Import work from year 2013-2014
This commit is contained in:
Benjamin Bertrand
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3e/DS/Brevet_140604/brevet_mai.tex
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\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classBrevet}
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\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
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\usepackage{lastpage}
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\usepackage{tikz}
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% Title Page
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\titre{}
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% \quatreC \quatreD \troisB \troisPro
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\classe{Troisième}
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\date{4 juin 2014}
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\duree{2 heures}
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%\sujet{%{{infos.subj%}}}
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\vqword{Éxercice}
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\begin{document}
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\thispagestyle{plain}
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\addpoints
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\begin{center}
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~\\[2cm]
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\Huge Brevet Blanc \\ [1cm]
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\LARGE 4 Juin 2014 \\[1cm]
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\fbox{
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\parbox{0.7\textwidth}{~\\[0.5cm] \large Épreuve de : \\ \Huge MATHÉMATIQUES \\ \Large Durée de l'épreuve: 2h00 \\[0.5cm] }
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}
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~\\[1cm]
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\normalsize
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Ce sujet comporte \pageref{LastPage} pages, numérotées de 1 / \pageref{LastPage} à \pageref{LastPage} / \pageref{LastPage} \\
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Dès qu'il vous est remis, assurez vous qu'il est complet.
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\\[1cm]
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L'utilisation de la calculatrice est autorisée. \\
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L'usage du dictionnaire n'est pas autorisé. \\[1cm]
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\begin{center}
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\pointtable[h][questions]
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\end{center}
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4 points sont réservés à la présentation et à la clarté de la rédaction.
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\end{center}
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\clearpage
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\begin{questions}
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\question[6]
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Emma et Arthur ont acheté pour leur mariage 2002 dragées au chocolat et 3731 dragées aux amandes.
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\begin{parts}
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\part Arthur propose de répartir ces dragées de façon identique dans 20 corbeilles. Chaque corbeille doit avoir la même composition.\\
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Combien lui reste-t-il de dragées non utilisées?
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\part Emma et Arthur changent d'avis et décident de proposer des petits ballotins* dont la composition est identique. Ils souhaitent qu'il ne leur reste pas de dragées.
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\begin{subparts}
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\subpart Emma propose d'en faire 90. Ceci convient-il? Justifier.
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\subpart Ils se mettent d'accord pour faire un maximum de ballotins. Combien en feront-ils et quelle sera leur composition?
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\end{subparts}
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\end{parts}
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\textit{* Un ballotin est un emballage pour confiseries, une boîte par exemple.}
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\clearpage
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\question[5]
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Cet exercice est un questionnaire à choix multiple (QCM). Pour chaque ligne du tableau, trois réponses sont proposées, mais une seule est exacte. Toute réponse exacte vaut 1 point. Tout réponse inexacte ou toute absence de réponse n'enlève pas de point.
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Indiquez sur votre copie le numéro de la question et, sans justifier, recopier la réponse exacte (A, B ou C)
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\hspace{-1cm}
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\begin{tabular}{|p{5.5cm}|*{3}{p{3.5cm}|}}
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\hline
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& A & B & C \\
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\hline
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1) $\sqrt{(-7)^2}$ & N'existe pas & Est égal à -7 & Est égal à 7 \\
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\hline
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2) Si deux surfaces ont la même aire alors & elles sont superposables. & elles ont le même périmètre. & leurs périmètres ne sont pas forcement égaux. \\
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\hline
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3) Soit $f$ la fonction définir par:
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\begin{eqnarray*}
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f(x) = 3x - (2x + 7) + (3x + 5)
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\end{eqnarray*}
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& $f$ est une fonction affine. & $f$ n'est pas forcement une fonction affine. & $f$ est une fonction linéaire. \\
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\hline
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4) Une expression factorisée de $(x- 1)^2 - 9$ est ... & $x^2 - 2x - 15$ &$ (x+2)(x-4)$ & $(x-3)(x+3)$ \\
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\hline
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5) Dume a récupéré les résultats d'une enquête sur les numéros qui sont sortis ces dernières années au loto. Il souhaite jouer lors du prochain tirage.
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& Il vaut mieux qu'il joue les numéros qui sont souvent sortis & Il vaut mieux qu'il joue les numéros qui ne sont pas souvent sortis. & L'enquête ne peut pas l'aider. \\
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\hline
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\end{tabular}
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\vfill
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\question[3]
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"Je prends un nombre entier. Je lui ajoute 3 et je multiplie le résultat par 7. J'ajoute le triple du nombre de départ au résultat et j'enlève 21. J'obtiens toujours un multiple de 10."
