import work from year 2015-2016
This commit is contained in:
Benjamin Bertrand
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3e/DS/BB_16_05_18/BB_16_05_28.pdf
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3e/DS/BB_16_05_18/BB_16_05_28.tex
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3e/DS/BB_16_05_18/BB_16_05_28.tex
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\documentclass[a4paper,12pt, table]{/media/documents/Cours/Prof/Enseignements/tools/style/classExamen}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2015_2016}
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% Title Page
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\titre{Brevet Blanc}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Troisième}
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\date{Samedi 28 mai 2015}
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\duree{2 heures}
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%\sujet{}}
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% DS DSCorr DM DMCorr Other
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\typedoc{Other}
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\ptpres{4}
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\begin{document}
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\titlepage
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\renewcommand{\arraystretch}{1}
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\begin{questions}
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\question[5]
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\input{./Juin_2014_Asie_Exo2.tex}
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\pagebreak
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\question[5]
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\input{./Juin_2014_Metro_Exo3.tex}
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\pagebreak
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\question[6]
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\input{./Dec_2014_NC_Exo3.tex}
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\question[9]
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\input{./Sept_2012_Metro_PB.tex}
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\pagebreak
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\question[5]
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\input{./Nov_2014_AMsud_Exo3.tex}
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\pagebreak
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\question[3]
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\input{./Juin_2014_Metro_Exo4.tex}
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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/BB_16_05_18/Bilan/bilan313.pdf
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3e/DS/BB_16_05_18/Bilan/bilan313.pdf
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3e/DS/BB_16_05_18/Bilan/bilan313.tex
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3e/DS/BB_16_05_18/Bilan/bilan313.tex
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12
3e/DS/BB_16_05_18/Dec_2014_NC_Exo3.tex
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3e/DS/BB_16_05_18/Dec_2014_NC_Exo3.tex
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\begin{parts}
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\part
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\begin{subparts}
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\subpart Construire un triangle ABC isocèle en A tel que AB = 5~cm et BC = 2~cm.
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\subpart Placer le point M de [AB] tel que BM = 2~cm.
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\subpart Tracer la parallèle à [BC] passant par M. Elle coupe [AC] en N.
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\end{subparts}
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\part Calculer les longueurs MN et AN en justifiant.
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\part Montrer que les périmètres du triangle AMN et du quadrilatère BMNC sont égaux.
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\end{parts}
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51
3e/DS/BB_16_05_18/Juin_2014_Asie_Exo2.tex
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3e/DS/BB_16_05_18/Juin_2014_Asie_Exo2.tex
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Une corde de guitare est soumise à une tension $T$, exprimée en Newton (N),
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qui permet d'obtenir un son quand la corde est pincée.
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Ce son plus ou moins aigu est caractérisé par une fréquence $f$exprimée en Hertz (Hz).
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\medskip
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\parbox{0.45\linewidth}{La fonction qui à une tension $T$ associe
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sa fréquence est définie par la relation :
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$f(T) = 20\sqrt{N}$.
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On donne ci-contre la représentation
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graphique de cette fonction.}\hfill
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\parbox{0.5\linewidth}{
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\includegraphics[scale=1]{./fig/juin_2014_Asie_Exo2_Graph}
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}
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\medskip
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\textbf{Tableau des fréquences (en Hertz) de différentes notes de musique}
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\medskip
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\hspace{-2.2cm}
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\begin{tabular}{|m{2cm}|*{14}{p{0.8cm}|}}
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\hline
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Notes& Do2& Ré2& Mi2& Fa2& Sol2 &La2& Si2& Do3& Ré3& Mi3& Fa3& Sol3& La3& Si3\\
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\hline
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Fréquences (en Hz)&132& 148,5& 165& 176& 198& 220& 247,5& 264 &297 &330& 352& 396& 440& 495\\
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\hline
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\end{tabular}
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\medskip
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\begin{parts}
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\part Déterminer graphiquement une valeur approchée de la tension à appliquer sur la corde pour obtenir un \og La3 \fg.
