From 3a21eb6b6c988465faa37e5ccd9c0e58ae2de6ef Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Mon, 1 May 2023 11:07:51 +0200 Subject: [PATCH] feat(1ST): ajoute DS6 --- .../DS_2023-05-03/automatismes.pdf | Bin 0 -> 25798 bytes .../DS_2023-05-03/automatismes.tex | 36 +++++++ 1ST/Evaluations/DS_2023-05-03/exercises.tex | 99 ++++++++++++++++++ 1ST/Evaluations/DS_2023-05-03/sujet.pdf | Bin 0 -> 36094 bytes 1ST/Evaluations/DS_2023-05-03/sujet.tex | 27 +++++ 5 files changed, 162 insertions(+) create mode 100644 1ST/Evaluations/DS_2023-05-03/automatismes.pdf create mode 100644 1ST/Evaluations/DS_2023-05-03/automatismes.tex create mode 100644 1ST/Evaluations/DS_2023-05-03/exercises.tex create mode 100644 1ST/Evaluations/DS_2023-05-03/sujet.pdf create mode 100644 1ST/Evaluations/DS_2023-05-03/sujet.tex diff --git a/1ST/Evaluations/DS_2023-05-03/automatismes.pdf b/1ST/Evaluations/DS_2023-05-03/automatismes.pdf new file mode 100644 index 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TeX-master: "master" +%%% End: diff --git a/1ST/Evaluations/DS_2023-05-03/exercises.tex b/1ST/Evaluations/DS_2023-05-03/exercises.tex new file mode 100644 index 0000000..9305032 --- /dev/null +++ b/1ST/Evaluations/DS_2023-05-03/exercises.tex @@ -0,0 +1,99 @@ +\begin{exercise}[subtitle={Automatismes}, step={1}, origin={ma tête}, topics={ }, tags={ }] + \begin{enumerate} + \item Développer l'expression suivante $(7-3x)(7+3x)$ + \vfill + \item Calculer l'image de -1 par la fonction $f(x)=-2x^2 - 3$ + \vfill + \item Résoudre l'équation $5x - 7 = 3x - 19$. + \vfill + \item Dériver la fonction suivante: $f(x) = 5x^3 - 10x^2 + 3x - 1$ + \vfill + \item Dériver la fonction suivante: $f(x) = 5x^3 - 10x^2 + 3x - 1$ + \vfill + \item Dans une ferme, il y a 15 poules ce qui représente 25\% du total des animaux. \\Combien y a-t-il d'animaux en tout? + \vfill + \item Une quantité est augmenté de 40\%. Par combien est-elle augmentée? + \vfill + \item On décide de diminuer la production de déchets de 4\% par ans. Aujourd'hui on est à \np{40000} tonnes de déchets par ans. + On modélise la quantité de déchets produit par ans par la suite $(u_n)$. + + Quelle est la nature de la suite ? Préciser les paramètres. + \vfill + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Étude de fonction}, step={2}, origin={ma tête}, topics={ Fonctions, Dérivation }, points={9}] + On considère la fonction $f$ définie sur $\R$ par $f(x) = 0.5x^2 + x - 1.5$ + \begin{enumerate} + \item Parmi les nombres $a$, $b$ et $c$, lesquels sont des racines de $f$ ? + \[ + a = 1 \qquad b = 2 \qquad c = -3 + \] + \item Montrer que la forme factorisée de la fonction $f$ est $f(x) = 0.5(x-1)(x+3)$. + \item Tracer le tableau de signe de la fonction $f$. + \item On souhaite étudier les variations de la fonction $f$. + \begin{enumerate} + \item Calculer $f'(x)$ la fonction dérivée de $f$. + \item Étudier le signe de $f'(x)$. + \item En déduire le tableau de variations de $f(x)$. + \end{enumerate} + \item Parmi les courbes ci-dessous, déterminer celle représentant la fonction $f$. Vous justifierez votre choix. + + \begin{center} + \begin{tikzpicture}[xscale=0.8, yscale=0.8] + \tkzInit[xmin=-5,xmax=5,xstep=1, + ymin=-5,ymax=5,ystep=1] + \tkzGrid + \tkzAxeXY + \tkzFct[domain = -5:5,color=red,very thick]{0.5*(x-1)*(x+3)}; + \tkzFct[domain = -5:5,color=blue,very thick]{-0.5*(x-1)*(x+3)}; + \tkzFct[domain = -5:5,color=green,very thick]{0.5*(x+1)*(x-3)}; + \tkzFct[domain = -5:5,color=gray,very thick]{(x+1)*(x-3)}; + \end{tikzpicture} + \end{center} + + \end{enumerate} + + \pagebreak +\end{exercise} + +\begin{exercise}[subtitle={Probabilités conditionnelles}, step={2}, origin={ma tête}, topics={ Probabilités conditionnelles }, points={6}] + Une agence a lancé une campagne de publicité afin de faire connaître un nouveau produit. Elle a réalisé un sondage sur 1200 d'une zone géographique déterminée afin de connaître l'impact de cette campagne. + \begin{itemize} + \item 28\% des personnes interrogées ont plus de 60 ans. Parmi elles, 40\% ont déclaré connaître le produit. + \item 42\% des personnes interrogées ont entre 25 et 60 ans. Parmi elles, 55\% ont déclaré connaître le produit. + \item Parmi les moins de 25 ans, 25\% ont déclaré ne par connaître le produit. + \end{itemize} + On choisit au hasard une personne interrogée par l’agence de publicité et on considère les évènements suivants : + \begin{itemize} + \item S : « la personne interrogée a plus de 60 ans » ; + \item M : « la personne interrogée a entre 25 et 60 ans » ; + \item J : « la personne interrogée a moins de 25 ans » ; + \item C : « la personne interrogée déclare connaitre le produit ». + \end{itemize} + \begin{enumerate} + \item Compléter le tableau suivant. Vous détaillerez vos calculs sur votre copie. + + \begin{center} + \begin{tabular}{|c|c|c|c|} + \hline + & Connaît le produit & Ne connaît pas & Total \\ + \hline + Plus de 60ans & & & \\ + \hline + Entre 25 et 60 ans & & & \\ + \hline + Moins de 25 ans& & & \\ + \hline + Total & & & \\ + \hline + \end{tabular} + \end{center} + + \item Calculer la probabilité que la personne interrogée ait entre 25 et 60 ans et déclare ne pas connaître le produit. Comment peut-on noter cette ensemble? + \item Pour chacun des ensembles suivants, le décrire en français puis calculer sa probabilité. + \[ + S\cap C \qquad \overline{C} \qquad J\cup C \qquad S \cup \overline{C} + \] + \end{enumerate} +\end{exercise} diff --git a/1ST/Evaluations/DS_2023-05-03/sujet.pdf b/1ST/Evaluations/DS_2023-05-03/sujet.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0e349d825c259fa22d9451486e58ec1f601175fe GIT binary patch literal 36094 zcmce-18`^U(k~i&VovyvZQFJ-vCWB{iJggUYhv4W@{euXPVW1D=YDtZsZiM&ZZbttaXKb?HaN10h2HtW<(YvYI94J?B0D21I9^^N22~GxQz8Zp z1tTj{V`m};6&EAt|DuT7Ioc92{C)ke9!x|G!oqg$MB0B1Wh7!^{9mUo5rdqev!mtT zbf*8+@?Y1#=*p%}b}o*_rcOj`f02~`n#$6~+0^l`yN#i*3oylK(WlevYJ6jMj zu@Uj}6aDuA=j7~YYG@1RzB-3ArARro4F&@J0eTH*`qSk9ZTaiz@9*dMYv%u)9Gw3) zIk^6#axnd^!GDiJnEnRAe@-Jz%>O<~{9ftR}&LZ9cCem8x`w$_@1c)5;`_cLhc9^c2q z{zI#d1Fa^!yNjbOJKvX0Y^e@eeIqkyb{>a)w|qXXUEI|79K*1Ini(DzSTYVDRj(55 zV%qHs*tVMtp0dOXm4&RBwz~QaF@&R#cb&Bl3GZe$*xkX?&w<%Hrap%^!(-F-$jff} 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