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Est-ce vrai? Justifier.
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\textbf{Si le travail n'est pas terminé, laisser tout de même une trace de la recherche; Elle sera prise en compte dans l'évaluation.}
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\vfill
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\clearpage
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\question[7]
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Une commune souhaite aménager des parcours de santé sur son territoire. On fait deux propositions au conseil municipale, schématisés ci-dessous:
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\begin{itemize}
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\item Le parcours ACDA
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\item Le parcours AEFA
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\end{itemize}
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Ils souhaitent faire un parcours dont la longueur s'approche le plus possible de 4km.
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\vfill
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Peux-tu les aider à choisir le parcours? Justifie
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\vfill
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\textbf{Attention: La figure proposée au conseil municipale n'est pas à l'échelle, mais les codages et les dimension données sont correctes.}
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\begin{minipage}{0.6\textwidth}
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\begin{tikzpicture}
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\coordinate (A) at (0,0);
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\coordinate (C) at (0,5);
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\coordinate (D) at (2,5);
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\coordinate (E') at (2,0.5);
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\coordinate (E) at (4,1);
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\coordinate (F') at (3,-0.5);
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\coordinate (F) at (6,-1);
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\draw (A) node [below] {$A$}
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-- (C) node [above] {$C$}
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-- (D) node [above] {$D$}
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-- (A);
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\draw (A) -- (E) node [above] {$E$}
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-- (F) node [right] {$F$}
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-- (A);
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\draw (E') node [above] {$E'$}
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-- (F') node [below] {$F'$};
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\draw[->, >=latex] (-2,-1) node [below] {Départ et arrivée.} -- (A);
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\end{tikzpicture}
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\end{minipage}
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\begin{minipage}{0.4\textwidth}
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\begin{itemize}
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\item $AC = 1,4km$
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\item $CD = 1,05km$
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\item $AE' = 0.5km$
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\item $AE = 1,3km$
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\item $AF = 1,6km$
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\item $E'F' = 0.4km$
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\item $(E'F') // (EF)$
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\item L'angle $\widehat{EAF}$ vaut $30^o$
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\end{itemize}
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\end{minipage}
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\vfill
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\clearpage
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\question[8]
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\begin{center}
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\fbox{\parbox{0.8\textwidth}{
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\textit{Les formules suivantes seront à connaître le jour du brevet.}
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\begin{itemize}
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\item Aire d'un disque: $\pi r^2$
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\item Volume d'une boule: $\frac{4}{3} \pi r^3$
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\item Volume d'un cône: $\frac{1}{3} \times $ aire de la base $\times$ hauteur
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\item Volume d'un cylindre: aire de la base $\times$ hauteur.
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\end{itemize}
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}}
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\end{center}
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Voici une bouteille constituée d'un cylindre et d'un tronc de cône surmonté par un goulot cylindrique. La bouteille est pleine lorsque elle est remplie jusqu'au goulot.
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Les dimensions sont notées sur le schéma.
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\begin{parts}
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\begin{minipage}{0.5\textwidth}
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\part Calculer le volume exact de la partie cylindrique de la bouteille puis donner un arrondis au $cm^3$.
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\part Réaliser le patron d'un cylindre de 3cm de rayon et de 5cm de hauteur.
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\end{minipage}
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\hspace{1cm}
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\begin{minipage}{0.4\textwidth}
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\includegraphics[scale=0.4]{./fig/bouteille}
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\end{minipage}
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\part Pour obtenir le tronc de cône, on a coupé un cône par un plan parallèle à la base passant pas $O'$. La hauteur $SO$ du grand cône est de 6cm et la hauteur $SO'$ du petit cône est égale à 2cm.Le rayon de la base du grand cône est de 5cm.
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\begin{minipage}{0.3\textwidth}
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\includegraphics[scale=0.2]{./fig/tronCone}
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\end{minipage}
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\begin{minipage}{0.6\textwidth}
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\begin{subparts}
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\subpart Calculer le volume $V_1$ du grand cône de hauteur $SO$ (donner la valeur exacte).
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\subpart Montrer que le volume $V_2$ du tronc de cône est égal à $\frac{1300\pi}{27}$. En donner une valeur arrondie au $cm^3$.
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\end{subparts}
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\end{minipage}
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\part Parmi les quatre graphiques ci-dessous, l'un d'entre eux représente le volume $V(h)$ de la bouteille en fonction de la hauteur $h$ de remplissage du bidon.
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Quel est ce graphique? Pourquoi les autres ne sont-ils pas convenables?
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\hspace{-2cm}
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\begin{minipage}{0.5\textwidth}
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\begin{tikzpicture}[xscale = {1/3}, yscale = {1/30}]
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\draw (0,0) grid[xstep = 3, ystep= 30] (22,250);
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\foreach \x in {0,3,...,21} \draw(\x,0)node[below]{\x};
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\foreach \x in {0,300,...,2400} \draw( 0,{\x / 10})node[left]{\x};
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\draw[->, >=latex, ultra thick] (0,-0.5) -- (0,260) node [above] {$V(h)$};
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\draw[->, >=latex, ultra thick] (-0,0) -- (22,0) node [above] {$h$};
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\newcommand{\volumes}{ (0,0) (15,120) (19,135) (21, 136)};
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\draw[thick] plot[mark=*] coordinates \volumes;
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\end{tikzpicture}
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\begin{center}
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Graphique 1
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\end{center}
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\end{minipage}
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\begin{minipage}{0.5\textwidth}
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\begin{tikzpicture}[xscale = {1/3}, yscale = {1/30}]
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\draw (0,0) grid[xstep = 3, ystep= 30] (22,250);
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\foreach \x in {0,3,...,21} \draw(\x,0)node[below]{\x};
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\foreach \x in {0,300,...,2400} \draw( 0,{\x / 10})node[left]{\x};
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\draw[->, >=latex, ultra thick] (0,-0.5) -- (0,260) node [above] {$V(h)$};
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\draw[->, >=latex, ultra thick] (-0,0) -- (22,0) node [above] {$h$};
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\newcommand{\volumes}{ (0,0) (15,120) (19,105) (21, 109)};
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\draw[thick] plot[mark=*] coordinates \volumes;
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\end{tikzpicture}
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\begin{center}
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Graphique 2
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\end{center}
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\end{minipage}
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\hspace{-2cm}
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\begin{minipage}{0.5\textwidth}
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\begin{tikzpicture}[xscale = {1/3}, yscale = {1/30}]
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\draw (0,0) grid[xstep = 3, ystep= 30] (22,250);
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\foreach \x in {0,3,...,21} \draw(\x,0)node[below]{\x};
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\foreach \x in {0,300,...,2400} \draw( 0,{\x / 10})node[left]{\x};
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\draw[->, >=latex, ultra thick] (0,-0.5) -- (0,260) node [above] {$V(h)$};
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\draw[->, >=latex, ultra thick] (-0,0) -- (22,0) node [above] {$h$};
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\newcommand{\volumes}{ (0,0) (15,120) (19,245) (21, 247)};
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\draw[thick] plot[mark=*] coordinates \volumes;
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\end{tikzpicture}
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\begin{center}
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Graphique 3
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\end{center}
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\end{minipage}
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\begin{minipage}{0.5\textwidth}
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\begin{tikzpicture}[xscale = {1/3}, yscale = {1/30}]
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\draw (0,0) grid[xstep = 3, ystep= 30] (22,250);
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\foreach \x in {0,3,...,21} \draw(\x,0)node[below]{\x};
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\foreach \x in {0,300,...,2400} \draw( 0,{\x / 10})node[left]{\x};
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\draw[->, >=latex, ultra thick] (0,-0.5) -- (0,260) node [above] {$V(h)$};
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\draw[->, >=latex, ultra thick] (-0,0) -- (22,0) node [above] {$h$};
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\newcommand{\volumes}{ (0,10) (15,125) (19,148) (21, 150)};
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\draw[thick] plot[mark=*] coordinates \volumes;
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\end{tikzpicture}
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\begin{center}
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Graphique 4
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\end{center}
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\end{minipage}
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\end{parts}
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\vfill
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\clearpage
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\question[7]
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Voici le classement des médailles d'or reçues pas les pays participants aux jeux olympiques pour le cyclisme masculin (Source: Wikipedia).
