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+\printcollection{banque} + +\newpage + +\maketitle + +\printcollection{banque} +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: diff --git a/1ST/Evaluations/DS_2022-11-28/exercises.tex b/1ST/Evaluations/DS_2022-11-28/exercises.tex new file mode 100644 index 0000000..2bff52f --- /dev/null +++ b/1ST/Evaluations/DS_2022-11-28/exercises.tex @@ -0,0 +1,124 @@ +\begin{exercise}[subtitle={Automatismes}, step={1}, origin={<++>}, topics={ Automatismes }, tags={ }, points={7}] + \begin{enumerate} + \item Faire le calcul suivant + \begin{flalign*} + \frac{2}{3} + \frac{4}{5} = + \end{flalign*} + \item Développer puis réduire l'expression suivante + \begin{flalign*} + (3x - 5)^2 = + \end{flalign*} + \item Calculer 60\% de 30. + \vspace{1cm} + \item Soit $f$ la fonction définie par $f(x) = 3x^2 - 4x +1$. Calculer $f(2)$ + \vspace{1cm} + \item Une robe coûte 120 \euro hors taxe. La TVA fait augmenter le prix de 20\%. À combien sera vendu la robe? + \vspace{1cm} + \item Un prix passe de 50 \euro à 45 \euro. Quel est le taux d’évolution de ce prix, exprimé en pourcentage ? + \vspace{1cm} + \begin{multicols}{2} + + \item Résoudre graphiquement l'équation $f(x) = 3$. + + \begin{tikzpicture}[yscale=0.3, xscale=1, baseline=(a.north)] + \tkzInit[xmin=0,xmax=4,xstep=1, + ymin=0,ymax=10,ystep=1] + \tkzGrid + \tkzAxeX[right space=0.2] + \tkzAxeY[up space=2, step=2] + \draw[very thick, color=red] plot [smooth,tension=0.2] coordinates{% + (0,0) (1,1) (2,3) (3, 5) (4,3) + }; + \draw (3,1) node[above right] {$\mathcal{C}_f$}; + \end{tikzpicture} + \columnbreak + \item Quelle droite correspond à la fonction $f(x) = 3x - 1$? (surligner la bonne) + + \begin{tikzpicture}[scale=0.7] + \begin{axis}[ + axis lines = center, + grid = both, + xlabel = {x}, + xtick distance=1, + ylabel = {$f(x)$}, + ytick distance=1, + ] + \addplot[domain=-2:2,samples=2, color=red, very thick]{3*x-1}; + \addplot[domain=-2:2,samples=2, color=blue, very thick]{-x+3}; + \addplot[domain=-2:2,samples=2, color=green, very thick]{2*x-1}; + \end{axis} + \end{tikzpicture} + \end{multicols} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Contrat hôtelier}, step={2}, origin={E3C}, topics={ Suites }, tags={ }, points={6}] + Un hôtelier loue un local à partir du 1er janvier 2019. Il a le choix entre deux contrats. Dans ces deux contrats, le loyer annuel initial est de 24 000 euros et le locataire s’engage à occuper le local pendant au moins sept ans. + \begin{itemize} + \item Contrat 1 : Le locataire accepte une augmentation annuelle forfaitaire de 1 000 euros du loyer de l’année précédente. On note $v(0)$, le loyer initial au 1er janvier 2019 et $v(n)$ le loyer au 1er janvier de l’année (2019 + n) avec le contrat 2. + \item Contrat 2 : Le locataire accepte une augmentation annuelle de 4 \% du loyer de l’année précédente. On note $u(0)$, le loyer initial au 1er janvier 2019 et $u(n)$ le loyer au 1er janvier de l’année (2019 + n) avec le contrat 1. + \end{itemize} + \begin{enumerate} + \item On s'intéresse au contrat 1. + \begin{enumerate} + \item Quel sera le loyer au 1er janvier 2020? + \item Quelle est la valeur de $v(0)$? + \item Calculer la valeur de $v(1)$ puis de $v(2)$. + \item Quelle est la nature de la suite $v(n)$? Préciser les paramètres. + \end{enumerate} + \item On s'intéresse au contrat 2. + \begin{enumerate} + \item Quel sera le loyer au 1er janvier 2020? + \item Quelle est la