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z6(a3VpdQGv7tk$a@W><$SNHXtuG=}?)HYr0rlxwD$2ilSRp!JE(cJ%D2tR)ZU;m&h Tt%put9waACCm^6{q(%215Vf-A literal 0 HcmV?d00001 diff --git a/TST_sti2d/DS/DS_20_09_17/DS_20_09_17.tex b/TST_sti2d/DS/DS_20_09_17/DS_20_09_17.tex new file mode 100644 index 0000000..0071cc0 --- /dev/null +++ b/TST_sti2d/DS/DS_20_09_17/DS_20_09_17.tex @@ -0,0 +1,112 @@ +\documentclass[a4paper,12pt]{article} +\usepackage{myXsim} +\usepackage[inline]{enumitem} +\usepackage{tasks} + +% Title Page +\title{DS 1} +\tribe{Terminale STI2D} +\date{17 septembre 2020} +\duree{30min} + +\begin{document} +\maketitle + +Le barème est donné à titre indicatif, il pourra être modifié. + +Une part importante de la note sera dédiée à la rédaction, aux explications et à l'utilisation des notations mathématiques. + +\begin{exercise}[subtitle={QCM}, points=4] + \emph{Pour chaque question, une seule des propositions est exacte. Une réponse exacte rapporte un point. Une réponse fausse, plusieurs réponses ou l'absence de réponse n'ajoutent ni ne retirent aucun point.\\ + Inscrire sur la copie la référence de la question et la lettre de la réponse choisie.\\ + Aucune justification n'est demandée.} + \begin{enumerate} + \item On donne ci-dessous la courbe $\mathcal{C}$ représentative d'une fonction $f$ définie et dérivable sur $\intFO{0}{+\infty}$. On pose + + \begin{minipage}{0.6\textwidth} + \[ + I = \int_{1}^{3} f(x)dx + \] + Un encadrement de $I$ est + \begin{tasks}(3) + \task $1 \leq I \leq 3$ + \task $2 \leq I \leq 4$ + \task $5 \leq I \leq 7$ + \end{tasks} + \end{minipage} + \begin{minipage}{0.4\textwidth} + \begin{tikzpicture}[scale=1, yscale=0.4] + \tkzInit[xmin=-0.1,xmax=5,ymax=5] + \tkzGrid + \tkzAxeXY + \tkzFct[color=red, very thick]{4*x**2/(x**2+1)} + \end{tikzpicture} + \end{minipage} + \item $(4i-2)(3i+1)$ est égale à + \begin{tasks}(4) + \task $-14 - 2i$ + \task $10i - 2$ + \task $10 - 2i$ + \task $10 - 10i$ + \end{tasks} + \item La partie imaginaire de $z = 5i + 3 - 2i + 1$ est égale à + \begin{tasks}(4) + \task $5$ + \task $4$ + \task $-2$ + \task $3$ + \end{tasks} + \item Les solutions de l'inéquations $3x - 3 \leq 5x + 1$ sont + \begin{tasks}(4) + \task $x \geq -2$ + \task $x \leq -2$ + \task $x \geq \frac{1}{2}$ + \task $x \leq \frac{1}{2}$ + \end{tasks} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Ressource en eau}, points=4] + Ci-dessous le débit d'un petit cours d'eau (en $m^3.h^{-1}$) en fonction de l'heure de la journée mesuré dans un barrage hydroélectrique. + + \begin{tikzpicture}[xscale=0.8, yscale=0.6] + \draw (0, 5) node [above] {Débit (en $m^3.h^{-1}$)}; + \draw (0, 0) node [below left] {0}; + \draw (0, 1) node [left] {1000}; + \draw (0, 2) node [left] {2000}; + \draw (12, 0) node [above right] {Heure (en $h$)}; + \draw (3, 0) node [below] {6}; + \draw (6, 0) node [below] {12}; + \draw (9, 0) node [below] {18}; + \draw (12, 0) node [below] {24}; + \draw[very thin, gray, xstep=0.5] (0,0) grid (12,5); + \draw[->, very thick] (-0.5,0) -- (12.5,0); + \draw[->, very thick] (0,-0.5) -- (0,5.1); + + \draw[very thick, color=red] plot coordinates{(0,2) (1.5,2) (3,4) (6,4) (9,1) (10,1) (12,2)}; + \end{tikzpicture} + + \begin{enumerate} + \item Quelle est la quantité total d'eau qui s'est écoulé dans le barrage entre 6h et 12h? + \item Quelle est la quantité total d'eau qui s'est écoulé dans le barrage pendant une journée? + \item Si l'on commencer à remplir un réservoir d'une capacité de \np{24000}$m^3$à 18h, quand sera-t-il plein? + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Technique}, points=3] + Calculer les quantités suivantes en illustrant la quantité calculée par un schéma. + \begin{tasks}(3) + \task $\ds \int_3^7 5 \; dx$ + \task $\ds \int_{0.4}^{0.5} 2x \; dx$ + \task $\ds \int_{10}^{15} x + 3 \; dx$ + \end{tasks} +\end{exercise} + + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: +