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\textbf{Bilant des médailles d'or de 1896 à 2008}
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\begin{tabular}{|c|c|}
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\hline
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Nation & Or \\
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\hline
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France & 40 \\
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\hline
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Italie & 32 \\
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\hline
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Royaume-Uni & 18 \\
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\hline
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Pays-bas & 15 \\
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\hline
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États-unis & 14 \\
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\hline
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Australie & 13 \\
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\hline
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Allemagne & 13 \\
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\hline
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Union soviétique & 11 \\
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\hline
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Belgique & 6 \\
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\hline
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Allemagnede l'Ouest & 6 \\
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\hline
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Espagne & 5 \\
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\hline
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Allemagne de l'Est & 4 \\
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\hline
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\end{tabular}
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\hspace{2cm}
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\begin{tabular}{|c|c|}
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\hline
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Nation & Or \\
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\hline
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Russie & 4 \\
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\hline
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Suisse & 3 \\
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\hline
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Suède & 3 \\
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\hline
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Tchécoslovaquie & 2 \\
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\hline
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Norvège & 2 \\
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\hline
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Canada & 1 \\
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\hline
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Afrique du Sud & 1 \\
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\hline
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Grèce & 1 \\
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\hline
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Nouvelle-Zélande & 1 \\
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\hline
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Autriche & 1 \\
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\hline
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Estonie & 1 \\
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\hline
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Argentine & 1 \\
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\hline
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\end{tabular}
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\begin{parts}
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\part Voici un extrait du tableur.
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\hspace{-2cm}
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\includegraphics[scale=0.6]{./fig/tableur}
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Quelle formule a-t-on saisie dans la cellule \texttt{O2} pour obtenir le nombre total de pays ayant eut une médaille d'or?
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\part
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\begin{subparts}
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\subpart Calculer la moyenne de cette série (arrondir à l'unité).
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\subpart Déterminer la médiane de cette série.
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\subpart En observant les valeurs prises par la série, donner un argument qui explique pourquoi les valeurs de la moyenne et de la médiane sont différentes?
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\end{subparts}
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\part Pour le cyclisme masculin, 70\% des pays médaillés ont obtenu au moins une médaillés. Quel est le nombre de pays qui on obtenu que des médailles d'argent ou de bronze (arrondir le résultat à l'unité)?
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\textbf{Si le travail n'est pas terminé, laisser tout de même une trace de la recherche. Elle sera prise en compte dans l'évaluation.}
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\end{parts}
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\end{questions}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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3e/DS/Brevet_140604/fig/2014-05-27_16-17-1401200228.jpg
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3e/DS/Brevet_140604/fig/2014-05-27_16-17-1401200228.jpg
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After Width: | Height: | Size: 14 KiB |
BIN
3e/DS/Brevet_140604/fig/bouteille.png
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3e/DS/Brevet_140604/fig/bouteille.png
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378
3e/DS/Brevet_140604/fig/boutielle.svg
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378
3e/DS/Brevet_140604/fig/boutielle.svg
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@@ -0,0 +1,378 @@
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||||
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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||||
<!-- Created with Inkscape (http://www.inkscape.org/) -->
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||||
|
||||
<svg
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||||
xmlns:dc="http://purl.org/dc/elements/1.1/"
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xmlns:cc="http://creativecommons.org/ns#"
|
||||
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
|
||||
xmlns:svg="http://www.w3.org/2000/svg"
|
||||
xmlns="http://www.w3.org/2000/svg"
|
||||
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
|
||||
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
|
||||
width="1052.3622"
|
||||
height="744.09448"
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23
3e/DS/Brevet_140604/index.rst
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23
3e/DS/Brevet_140604/index.rst
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|
||||
Notes sur un brevet blanc
|
||||
#########################
|
||||
|
||||
:date: 2014-06-04
|
||||
:modified: 2014-07-01
|
||||
:tags: DS, Nombres Calculs, Géométrie, Organisation donnees
|
||||
:category: 3e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers brevet_mai.pdf <brevet_mai.pdf>`_
|
||||
|
||||
`Lien vers brevet_mai.tex <brevet_mai.tex>`_
|
||||
|
||||
`Lien vers fig/tableur.png <fig/tableur.png>`_
|
||||
|
||||
`Lien vers fig/tronCone.png <fig/tronCone.png>`_
|
||||
|
||||
`Lien vers fig/bouteille.png <fig/bouteille.png>`_
|
||||
|
||||
`Lien vers fig/2014-05-27_16-17-1401200228.jpg <fig/2014-05-27_16-17-1401200228.jpg>`_
|
||||
Reference in New Issue
Block a user