercise} + +% ----- + +\begin{exercise}[subtitle={Développer et factoriser}, step={1}, origin={Création}, topics={ }, tags={ }, points=5] + \begin{enumerate} + \item Développer les deux expressions suivantes + \begin{multicols}{2} + \begin{enumerate}[label={$\Alph*=$}] + \item $5x(2x - 4)$ + \item $(x - 1)(-3x + 1)$ + \end{enumerate} + \end{multicols} + \item Factoriser les expressions suivantes + \begin{multicols}{3} + \begin{enumerate}[label={$\Alph*=$}] + \item $4x^2 - 10x$ + \item $9x^2 - 12x + 4$ + \item $81x^2 - 36$ + \end{enumerate} + \end{multicols} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Développer et factoriser}, step={2}, origin={Création}, topics={ }, tags={ }, points=5] + \begin{enumerate} + \item Développer les deux expressions suivantes + \begin{multicols}{2} + \begin{enumerate}[label={$\Alph*=$}] + \item $3x(4x - 3)$ + \item $(5x - 10)(-2x + 1)$ + \end{enumerate} + \end{multicols} + \item Factoriser les expressions suivantes + \begin{multicols}{3} + \begin{enumerate}[label={$\Alph*=$}] + \item $3x^2 - 9x$ + \item $25x^2 - 40x + 16$ + \item $49x^2 - 64$ + \end{enumerate} + \end{multicols} + \end{enumerate} +\end{exercise} + +% ----- + +\begin{exercise}[subtitle={Vecteurs}, 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 leur 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 $\vect{u} + 2\vect{v}$. + \item Soient $A(0; 2)$, $B(2, 1)$ et $C(20, -8)$ trois points. + \begin{enumerate} + \item Calculer les coordonnées de $\vect{AB}$ et $\vect{AC}$. + \item Est-ce que le vecteur $\vect{AB}$ est colinéaire au vecteur $\vect{w}$? + \item Déterminer si les points $A$, $B$ et $C$ sont alignés. + \end{enumerate} + \item On définit un point $M(1; y)$. Déterminer la valeur de $y$ pour que $\vect{AM}$ et $\vect{v}$ soient colinéaires. + \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={Vecteurs}, step={2}, origin={Création}, topics={ }, tags={ }, points=6] + \begin{minipage}{0.55\linewidth} + On définit $\vect{z}$ $\vect{w}$ dans le repère ci-contre et $\vect{u} \vectCoord{2}{3}$ et $\vect{v} \vectCoord{-3}{-4}$ par leur 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 $\vect{u} + 2\vect{v}$. + \item Soient $A(0; 2)$, $B(4, 0)$ et $C(20, -8)$ trois points. + \begin{enumerate} + \item Calculer les coordonnées de $\vect{AB}$ et $\vect{AC}$. + \item Est-ce que le vecteur $\vect{AB}$ est colinéaire au vecteur $\vect{w}$? + \item Déterminer si les points $A$, $B$ et $C$ sont alignés. + \end{enumerate} + \item On définit un point $M(1; y)$. Déterminer la valeur de $y$ pour que $\vect{AM}$ et $\vect{v}$ soient colinéaires. + \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] {$\vect{x}$} ++(3, -2); + \draw [->, very thick] (0, 0) -- node [midway, above] {$\vect{w}$} ++(-2, 1); + + \end{tikzpicture} + \end{minipage} +\end{exercise} + +% ----- + +\begin{exercise}[subtitle={Équation de droite}, step={1}, origin={Création}, topics={ }, tags={ }, points=5] + Dans cet exercice, les questions sont indépendantes. Pour répondre à une question, il n'est donc pas nécessaire d'avoir répondu aux questions précédentes. + \begin{enumerate} + \item Proposer une équation de droite qui correspond à la description suivante: "l'ordonnée est égale à deux fois l'abscisse plus 1" + \item On définit la droite $(d)$ par l'équation $y = 2x - 5$. Parmi les points suivants le(s)quel(s) sont sur cette droite? + \[ + A(1; -3) \qquad B(4; 1) \qquad C(-2; -9) + \] + \item On définit la droite $(c)$ par l'équation $y = 5x - 1$. Quel doit être l'ordonnée du point $A(2; y)$ pour qu'il soit sur cette droite? + \item La droite $(e)$ passe par les points $A(2; 5)$ et $B(-2; 0)$. + \begin{enumerate} + \item Rappeler la forme cartésienne d'une équation de droite. + \item Calculer le coefficient directeur de la droite $(e)$. + \item Déterminer l'équation de la droite $(e)$. + \end{enumerate} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Équation de droite}, step={2}, origin={Création}, topics={ }, tags={ }, points=5] + Dans cet exercice, les questions sont indépendantes. Pour répondre à une question, il n'est donc pas nécessaire d'avoir répondu aux questions précédentes. + \begin{enumerate} + \item Proposer une équation de droite qui correspond à la description suivante: "l'ordonnée est égale à trois fois l'abscisse moins 4" + \item On définit la droite $(d)$ par l'équation $y = 5x - 2$. Parmi les points suivants le(s)quel(s) sont sur cette droite? + \[ + A(1; 3) \qquad B(-2; -12) \qquad C(2; 12) + \] + \item On définit la droite $(c)$ par l'équation $y = 3x - 5$. Quel doit être l'ordonnée du point $A(2; y)$ pour qu'il soit sur cette droite? + \item La droite $(e)$ passe par les points $A(3; 6)$ et $B(0; -3)$. + \begin{enumerate} + \item Rappeler la forme cartésienne d'une équation de droite. + \item Calculer le coefficient directeur de la droite $(e)$. + \item Déterminer l'équation de la droite $(e)$. + \end{enumerate} + \end{enumerate} +\end{exercise} diff --git a/2nd/Evaluations/DS_2022-05-20/sujet.pdf b/2nd/Evaluations/DS_2022-05-20/sujet.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c2e91cf55475bfc4b49e68045e357ce46048972b GIT binary patch literal 33985 zcmce;1F&sNwk^7B+t|ytv6pSzwrz7S+qP}nwryMgocsQLRX<)u#g7+JcSa0EjyW@D zkJb{sx1NJUPDq4?ftCe|WOAu*acFgRa2Sf2fS$nCzygY!n}ANq-OiYRPEFRp!r0J> zfKJib!0EqAL~I?b3F!Vl|JOGd2OQD_+L-{ z>-<-_g0Z8mvxA|rBLT}_MGAjaWp3qU?C{ssO5e#?$k@=<=&yFAjBQMv%m^4*2zYr3 z{`&*v=;UCmZw=+Pz5qWhM?Sp^1OWa8cnf80WAy(%`RnfQ|IhYU&HrZ&G;P@Z4 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b/2nd/Evaluations/DS_2022-05-20/sujet.tex @@ -0,0 +1,28 @@ +\documentclass[a4paper,12pt]{article} +\usepackage{myXsim} + +% Title Page +\title{ DS9 \hfill Sujet 1} +\tribe{2nd} +\date{2022-05-20} +\duree{1h} + +\DeclareExerciseCollection[step=1]{banque} +\xsimsetup{collect} + + +\begin{document} +\thispagestyle{empty} +\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: + diff --git a/2nd/Evaluations/DS_2022-05-20/sujet_2.pdf b/2nd/Evaluations/DS_2022-05-20/sujet_2.pdf new file mode 100644 index 0000000000000000000000000000000000000000..19479533fdaa8ddb48a0ec7b46fad73ee877a885 GIT binary patch literal 33280 zcmce;1CS`q(k48%ZQHhO+qP|c&e-M|+qP}nGiPkizVGh8dvCWb{{ z%F4*>?816^sP*LPGW)1loVy%0R%#@V|Cl0(x0P7bnZV>5TvD z%>QivqAQs?+q*g$n>rJ){zX#yYbZ+_7gMLdjy8rarXr@s_9lPvl`*w5cd;N~WF_F^ 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HcmV?d00001 diff --git a/2nd/Evaluations/DS_2022-05-20/sujet_2.tex b/2nd/Evaluations/DS_2022-05-20/sujet_2.tex new file mode 100644 index 0000000..95c351e --- /dev/null +++ b/2nd/Evaluations/DS_2022-05-20/sujet_2.tex @@ -0,0 +1,28 @@ +\documentclass[a4paper,12pt]{article} +\usepackage{myXsim} + +% Title Page +\title{ DS9 \hfill Sujet 2} +\tribe{2nd} +\date{2022-05-20} +\duree{1h} + +\DeclareExerciseCollection[step=2]{banque} +\xsimsetup{collect} + + +\begin{document} +\thispagestyle{empty} +\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: +