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\part Déterminer par le calcul la note obtenue si on pince la corde avec une tension de 220~N environ.
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\part La corde casse lorsque la tension est supérieure à 900~N.
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Quelle fréquence maximale peut-elle émettre avant de casser?
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\end{parts}
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18
3e/DS/BB_16_05_18/Juin_2014_Metro_Exo3.tex
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3e/DS/BB_16_05_18/Juin_2014_Metro_Exo3.tex
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Voici un programme de calcul:
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\begin{center}
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\includegraphics[scale=1.4]{./fig/juin_2014_Metro_Exo3_pgm}
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\end{center}
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\begin{parts}
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\part Montrer que si on choisit 8 comme nombre de départ, le programme donne 12 comme résultat.
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\part Pour chacune des affirmations suivantes, indiquer si elle est vraie ou fausse. On rappelle que les réponses doivent être justifiées.
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\begin{subparts}
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\subpart \textbf{Proposition 1 : } Le programme peut donner un résultat négatif.
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\subpart \textbf{Proposition 2 : } Si on choisit $\frac{1}{ 2}$ comme nombre de départ, le programme donne $\frac{33}{4}$ comme résultat.
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\subpart \textbf{Proposition 3 :} Le programme donne 0 comme résultat pour exactement deux nombres.
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\subpart \textbf{Proposition 4 :} La fonction qui, au nombre choisi au départ, associe le résultat du programme est une fonction linéaire.
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\end{subparts}
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\end{parts}
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3e/DS/BB_16_05_18/Juin_2014_Metro_Exo4.tex
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3e/DS/BB_16_05_18/Juin_2014_Metro_Exo4.tex
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Un sac contient 20 jetons qui sont soit jaunes, soit verts, soit rouges, soit bleus. On considère l'expérience suivante : tirer au hasard un jeton, noter sa couleur et remettre le jeton dans le sac. Chaque jeton a la même probabilité d'être tiré.
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\medskip
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\begin{parts}
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\part Le professeur, qui connaît la composition du sac, a simulé un grand nombre de fois l'expérience avec un tableur. Il a représenté ci-dessous la fréquence d'apparition des différentes couleurs après \np{1000} tirages.
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\begin{center}
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\includegraphics[width=11cm]{./fig/juin_2014_Metro_Exo4_graph}
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\end{center}
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\begin{subparts}
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\subpart Quelle couleur est la plus présente dans le sac ? Aucune justification n'est attendue.
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Le professeur a construit la feuille de calcul suivante :
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\hspace{-2cm}
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\renewcommand{\arraystretch}{0.9}
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\begin{tabularx}{1.1\linewidth}{|c|*{3}{>{\centering \arraybackslash}X|}}\hline
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&A& B& C\\ \hline
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1& Nombre de tirages& Nombre de fois où un jeton rouge est apparu&Fréquence d'apparition de la couleur rouge\\ \hline
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2 & 1 & 0& 0\\ \hline
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3 & 2 & 0& 0\\ \hline
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4 & 3 & 0& 0\\ \hline
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5 & 4 & 0& 0 \\ \hline
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6 & 5 & 0& 0\\ \hline
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7 & 6 & 1& \np{0,166666667}\\ \hline
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8 & 7 & 1& \np{0,142857143}\\ \hline
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9 & 8 & 1& 0,125 \\ \hline
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10 & 9 & 1& \np{0,111111111}\\ \hline
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11 & 10 & 1& 0,1 \\ \hline
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\end{tabularx}
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\renewcommand{\arraystretch}{1}
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\subpart Quelle formule a-t-il saisie dans la cellule C2 avant de la recopier vers le bas ?
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\end{subparts}
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\part On sait que la probabilité de tirer un jeton rouge est de $\dfrac{1}{5}$.
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Combien y a-t-il de jetons rouges dans ce sac?
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\end{parts}
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3e/DS/BB_16_05_18/Nov_2014_AMsud_Exo3.tex
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3e/DS/BB_16_05_18/Nov_2014_AMsud_Exo3.tex
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Le document ci-dessous indique les tarifs postaux pour un envoi depuis la France métropolitaine d'une lettre ou d'un paquet en mode \og lettre prioritaire \fg.