valeur de $u(0)$? + \item Calculer la valeur de $u(1)$ puis de $u(2)$. + \item Quelle est la nature de la suite $u(n)$? Préciser les paramètres. + \end{enumerate} + \item On a préparé le tableur suivant + \begin{center} + \includegraphics[scale=0.6]{./fig/tableur} + \end{center} + Quelle formule peut-on entrer dans la cellule C3, puis recopier sur la droite, pour avoir les premiers termes de la suite ? + \end{enumerate} + \pagebreak +\end{exercise} + +\begin{exercise}[subtitle={Production de repas}, step={2}, origin={E3C}, topics={ Fonctions }, tags={ }, points={7}] + Un traiteur propose des repas gastronomiques au prix unitaire de 80 \euro. + + On admet que l’on peut modéliser le coût total de fabrication des repas, exprimé en euro, en fonction du nombre de repas fabriqués, par la fonction représentée graphiquement ci-dessous : + + \begin{center} + \begin{tikzpicture} + \begin{axis}[ + width=0.8\textwidth, + height=0.8\textwidth, + axis lines = center, + grid = both, + minor tick num=4, + major grid style={line width=.5pt,draw=black}, + every minor tick/.style={minor tick length=0pt}, + xlabel = {Production (en repas)}, + ylabel = {Coût (en \euro)}, + ] + \addplot[domain=0:120,samples=50, color=red, very thick]{0.5*x^2 + 19.3*x + 55}; + \end{axis} + \end{tikzpicture} + \end{center} + \begin{enumerate} + \item Par lecture et à la précision que vous permet le graphique : + \begin{enumerate} + \item Déterminer le coût total de fabrication de 50 repas. + \item Déterminer le nombre de repas fabriqués pour un coût total de 4 000 €. + \item Calculer le taux de variation du coût de production 10 repas et 120 repas. + \item On note $C(x)$ la fonction représentée par le graphique ci-dessus. + + Résoudre l'inéquation $C(x) \geq \np{3000}$. + \end{enumerate} + \item On rappelle qu’une « recette » est simplement le fruit d’une vente, sans tenir compte de son coût. + \begin{enumerate} + \item Calculer la recette obtenue pour la vente de 50 repas. + \item On note $R(x)$ la recette en euro obtenue pour la vente de $x$ repas. Tracer la courbe représentative de $R(x)$ sur le graphique. + \item Déterminer, à l’aide du graphique, pour quelles valeurs de la recette est supérieure au coût total de fabrication. Expliquer la démarche utilisée. + \end{enumerate} + \end{enumerate} +\end{exercise} diff --git a/1ST/Evaluations/DS_2022-11-28/fig/graph.png b/1ST/Evaluations/DS_2022-11-28/fig/graph.png new file mode 100644 index 0000000000000000000000000000000000000000..4d4999fc70cc9a085eb0cbae11bf3d5c1d3d7f6f GIT binary patch literal 26330 zcmdqIcRbba8$WIw9LcdM9h^91WY0r%PL7bhGBOK^tYejtos}(nC0i7dnNYGLl%2g- znPud6ANBscKi|*q`*{5R|Mhq@yk7U~9@ltY&+EGG!Zg(tDbFyUAs`^2R93=j6A%zX z2?z+|p~T?N?wMU?@Pg1qTk#q}*(dli_yKYkqlO_MD37K%vLGQKATrfd)l~q`@7=q1 za&q$i{d-?uUq3&;wzjsXPoG*?SlqsSdu?sa+S)oNCnr5UeQs{<>eZ{{%Y;JD;_U#)EhpVoxrlzLm+1uND^ytyl z)Kq7y?giO&6}S;f7;pE+1S{;eEBjo zG&C(OZES4J+uQr$!-rvEVV#|wEiEmPk&*rV{S_4z85tSj;o-Ejw63nM0RaJ4R#vgG zu`gb{c>etP;^N}{`}aS7{FtAgf9cXC2?>ef;^Ksa1Ox)n)YPP>r)O+zeEs_M%*@Pl z=g!sE*0Qp)Ub%AR!-o$dA|k}Z#By?SadB}yJw2wTrc6vsUS3}F^YgvEy{})t{`&Rn zojZ53va)X7x>Zu*qcdmDR9051si_?v9#T?L?(gr@)6+{!OJBQo z&DPd7H8oX9Ny*aEl7WGNj*d=QSve{yN=QhksHn)<+4;eP2MP)bVq#*#!ouq6>b$(X 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+\pgfplotsset{compat=1.18} + +% Title Page +\title{ DS2 \hfill } +\tribe{1ST} +\date{28 novembre 2022} +\duree{1h} + +\DeclareExerciseCollection[step=2]{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: