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\begin{question}{Exponentielle vers algébrique} + La forme algébrique du nombre $z = 2e^{\frac{\pi}{3}i}$ est + \begin{reponseshoriz} + \bonne{$1 + \sqrt{3}i$} + \mauvaise{$\sqrt{3} + i$} + \mauvaise{$\sqrt{2} + \sqrt{2}i$} + \mauvaise{$\frac{1}{2} - \frac{\sqrt{3}}{2} i$} + \end{reponseshoriz} + \end{question} +} + +\element{expComplexe}{ + \begin{question}{Multiplication complexes} + Soit $z_A = 2e^{\frac{\pi}{2}i}$ et $z_B = 4e^{\pi i}$. Alors $z_A \times z_B$ vaut + \begin{reponseshoriz} + \bonne{$8e^{i \frac{3\pi}{2}}$} + \mauvaise{$8e^{i\pi}$} + \mauvaise{$2e^{-i^2}$} + \mauvaise{impossible} + \end{reponseshoriz} + \end{question} +} + +\element{expComplexe}{ + \begin{question}{Quotient complexes} + Soit $z_A = 3e^{\frac{\pi}{6}i}$ et $z_B = e^{\frac{\pi}{2}i}$. Alors $\frac{z_A}{z_B}$ vaut + \begin{reponseshoriz} + \bonne{$3e^{-i\frac{\pi}{3}}$} + \mauvaise{$3e^{i\frac{\pi}{3}}$} + \mauvaise{$3e^{-i\times0}$} + \end{reponseshoriz} + \end{question} +} +\setgroupmode{expComplexe}{withreplacement} + +\element{exponentielle}{ + \begin{question}{Dérivation} + Soit $f(x) = (4x - 2)e^{5x}$ alors sa dérivée est + \begin{reponseshoriz} + \bonne{$f'(x) = e^{5x}(20x-6)$} + \mauvaise{$f'(x) = (4x+2)e^{5x}$} + \mauvaise{$f'(x) = 20e^{5x}$} + \mauvaise{$f'(x) = 4 + 5e^{5x}$} + \end{reponseshoriz} + \end{question} +} + +\element{exponentielle}{ + \begin{question}{Primitive} + Soit $g(x) = 24e^{-6x}$ alors sa primitive est + \begin{reponseshoriz} + \bonne{$F(x) = -4e^{-6x}$} + \mauvaise{$F(x) = -144e^{-6x}$} + \mauvaise{$F(x) = \frac{1}{-6}e^{-6x}$} + \mauvaise{$F(x) = 24 - 6e^{-6x}$} + \end{reponseshoriz} + \end{question} +} + +\element{exponentielle}{ + \begin{question}{Calculer intégrale} + La valeur exacte de $\displaystyle \int_0^5 e^{2x} \; dx$ vaut + \begin{reponseshoriz} + \bonne{$0.5(e^{10} - 1)$} + \mauvaise{$0.5e^{5} - 0.5$} + \mauvaise{$2(e^{10} - 1)$} + \mauvaise{$2e^{10}$} + \end{reponseshoriz} + \end{question} +} + +\element{exponentielle}{ + \begin{question}{Vérifier une primitive} + Soit $f(x) = (3x^2 + 2x + 3)e^{3x}$. Alors une primitive de $f(x)$ est + \begin{reponseshoriz} + \bonne{$F(x) = (x^2 + 1)e^{3x} + 100$} + \mauvaise{$F(x) = (9x + 6)e^{3x}$} + \mauvaise{$F(x) = (x^2+2)e^{3x}$} + \end{reponseshoriz} + \end{question} +} +\setgroupmode{exponentielle}{withreplacement} + +\exemplaire{2}{ + + \noindent{\bf QCM \hfill DS 6} + + \begin{minipage}{.4\linewidth} + \centering\Large\bf DS 6 - Tsti2d \\ 25/02/2021 + + %\normalsize Durée : 10 minutes. + \end{minipage} + \begin{minipage}{.6\linewidth} + \champnom{% + \fbox{ + \begin{minipage}{0.8\linewidth} + Nom, prénom, classe: + + \vspace*{.5cm}\dotfill + \vspace*{1mm} + \end{minipage} + } + + } + + \AMCcodeGridInt[h]{etu}{2} + \end{minipage} + + \begin{center}\em + + Aucun document n'est autorisé. + L'usage de la calculatrice est interdit. + + \end{center} + + %%% fin de l'en-tête + + \restituegroupe[4]{expComplexe} + \restituegroupe[4]{exponentielle} + + %\AMCaddpagesto{2} +} + +\end{document}