From 6e740a827d5142a5c5b63c093c00b4182832e617 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 10 Dec 2020 11:27:57 +0100 Subject: [PATCH] Feat: DS4 pour les TST --- TST/DS/DS_20_12_11/DS_20_12_11.pdf | Bin 0 -> 78875 bytes TST/DS/DS_20_12_11/DS_20_12_11.tex | 31 ++++++++++ TST/DS/DS_20_12_11/DS_20_12_11_QF.pdf | Bin 0 -> 76955 bytes TST/DS/DS_20_12_11/DS_20_12_11_QF.tex | 51 +++++++++++++++++ TST/DS/DS_20_12_11/exercises.tex | 78 ++++++++++++++++++++++++++ 5 files changed, 160 insertions(+) create mode 100644 TST/DS/DS_20_12_11/DS_20_12_11.pdf create mode 100644 TST/DS/DS_20_12_11/DS_20_12_11.tex create mode 100644 TST/DS/DS_20_12_11/DS_20_12_11_QF.pdf create mode 100644 TST/DS/DS_20_12_11/DS_20_12_11_QF.tex create mode 100644 TST/DS/DS_20_12_11/exercises.tex diff --git a/TST/DS/DS_20_12_11/DS_20_12_11.pdf b/TST/DS/DS_20_12_11/DS_20_12_11.pdf new file mode 100644 index 0000000000000000000000000000000000000000..464c246b8e8fe8a445c5c2dc1b0533235c68f9c7 GIT binary patch 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b/TST/DS/DS_20_12_11/DS_20_12_11.tex new file mode 100644 index 0000000..3e5d233 --- /dev/null +++ b/TST/DS/DS_20_12_11/DS_20_12_11.tex @@ -0,0 +1,31 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} +\usepackage{tasks} + +% Title Page +\title{DS 4 } +\tribe{TST} +\date{11 décembre 2020} +\duree{1h} + +\DeclareExerciseCollection{banque} +\xsimsetup{ + %tribe=TST1, + type=Exercise, +} + + +\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: + diff --git a/TST/DS/DS_20_12_11/DS_20_12_11_QF.pdf b/TST/DS/DS_20_12_11/DS_20_12_11_QF.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7fbc841ca56be63e92fa8f40a706723ff12f5288 GIT binary patch literal 76955 zcmce-W2`XUvMs!9+qP}n>shvK+qP}ew1J`*60&nA&|>(t(aV_FnmL;jFtQT-@8h3UEUcYP90};ftPPw^L`;nAj7^~U_@JDe 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Est-ce que le point $A(3; 11)$ appartient à la droite? + \vfill + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Fonctions polynômes}, points=8, tribe={TST1}, type={Exercise}] + Soit $f$ la fonction définie sur $\intFF{0}{5}$ par + \[ + f(x) = x^3 - 7,5x^2 + 18x - 11,5 + \] + \begin{enumerate} + \item Calculer $f(1)$ puis interpréter. + \item + \begin{enumerate} + \item Calculer $f'(x)$ la dérivée de $f(x)$. + \item Démontrer que $x=3$ et $x=2$ sont des racines de $f'(x)$. + \end{enumerate} + Dans la suite, on supposera que l'on a $f'(x) = 3(x-3)(x-2)$. + \begin{enumerate} + \setcounter{enumii}{2} + \item Tracer le tableau de signe de $f'(x)$ et en déduire les variations de $f$ sur $\intFF{0}{5}$. + \end{enumerate} + \item (Vrai/faux) Les phrases suivantes sont-elles vraies ou fausses. Vous justifierez vos réponses. + \begin{enumerate} + \item $f$ est croissante sur l'intervalle $\intFF{0}{2}$ et décroissante sur l'intervalle $\intFF{2}{3}$. + \item $f$ est une fonction polynôme de degré 2. + \item $f(x)$ a pour maximum 2,5. + \end{enumerate} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Placements}, points=7, tribe={TST1}, type={Exercise}] + \begin{enumerate} + \item Bob a placé, en 2015, \np{2000}\euro sur un compte avec un rendement de 2,5\% par ans. + \begin{enumerate} + \item Quel sera le solde du compte en 2016, et 2020? + \item Si on modélise le solde du compte par la suite $(u_n)$. Quelle est la nature de la suite? Préciser les paramètres. + \item Exprimer $u_n$ en fonction de $n$. + \end{enumerate} + \item Sa copine Sarah a fait un placement similaire qui a débuté en 2015. On note $v_n$ la suite qui modélise le solde de son compte. On supposera qu'elle est géométrique et on a les valeurs suivantes + \[ + u_1 = 2500 \qquad \qquad u_3 = 2700 + \] + \begin{enumerate} + \item Calculer la moyenne géométrique de $u_1$ et de $u_3$ pour démontrer que la valeur de $u_2$ est d'environ \np{2598}. + \item Démontrer que la raison de la suite est $q=1,39$. + \item En déduire le rendement du placement de Sarah. + \item Quelle était la somme que Sarah a placé sur son compte en 2015? + \end{enumerate} + \end{enumerate} +\end{exercise} + + +\collectexercisesstop{banque}