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import work from year 2016-2017

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Benjamin Bertrand
2017-06-16 09:49:23 +03:00
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\documentclass[a4paper,12pt, table]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExamen}
\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
% Title Page
\titre{Diplôme National du Brevet
Série professionnelle}
% \seconde \premiereS \PSTMG \TSTMG
%\classe{308}
\date{Février 2017}
\duree{2 heures}
%\sujet{}}
% DS DSCorr DM DMCorr Other
\typedoc{Other}
\ptpres{5}
\newcolumntype{C}[1]{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}p{#1}}
\begin{document}
\titlepage
\begin{questions}
\question[6]
Pour chacune des affirmations suivantes, indiquer la bonne réponse parmi celles qui sont proposées.
Aucune justification n'est demandée.
\begin{enumerate}
\item Dans un aquarium, il y a 6 poissons rouges, 2 poissons jaunes et 4 poissons verts. On pèche au hasard un poisson.
La probabilité de pecher un poisson vert vaut :
\begin{tabular}{|*{4}{C{3cm}|}}
\hline
$\dfrac{1}{4}$ & $\dfrac{1}{3}$ & $\dfrac{1}{2}$ & $4$ \\
\hline
\end{tabular}
\vfill
\item Une recette de quatre-quarts prévoit pour 8 personnes : 200 g de farine, 200 g de sucre, 200 g de beurre, un sachet de levure et 4 œufs. Avec la même recette, la quantité de farine nécessaire pour 6 personnes est de :
\begin{tabular}{|*{4}{C{3cm}|}}
\hline
100 g & 150 g& 198 g& 266 g \\
\hline
\end{tabular}
\vfill
\item
\begin{minipage}[t]{0.6\textwidth}
Un écran d’ordinateur de forme rectangulaire a pour dimensions L = 30,5 cm et h = 22,9 cm. La longueur de sa diagonale est :
\end{minipage}
\hspace{0.5cm}
\begin{minipage}{0.4\textwidth}
\includegraphics[scale=0.8]{./fig/ecran_ordi}
\end{minipage}
\begin{tabular}{|*{4}{C{3cm}|}}
\hline
26,7 cm & 38,14 cm & 53,4 cm & 1454,66 cm \\
\hline
\end{tabular}
\vfill
\item Le pouce est une unité de longueur, notamment utilisée dans les pays anglo-saxons. Sachant qu’un pouce vaut 2,54 cm, une longueur de 55 pouces mesure :
\begin{tabular}{|*{4}{C{3cm}|}}
\hline
21,65 cm & 57,54 cm & 139,7 cm & 1397 cm \\
\hline
\end{tabular}
\end{enumerate}
\vfill
\pagebreak
\question[6]
\begin{parts}
\part On sait que $RS = 31cm$ et que $ST=13cm$. Calculer la longueur $RT$.
\includegraphics[scale=0.7]{./fig/pythagore}
\part Calculer la longueur $OD$
\begin{minipage}{0.4\textwidth}
\includegraphics[scale=0.5]{./fig/thales}
\end{minipage}
\begin{minipage}{0.4\textwidth}
\begin{itemize}
\item $(AB)$ et $(DC)$ sont parallèles
\item $OA = 4cm$
\item $DC = 15cm$
\item $BA = 6cm$
\item $BC = 8cm$
\end{itemize}
\end{minipage}
\end{parts}
\question[8]
Une entreprise spécialisée dans la distribution de l’eau a établi une facture à l’aide d’un tableur.
\includegraphics[scale=0.4]{./fig/tableau_consomation_eau}
\begin{parts}
\part Combien coûte la consomation d'eau dans cette facture?
\part Que lit-on dans la cellule \texttt{C4}?
\part Pour déterminer le montant de la consommation hors taxe, on a saisi dans la cellule \texttt{D3} la formule \texttt{=B3*C3}.
Si on glisse celle-ci vers le bas, quelle formule obtiendra-t-on dans la cellule \texttt{D5}?
\part Compléter la facture en indiquand les calculs effectués.
\end{parts}
\pagebreak
\question[5]
\begin{center}
\includegraphics[scale=0.4]{./fig/labyrinthe}
\end{center}
On a créé trois programmes pour permettre au poisson de regagner les issues A, B ou C.
\begin{center}
\includegraphics[scale=0.4]{./fig/programmes}
\end{center}
\begin{parts}
\part Quel programme permet d'aller en A? En B? En C?
\part On souhaite simplifier le programme 3, en utilisant un boucle de la forme ci-contre.
\begin{minipage}{0.7\textwidth}
Quelles instructions va-t-on placer à l’intérieur de cette boucle?
\end{minipage}
\begin{minipage}{0.3\textwidth}
\includegraphics[scale=0.3]{./fig/boucle_for}
\end{minipage}
\end{parts}
\pagebreak
\question[7]
Lors de la fête du collège, des bouteilles ont été donnée aux élèves pour qu'ils s'hydratent bien.
