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a/TST_sti2d/DS/DS_20_12_14/DS_20_12_14_rattrap.tex b/TST_sti2d/DS/DS_20_12_14/DS_20_12_14_rattrap.tex new file mode 100644 index 0000000..55aacc9 --- /dev/null +++ b/TST_sti2d/DS/DS_20_12_14/DS_20_12_14_rattrap.tex @@ -0,0 +1,110 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DS 4} +\tribe{Terminale STI2D} +\date{14 décembre 2020} +\duree{30min} + +\pagestyle{empty} +\newcommand{\reponse}[1]{% + \begin{bclogo}[barre=none, logo=]{Réponse} + \vspace{#1} + \end{bclogo} +} + +\begin{document} +\maketitle + +Le barème est donné à titre indicatif, il pourra être modifié. Les questions plus difficiles sont marqués du symbole (*). + +\begin{exercise}[subtitle={Complexes}, points=4] + \noindent + \begin{minipage}{0.6\textwidth} + \begin{enumerate} + \item Soit $z_1 = -2 - 2\sqrt{3}i$. Calculer son module et son argument. + \reponse{5cm} + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.35\textwidth} + \begin{tikzpicture}[baseline=(a.north), xscale=0.6, yscale=0.6] + \tkzInit[xmin=-5,xmax=5,xstep=1, + ymin=-5,ymax=5,ystep=1] + \tkzGrid + \draw (1, 0) node [below right] {1}; + \draw (0, 1) node [above left] {$i$}; + \draw [->, very thick] (-5, 0) -- (5, 0); + \draw [->, very thick] (0, -5) -- (0, 5); + %\tkzAxeXY + \foreach \x in {0,1,...,5} { + % dots at each point + \draw[black] (0, 0) circle(\x); + } + \end{tikzpicture} + \end{minipage} + + \begin{enumerate} + \setcounter{enumi}{1} + \item Soit $z_2$ le complexe de module $r = 2$ et d'argument $\theta = \dfrac{2\pi}{3}$. Déterminer la forme algébrique de $z_2$. + \reponse{2cm} + \item Placer ces deux points dans le plan complexe. + \item (*) Placer dans le plan complexe le point $\ds z = \frac{2i+3}{2 - i}$ + \reponse{3cm} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Intégration}, points=4] + \begin{enumerate} + \item Calculer la primitive des deux fonctions suivantes + \begin{enumerate} + \item $f(x) = 8x^3 - 6x^2 + 12$ + \reponse{2cm} + \pagebreak + \item $g(x) = 3x(x - x^2 + 1)$ + \reponse{2cm} + + \end{enumerate} + \item On note $f(x) = 0.3x^2 + \cos(x)$ et $F(x) = 0.1x^3 + \sin(x)$ une primitive de $f(x)$. + \begin{enumerate} + \item Calculer la quantité $\ds \int_1^3 0.3x^2 + \cos(x) \; dx$ + \reponse{3cm} + + \item Représenter sur le graphique à quoi correspond cette quantité. + + \begin{tikzpicture}[baseline=(a.north), xscale=1.5, yscale=0.5] + \tkzInit[xmin=-5,xmax=5,xstep=1, + ymin=0,ymax=5,ystep=1] + \tkzGrid + \tkzAxeXY + \tkzFct[domain=-5:5,color=red,very thick]% + { 0.3*\x**2 + cos(\x) }; + \end{tikzpicture} + \end{enumerate} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Vrai/faux}, points=2] + Pour chacune des quatre affirmations suivantes, indiquer si elle est vraie ou fausse, en justifiant la réponse. + Il est attribué un point par réponse exacte correctement justifiée. + Une réponse non justifiée n’est pas prise en compte. + Une absence de réponse n’est pas pénalisée. + \begin{enumerate} + \item L'accélération gravitationnelle se calcule avec la formule $g=\dfrac{G\times m}{r^2}$ où $m$ est la masse, $r$ le rayon et $G$ la constante de gravitation. + + \textbf{Affirmation 1:} Pour calculer la masse, on peut utiliser la formule $G = \dfrac{m\times G}{r^2}$ + \reponse{2cm} + + \item (*) \textbf{Affirmation 2:} $F(x) = \dfrac{1}{x}\sin(x)$ est une primitive de $f(x) = \dfrac{-1}{x^2}\sin(x) + \dfrac{\cos(x)}{x}$ + \reponse{2cm} + \end{enumerate} +\end{exercise} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: +