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Ces tarifs sont fonction du poids de la lettre.
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\begin{itemize}
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\item[$\bullet~~$] \textbf{Pour les envois vers :} La France, Monaco, Andorre et secteurs postaux (armée). Complément d’affranchissement aérien vers l'Outre-mer pour les envois de plus de 20~g
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\item[$\bullet~~$] \textbf{Service universel:} Jusqu'à 2~kg
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\item[$\bullet~~$] \textbf{Délai:} J + 1, indicatif
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\item[$\bullet~~$] \textbf{Dimensions:} Minimales : $14 \times 9$ cm, maximales : L + l + H = 100 cm, avec L $< 60$ cm
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\item[$\bullet~~$] \textbf{Complément aérien :}
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\begin{itemize}
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\item Vers zone OM1 : Guyane, Guadeloupe, Martinique, La Réunion, St Pierre et Miquelon, St-Barthélémy, St-Martin et Mayotte : 0,05~\euro{} par tranche de 10~g.
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\item Vers zone OM2 : Nouvelle-Calédonie, Polynésie française, Wallis-et~Futuna, TAAF. : 0,11~\euro{} par tranche de 10~g
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\end{itemize}
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\item[$\bullet~~$] \textbf{Exemple de complément :} Pour un envoi de 32~g vers la Guadeloupe : 1,10\euro{} + $4 \times 0,05$\euro{} = 1,3\euro.
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\end{itemize}
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\setlength\parindent{0mm}
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\begin{center}
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\begin{tabularx}{\linewidth}{|l *{2}{>{\centering \arraybackslash}X|}}\hline
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\multicolumn{2}{|c|}{POIDS JUSQU'À}&TARIFS NETS\\ \hline
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20~g & &0,66\euro \\ \hline
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50~g & &1,10\euro \\ \hline
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100~g & &1,65\euro \\ \hline
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250~g & &2,65\euro \\ \hline
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500~g & &3,55\euro \\ \hline
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1~kg & &4,65\euro \\ \hline
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2~kg & &6,00\euro \\ \hline
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3~kg & &7,00O\euro \\ \hline
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\end{tabularx}
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\end{center}
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\begin{parts}
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\part Expliquer pourquoi le coût d'un envoi vers la France Métropolitaine, en \og lettre prioritaire \fg, d'une lettre de 75~g est de 1,65\euro.
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\part Montrer que le coût d'un envoi à Mayotte, en \og lettre prioritaire \fg, d'une lettre de 109~g est de 3,20~\euro.
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\textbf{Dans cette question ci-dessous, il sera tenu compte de toute trace de réponse même incomplète dans l'évaluation.}
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\part Au moment de poster son courrier à destination de Wallis-et-Futuna, Loïc s'aperçoit qu'il a oublié sa carte de crédit et qu'il ne lui reste que 6,76~\euro{} dans son porte-monnaie.
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Il avait l'intention d'envoyer un paquet de 272 g, en \og lettre prioritaire \fg.
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Peut-il payer le montant correspondant ?
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\part Le paquet a les dimensions suivantes : L = 55~cm l = 30~cm et h = 20~cm. Le guichetier de l'agence postale le refuse. Pourquoi ?
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\end{parts}
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3e/DS/BB_16_05_18/Sept_2012_Metro_PB.tex
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3e/DS/BB_16_05_18/Sept_2012_Metro_PB.tex
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Rémi s'est inscrit à son premier triathlon \og distance olympique \fg.
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Il devra effectuer : 1,5 km de natation, puis 40 km de cyclisme, puis 10 km de course à pied.
