From ddc42ff62c2d5f0c0f22d7610666d7c3ee1d2b85 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Wed, 31 May 2023 10:00:31 +0200 Subject: [PATCH] Feat(1ST): DS8 --- .../DS_2023-06-01/automatismes.pdf | Bin 0 -> 28581 bytes .../DS_2023-06-01/automatismes.tex | 36 +++++++ 1ST/Evaluations/DS_2023-06-01/exercises.tex | 99 ++++++++++++++++++ 1ST/Evaluations/DS_2023-06-01/sujet.pdf | Bin 0 -> 29219 bytes 1ST/Evaluations/DS_2023-06-01/sujet.tex | 27 +++++ 5 files changed, 162 insertions(+) create mode 100644 1ST/Evaluations/DS_2023-06-01/automatismes.pdf create mode 100644 1ST/Evaluations/DS_2023-06-01/automatismes.tex create mode 100644 1ST/Evaluations/DS_2023-06-01/exercises.tex create mode 100644 1ST/Evaluations/DS_2023-06-01/sujet.pdf create mode 100644 1ST/Evaluations/DS_2023-06-01/sujet.tex diff --git a/1ST/Evaluations/DS_2023-06-01/automatismes.pdf b/1ST/Evaluations/DS_2023-06-01/automatismes.pdf new file mode 100644 index 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quantité vaut 100. Elle est augmenté deux fois de 50\%. Qu'elle est sa valeur finale? + \vfill + \item On diminue une quantité de 40\%. Quelle taux d'évolution doit-on appliqué pour la faire revenir à sa valeur initiale? + \vfill + \item Développer l'expression suivante : $(2x-1)(x+2)$ + \vfill + \item Quelles sont les racines du polynôme représenté ci-dessous + + \begin{tikzpicture}[xscale=0.6, yscale=0.3] + \tkzInit[xmin=-4,xmax=4,xstep=1, + ymin=-5,ymax=5,ystep=1] + \tkzGrid + \tkzAxeXY + \tkzFct[domain = -5:5,color=red,very thick]% + {-0.5*(x-3)*(x+2)*(x-1)}; + \end{tikzpicture} + + \item Tracer l'allure de la fonction $f(x) = 5x^3 - 2$ + \vfill + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Polynomes}, step={2}, origin={<++>}, topics={ }, tags={ }, points={3}] + On définit $P(x) = -3x^3 - 4x^2 + 2x + 4$ + \begin{enumerate} + \item Parmi les valeurs suivantes, lesquelles sont des racines de $P(x)$? + \[ + -2 \qquad -1 \qquad 0 \qquad 1 \qquad 2 + \] + \item On admet que l'on peut écrire le polynôme sous la forme $P(x) = -2(x-1)(x+2)(x+1)$. Dresser le tableau de signe de $P(x)$. + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Pharmacie}, step={2}, origin={<++>}, topics={ }, tags={ }, points={6}] + Une entreprise pharmaceutique souhaite commercialiser un test de dépistage d’une maladie infectieuse. Elle réalise une étude portant sur un échantillon représentatif de 2000 personnes ayant subi le test et qui vivent dans un territoire victime d’une épidémie de cette maladie. + + Les résultats de cette étude sont les suivants : + \begin{itemize} + \item 15\% des tests sont positifs + \item 85\% des tests sont négatifs. + \end{itemize} + Parmi les personnes qui ont un test positif, 98\% développent la maladie et 2\% sont sains. + Parmi les personnes dont le test est négatif, 1\% développe la maladie et 99\% sont sains. + \begin{enumerate} + \item Compléter le tableau suivant en indiquant les calculs sur votre copie. + + \begin{center} + \begin{tabular}{|c|*{3}{c|}} + \hline + & Tests Positif & Tests Négatifs & Total\\ + \hline + Malade & & & \\ + \hline + Sain & & & \\ + \hline + Total & & & \\ + \hline + \end{tabular} + \end{center} + \item Dans la suite, on note + \begin{itemize} + \item $M$ = "la personne est malade" + \item $N$ = "la personne a un test négatif" + \end{itemize} + \begin{enumerate} + \item Calculer la probabilité des évènements suivants en utilisant la bonne notation + \begin{itemize} + \item La probabilité qu'une personne soit malade + \item Parmi les personnes saines, la probabilité qu'une personne ait un test négatif. + \end{itemize} + \item Calculer les quantités suivantes et interpréter là dans le contexte de l'exercice. + \[ + P(M \cap \overline{N}) \qquad P(M \cup N) \qquad P_M(\overline{N}) + \] + \end{enumerate} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Notation}, step={2}, origin={T1CMATH03533}, topics={ }, tags={ }, points={6}] + On a observé sur 5 ans que la note sur 20, notée $f(x)$, d’un service au bout de $x$ année(s) est donnée par $f(x) = x^3 -6x^2 + 9x$ + +Par exemple, puisque $f(4,5) = 4,5^3 − 6 × 4,5^2 + 9 × 4,5 = 10,125$, le service obtient au bout de 4 ans et demi la note de 10,125 sur 20. + +\begin{enumerate} + \item + \begin{enumerate} + \item Quelle note le service obtient-il au bout d’une année ? + \item Justifier que le service donne pleine satisfaction au bout des 5 années. + \end{enumerate} + \item + \begin{enumerate} + \item Calculer $f'(x)$ sous forme développée. + \item Montrer que $f'(x) = 3(x-1)(x-3)$ + \item Étudier le signe de $f'$ pour en déduire les variations de $f(x)$. + \end{enumerate} +\end{enumerate} +\end{exercise} diff --git a/1ST/Evaluations/DS_2023-06-01/sujet.pdf b/1ST/Evaluations/DS_2023-06-01/sujet.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a5100fb38e7d0ac39d8e76bea766f0a91ceaf093 GIT binary patch literal 29219 zcmce-1#Bft(j{zWW@cu_HZ!!@ZZk78Gcz;WZDwX>W@ct)_TO*z|8}0VqtR-mnJZOQ zD(l|L8;Vn*I43el<%C6P8R=M|NGBG17Y0{m28N(m2p9-#^v$7u{2-uLaIk$_%M(8iTOw3Puh#PWA>y4g{=!rWF1>%FNQy$o|jOQqR#y*vP=f@Xxx^M%E^drUZ;jg721$yx%;5L}6aC&FuPo5(PfNXOtN1*)_~G0-Joee18~6 zp917e33u3~>-K(c1&S7>ma?#*ETGE)e0xFl>-O?^@9Y5{FPKZH4VM6%=j-l%J*J=) zq9!-gU3?hsF5ceyQV}@RMVX5y2)va7R)sZQVfC7NaG^Ia#5(3v?r)iPu?k70nCxj8C13&#dS8al1^*4r zudaaTE}m0gc-?$No97?Mq3opCTLp 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b/1ST/Evaluations/DS_2023-06-01/sujet.tex @@ -0,0 +1,27 @@ +\documentclass[a4paper,12pt]{article} +\usepackage{myXsim} + +% Title Page +\title{ DS8 \hfill } +\tribe{1ST} +\date{01 juin 2023} +\duree{1h} + +\DeclareExerciseCollection[step=2]{banque} +\xsimsetup{collect} + +\pagestyle{empty} + +\begin{document} +\maketitle + +Le barème est donné à titre indicatif, il pourra être modifié. + +\input{exercises.tex} +\printcollection{banque} +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: