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Première version du dnb blanc géné

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Bertrand Benjamin 2018-01-23 14:33:02 +03:00
parent cf9af94020
commit fa3afa8547
14 changed files with 1143 additions and 0 deletions
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Pour cuire des macarons, la température du four doit être impérativement de 150~\degres C.
Depuis quelques temps, le responsable de la boutique n'est pas satisfait de la cuisson de ses
pâtisseries. Il a donc décidé de vérifier la fiabilité de son four en réglant sur 150~\degres C et en prenant régulièrement la température à l'aide d'une sonde.
Voici la courbe représentant l'évolution de la température de son four en fonction du temps.
\begin{center}
\includegraphics[scale=1]{./fig/temperature}
\end{center}
\begin{enumerate}
\item La température du four est-elle proportionnelle au temps?
\item Quelle est la température atteinte au bout de $3$ minutes? Aucune justification n'est demandée.
\item De combien de degrés Celsius, la température a-t-elle augmenté entre la deuxième et la septième
minute ?
\item Au bout de combien de temps, la température de 150~\degres C nécessaire à la cuisson des macarons
est-elle atteinte ?
\item Passé ce temps, que peut-on dire de la température du four? Expliquer pourquoi le responsable
n'est pas satisfait de la cuisson de ses macarons.
\end{enumerate}

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\documentclass[a4paper,12pt]{article}
\usepackage{myXsim}
% Title Page
\title{Diplôme National du Brevet
Série générale}
\date{Février 2018}
\duree{2 heures}
\newcolumntype{C}[1]{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}p{#1}}
\begin{document}
\titlepage
\begin{exercise}[subtitle={QCM}]
\subimport{./QCM/}{subject.tex}
\end{exercise}
\begin{exercise}[subtitle={Boite de chocolats}]
\subimport{./Proba/}{subject.tex}
\end{exercise}
\begin{exercise}[subtitle={ASSR}]
\subimport{./Scratch/}{subject.tex}
\end{exercise}
\begin{exercise}[subtitle={Programme de calcul}]
\subimport{./pgm_calc/}{subject.tex}
\end{exercise}
\begin{exercise}[subtitle={Macaron}]
\subimport{./CE_16_graph/}{subject.tex}
\end{exercise}
\begin{exercise}[subtitle={Inspécteur}]
\subimport{./Geo_conso/}{subject.tex}
\end{exercise}
\begin{exercise}[subtitle={La maladroite!}]
\subimport{./TC/}{subject.tex}
\end{exercise}
\end{document}
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% origin: Pondichery Avril 2017 exercice
% theme: Géométrie, Pythagore, consommation
L'inspecteur G. est en mission dans l'Himalaya. Un hélicoptère est chargé de le transporter en haut
d'une montagne puis de l'amener vers son quartier général.
Le pilote : \og Alors, je vous emmène, inspecteur ? \fg
L'inspecteur : \og OK, allons-y ! Mais d'abord, puis-je voir le plan de vol ?\fg
\medskip
Le trajet ABCDEF modélise le plan de vol. Il est constitué de déplacements rectilignes. On a de plus
les informations suivantes :
\begin{itemize}
\item AF= 12,5 km ; AC = 7,5 km ; CF = 10 km ; AB = 6 km ; DG = 7 km et EF = 750 m.
\item (DE) est parallèle à (CF).
\item ABCH et ABGF sont des rectangles
\end{itemize}
\includegraphics[scale=0.4]{./fig/plan_de_vol}
Le pilote : \og Je dois faire le plein \ldots \fg
L'inspecteur : \og Combien consomme votre hélico ? \fg
Le pilote : \og 1,1~L par km pour ce genre de trajet \fg
L'inspecteur : \og Mais le plein nous surchargerait ! 20 L de carburant seront très largement suffisants.\fg
\medskip
\begin{enumerate}
\item Vérifier que la longueur du parcours est de 21 kilomètres.
\item Le pilote doit-il avoir confiance en l'inspecteur G ? Justifier votre réponse.
\end{enumerate}
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Une boîte «Chocodor» contient exactement 10 chocolats au lait, 8 chocolats noirs et 6 chocolats blancs.
Tous les chocolats ont la même forme et sont indiscernables au toucher.
\begin{enumerate}
\item Si l’on prend un chocolat au hasard dans cette boîte, quelle est la probabilité que ce soit un chocolat au lait ?
\item Alexis a acheté une boîte «Chocodor» et a déjà pris un chocolat de chaque sorte. Par gourmandise, il veut en prendre un quatrième sans regarder. Quelle est la probabilité que ce soit un chocolat noir ?
\item Je prends une nouvelle boîte. Comment dois-je modifier la composition de cette boite pour avoir une chance sur trois de prendre un chocolat au lait?
\end{enumerate}

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Cet exercice est un questionnaire à choix multiples (QCM). Pour chaque question, une seule des trois réponses proposées est exacte. Sur la copie, indiquer le numéro de la question et recopier, sans justifier, la réponse choisie. Aucun point ne sera enlevé en cas de mauvaise réponse :
\medskip
\begin{tabular}{|c|p{5cm}|*{3}{p{3cm}|}}
\hline
&Question& Réponse A& Réponse B& Réponse C \\
\hline
1&$\dfrac{1}{9} + \dfrac{1}{6}$ & $\dfrac{2}{15}$ & $ \dfrac{5}{18}$ & $ 0,277 $\\
\hline
2& Un article coûte \np{1240}\euro. Son prix diminue de 5\%. Le montant de cette réduction est égale à :& 5\euro & 620\euro & 62\euro \\
\hline
3& Les diviseurs communs à 30 et à 42 sont: & 1; 2; 3; 5; 6 et 7& 1; 2; 3 et 6& 1; 2; 3; 5 et 7 \\
\hline
4& Dans un sac il y 10 boules blanches et 5 boules noires. On tire au hasard une boule. La probabilité de tirer une noir est & $\dfrac{1}{3}$ & $\dfrac{1}{2}$ & $\dfrac{1}{5}$ \\
\hline
5& $\dfrac{10^{-6}\times 10^4}{10^{-5}}$ est égal à & $10^{-7}$ & $10^{-15}$ & $10^3$ \\
\hline
\end{tabular}
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Voici un programme Scratch:
\begin{center}
\begin{scratch}
\blockinit{quand \greenflag est cliqué}
\blockpen{effacer tout}
\blocksensing{demander \txtbox{Quel est ton âge?} et attendre}
\blockvariable{mettre \ovalvariable{x} à \ovalsensing{réponse}}
\blockifelse{Si \booloperator{\booloperator{\ovalvariable{x} = \txtbox{14}} ou \booloperator{\ovalvariable{x} > \txtbox{14}}} alors }
{
\blocklook{dire \txtbox{Tu as l'âge de conduire un scooter!}}
}{
\blocklook{dire \txtbox{Tu es trop jeune pour conduire un scooter!}}
}
\end{scratch}
\end{center}
\begin{enumerate}
\item Que fait le programme?
\item Que dit le lutin si tu réponds 13?
\item A partir de quel âge a-t-on le droit de conduire un scooter $50cm^3$?
\end{enumerate}

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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?

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3e/DS/DNB_blanc1/pgm_calc/subject.tex Normal file
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On considère le programme de calcul suivant:
\begin{center}
\Ovalbox{
\hspace{1cm}
\begin{minipage}{0.4\textwidth}
Choisir un nombre de départ \\
multiplier ce nombre pas $(-2)$ \\
ajouter 5 au produit \\
multiplier le résultat par 5\\
écrire le résultat obtenu
\end{minipage}
}
\end{center}
\begin{enumerate}
\item
\begin{enumerate}
\item Vérifier que, lorsque le nombre de départ est 2, on obtient 5.
\item Lorsque le nombre de départ est 3, quel résultat obtient-on?
\end{enumerate}
\item Quel nombre faut-il choisir au départ pour que le résultat obtenu soit 0?
\item Arthur prétend que, pour n'importe quel nombre de départ $x$, l'expression $-10x +25$ permet d'obtenir le résultat du programme de calcul. A-t-il raison?
\end{enumerate}