Chaque bouteille coûtait 4 \euro. Au total, cela à couté 344 \euro.
\begin{minipage}{0.5\textwidth}
La gestionnaire a fait tombé du café sur la feuille où été indiqué des quantités de bouteilles de chaque type acheté.
Mais elle croit se rappeler qu'elle avait commandé autant de bouteille de boissons sucrées que de jus de fruits.
\end{minipage}
\begin{minipage}{0.5\textwidth}
\includegraphics[scale=0.5]{./fig/tab_diag}
\end{minipage}
Pensez vous que la gestionnaire a raison?
\vfill
\question[7]
\begin{minipage}{0.5\textwidth}
Une affiche rectangulaire a pour dimensions 2 m de hauteur et 3 m de largeur.
\end{minipage}
\begin{minipage}{0.5\textwidth}
\includegraphics[scale=0.9]{./fig/affiche}
\end{minipage}
\begin{parts}
\part
\begin{subparts}
\subpart Calculer l'aire de cette affiche.
\subpart On voudrait agrandir cette affiche pour qu'elle mesure 4 m de hauteur. Quelle serait alors sa largeur?
\end{subparts}
\part Sur cette affiche, on voit une règle qui mesure 60 cm alors qu'elle mesure 20 cm en réalité.
\begin{subparts}
\subpart On mesure le poisson sur l'affiche et on trouve 90 cm. Quelle est la taille de ce poisson en vrai?
\subpart On voudrait dessiner un autre poisson à côté. En vrai, ce poisson mesure 10 cm. Quelle taille va-t-il avoir sur l'affiche?
\end{subparts}
\end{parts}
\vfill
\pagebreak
\question[6]
\begin{minipage}{0.6\textwidth}
Un récupérateur d’eau de pluie, de forme cylindrique, a une hauteur de 80 cm et un diamètre de 60 cm.
L’eau qu’il contient est utilisée pour arroser un jardin.
\end{minipage}
\hspace{1cm}
\begin{minipage}{0.3\textwidth}
\includegraphics[scale=0.4]{./fig/reservoir}
\end{minipage}
\begin{minipage}{0.6\textwidth}
Le volume $V$ d'un cylindre de diamètre $d$ et de hauteur $h$ est donné par la formule:
\begin{eqnarray*}
V = \pi \times \dfrac{d^2}{4} \times h
\end{eqnarray*}
\end{minipage}
\hspace{1cm}
\begin{minipage}{0.3\textwidth}
\includegraphics[scale=0.9]{./fig/cylindre}
\end{minipage}
On rappelle que $\np{1000} cm^3 = 1 L$.
\begin{parts}
\part Montrer que le volume de ce récupérateur est d'environ 226 L.
\part Combien d'arrosoirs de 10 litres peut-on remplir si le récupérateur est rempli?
\part Combien d'arrosoirs peut-on remplir si le récupérateur est rempli aux trois quart?
\end{parts}
%Soit $d$ un entier strictement positif. Soient $A_1, A_2,... A_{d+1}$ des éléments de $\Q^d$. On suppose qu'il n'existe aps d'hyperplan affine de $\R^d$ contenant l'ensemble $S = \{A_1,... A_{d+1}\}$. Soit $\matcal{S}S$ l'eveloppe convexe de l'ensemle $S$. Pour tout $n \in \N$ on pose
%\begin{eqnarray*}
% w_n & = & Card(n\matcal{S}\cap \Z^d)
%\end{eqnarray*}
%On concidère la série formelle
%\begin{eqnarray*}
% W & = & \sum_{n\in\N} w_nT^n
%\end{eqnarray*}
%\begin{enumerate}
% \item Décrire l'ensemble des entiers $q\in\Z$ tel que $qA_i\in\Z^d$ pour tout i de $\{1,...,d+1\}.
%\end{enumerate}
\end{questions}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
\usepackage{multirow}
% Title Page
\titre{EPI VMA}
% \seconde \premiereS \PSTMG \TSTMG
\classe{Troisième}
\date{Mars 2017}
\renewcommand{\arraystretch}{2}
\newcommand{\lexo}{%
\begin{center}
{\Large Aides exercice 3}
\end{center}
Ces aides ne portent que sur la question 4.
\begin{itemize}
\item En \texttt{D6}, on calcule la somme des "Prix HT".
\item En \texttt{D7}, on calcule 6\% de du "Total HT".
\item En \texttt{D8}, on calcule le "total HT" plus la "TVA".
\end{itemize}
\begin{center}
{\Large Aides exercice 5}
\end{center}
Voici quelques questions qui peuvent permettre d'arriver à une réponse.
\begin{itemize}
\item Que dit la gestionnaire?
\item Combien de bouteilles de Thé ont été vendues?
\item Combien de boutielles ont été vendues en tout?
\item Combien de boutielles de jus ont été vendues?
\end{itemize}
}
\geometry{left=15mm,right=15mm, bottom= 15mm, top=15mm}
\pagestyle{empty}
\begin{document}
\lexo
\vfill
\lexo
\vfill
\lexo
\vfill
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "master"
%%% End:

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