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Il a reçu les informations suivantes (Les deux schémas ne sont pas à l'échelle):
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\medskip
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\parbox{0.6\linewidth}{
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\textbf{Natation:} \\
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Partir du point D, rejoindre la bouée A à 250 m du départ, la contourner à 900 sur la gauche, aller jusqu'à la bouée B, la contourner encore à gauche et rejoindre le point de départ D qui est à 650 m de la bouée B.}\hfill
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\parbox{0.3\linewidth}{
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\includegraphics[scale=1]{./fig/Sept_2012_Metro_PB_nage}
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}
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\medskip
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\parbox{0.6\linewidth}{
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\textbf{Cyclisme:} \\
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Départ au point P au pied du col, montée régulière de 20 km jusqu'au sommet S du col avec un dénivelé de 800 m, puis descente par la même route et retour au point P.}
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\hfill
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\parbox{0.3\linewidth}{
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\includegraphics[scale=1]{./fig/Sept_2012_Metro_PB_deniv}
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}
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\medskip
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\textbf{Course à pied} \\
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Circuit de 5 km à parcourir 2 fois.
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\medskip
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\begin{parts}
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\part Partie natation
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Rémi prévoit de parcourir 1~km toutes les 20~minutes.
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Expliquer pourquoi, s'il nage régulièrement, il devrait mettre 30minutes pour la partie natation.
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\part Partie cyclisme
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\begin{subparts}
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\subpart Vérifier par un calcul que la valeur arrondie au mètre près de PH est 19 984 mètres.
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\subpart Rémi sait qu'avec une telle pente il peut prévoir 1 h 30 min pour cette subpartie du triathlon.
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\medskip
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\fbox{
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\parbox{0.5\linewidth}{La pente moyenne $p$ d'une route est un pourcentage qui se calcule de la façon suivante :
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\[p = \dfrac{d}{l} \times 100\]
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où $d$ et $l$ sont exprimées dans la même unité.}\hfill
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\parbox{0.4\linewidth}{
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\includegraphics[scale=1]{./fig/Sept_2012_Metro_PB_pente}
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}}
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\medskip
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Calculer la pente moyenne du col que doit escalader Rémi.
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\end{subparts}
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\part Partie course à pied
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Pour la dernière partie de son triathlon, Rémi prévoit de mettre 20~minutes pour chacun des deux tours du circuit de 5~km.
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Déterminer en km/h sa vitesse moyenne pour la course à pied s'il respecte ses prévisions.
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\part Totalité du triathlon
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Recopier puis completer le tableau suivant \textit{(les temps seront donnés en heures et en minutes)}.
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\begin{tabular}{|c|*{4}{p{2.6cm}|}}
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||||
\hline
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Épreuve & Natation & Cyclisme & Course à pied & Total \\
|
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\hline
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Temps prévus & & 1h30min & & \\
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\hline
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\end{tabular}
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\end{parts}
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7
3e/DS/BB_16_05_18/Sept_2014_poly_Exo1.tex
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3e/DS/BB_16_05_18/Sept_2014_poly_Exo1.tex
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Voici trois calculs effectués à la calculatrice. Détailler ces calculs afin de comprendre les résultats donnés par la calculatrice :
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||||
Calcul \no 1: $\dfrac{5}{6} - \dfrac{3}{4} = \dfrac{1}{12}$
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||||
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Calcul \no 2 : $\sqrt{18} = 3\sqrt{2}$
|
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Calcul \no 3 : $8 \times 10^{15} + 2 \times 10^{15} = 1 \times 10^{16}$
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3e/DS/BB_16_05_18/fig/Sept_2012_Metro_PB_deniv.pdf
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3e/DS/BB_16_05_18/fig/Sept_2012_Metro_PB_deniv.pdf
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3e/DS/BB_16_05_18/fig/Sept_2012_Metro_PB_deniv.svg
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Notes sur BB_16_05_28 pour les 3e
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#################################
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:date: 2016-05-22
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:modified: 2016-05-22
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:tags: DS
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:category: 3e
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:authors: Bertrand Benjamin
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:summary: Note sur le dernier brevet blanc.
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Il y a une erreur dans l'exercice 4. La partie sur la natation n'est pas cohérente entre le schéma et le texte.
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Reference in New Issue
Block a user