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+\usetikzlibrary{decorations.markings} +\pgfplotsset{compat=1.18} + +% Title Page +\title{ DS4 \hfill Automatismes} +\tribe{1ST} +\date{1 février 2023} +\duree{1h} + +\DeclareExerciseCollection[step=1]{banque} +\xsimsetup{collect} + +\pagestyle{empty} + +\begin{document} +\input{exercises.tex} + +\maketitle + +\printcollection{banque} + +\newpage + +\maketitle + +\printcollection{banque} +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: diff --git a/1ST/Evaluations/DS_2023-02-01/exercises.tex b/1ST/Evaluations/DS_2023-02-01/exercises.tex index 016ffc6..f29e8fe 100644 --- a/1ST/Evaluations/DS_2023-02-01/exercises.tex +++ b/1ST/Evaluations/DS_2023-02-01/exercises.tex @@ -1,7 +1,72 @@ -\begin{exercise}[subtitle={Technique}, points=6] +\begin{exercise}[subtitle={Automatismes}, step={1}, points=6] + \begin{enumerate} + \item Mettre sous la forme d'une seule puissance \\ + $10^3 \times 10^{-7} = $ + \vfill + \item Mettre sous la forme d'une seule puissance \\ + $\dfrac{(10^{-1})^2}{10^2}=$ + \vfill + + \item Augmenter de 15\% revient à multiplier par: + \vfill + \item Développer et réduire \\ + $(6x-3)(2x-1) = $ + \vfill + \item Résoudre l'inéquation suivante\\ + $-6x + 30 \geq 4x$ + \vfill + + \item On nous propose un placement qui rapporte 100\euro par ans si l'on dépose la somme de \np{4000}\euro à l'ouverture. + + On modélise la quantité d'argent de ce placement par la suite $(u_n)$. + + Quelle est la nature de la suite ? Préciser les paramètres. + \vfill + + \item Soit $(u_n)$ la suite géométrique de raison 5 et de premier terme 100. Calculer la valeur de $u_3$. + \vfill + + \item Tracer le tableau de signes de la fonction $f$ représentée par le graphique ci-dessous. + + \begin{tikzpicture}[scale=0.5] + \begin{axis}[ + axis lines = center, + grid = both, + xlabel = {x}, + xtick distance=1, + ylabel = {$f(x)$}, + ytick distance=1, + ] + \addplot[domain=-2:4,samples=20, color=red, very thick]{-(x-3)*(x+1)}; + \end{axis} + \end{tikzpicture} + \end{enumerate} \end{exercise} -\begin{exercise}[subtitle={Le virus!}, points=6] +\begin{exercise}[subtitle={Technique}, step={2}, points=6] + On définit la fonction $f(x) = 0.5x^2 - 3x + 10$. On souhaite étudier les variations de cette fonction. + \begin{enumerate} + \item Calculer la dérivée $f'$ de la fonction $f$. + \item Étudier le signe de $f'(x)$. Pour quelle valeurs de $x$ le nombre $f'(x)$ est positif? + \item En déduire les variations de la fonction $f$. Vous représenterez ces variations sous forme de tableau. + \item Tracer sur l'annexe le graphique d'une fonction dont les variations correspondent au tableau obtenu à la question précédente. + \end{enumerate} +\end{exercise} + +\begin{annexe} + \begin{center} + \begin{tikzpicture}[scale=1] + \tkzInit[xmin=-5,xmax=5, + ymin=-20,ymax=20, + xstep=1,ystep=5] + \tkzAxeX[thick, poslabel=right,label=] + \tkzAxeY[thick, poslabel=above,label=] + \tkzGrid + \end{tikzpicture} + \end{center} +\end{annexe} + +\begin{exercise}[subtitle={Le virus!}, step={2}, points=6] On s'intéresse à la propagation d'une maladie dans une ville de 130000 habitants. La fonction $f$ définie sur l'intervalle $\intFF{0}{40}$ par \begin{align*} f(x) &= -30x^2 + 1260x + 4000 @@ -43,5 +108,13 @@ \end{tikzpicture} \end{annexe} -\begin{exercise}[subtitle={Probailités}, points=6] +\begin{exercise}[subtitle={Probabilités}, step={2}, points=6] + On joue 3 fois au même jeu de hasard où l'on sait que l'on a 1 chance sur 3 de gagner à chaque partie. + \begin{enumerate} + \item Faire un arbre représentant la situation. + \item Lister les issues possibles. A-t-on une situation d'équiprobabilité? + \item Quelle est la probabilité de gagner aux deux premières parties puis de perdre la dernière? + \item Quelle est la probabilité de gagner une seule partie? + \end{enumerate} + \end{exercise} diff --git a/1ST/Evaluations/DS_2023-02-01/sujet.pdf b/1ST/Evaluations/DS_2023-02-01/sujet.pdf index a3604429763cca1ae936ea65913e3a52e9dacd1d..ea478b6299e12c1bc0aeff108692f632a8734b22 100644 GIT binary patch literal 40158 zcmce-1CS_9w=LMVZQHhO+qP}nwr$(yY1=w&>$JP)eD}?pdn4YR8xs@p{}qu{6P*1;w@c}-DN7p{Q>VXI8$%aU5mRG(lfQmtOzq5FEC?7`3HbO3 z{`Udp?BZl1Ll8CB+UOz!T*h}|Ea_?Gc&ONXOaKU62GE78Hdw}*!!aX8$RL?X*)m&aHXma z@Wf2JeK2PXProMk^l;DJ0iG#Sx>XBY&`QM=EfZ$!!N~aGcn@0N&-37j9C^P}i({z( z)Q_XGMeBP=|Fr+}D?NR!o<1Lcl?ExpHSO~FGM}CU;3rZPFjK!q z)q)I{#`pW$!|C+iM3s)#{Hp|I2yA@XCTFHv?vDr?Ey$x5v^2YJ1VbLD@l;u;Ot#wl zyChJ*!@=zvHagL#UfqBm=>F-9a~2S0Q0=#C_s`?}*B9zp zrCr*eXyblbDJrn-!O^8bYe|GMnIgD;$DVlN 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