Import work from year 2013-2014
This commit is contained in:
Benjamin Bertrand
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4e/DS/4eC/10_milieux_stat/10_milieux_stat.pdf
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4e/DS/4eC/10_milieux_stat/10_milieux_stat.pdf
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4e/DS/4eC/10_milieux_stat/10_milieux_stat.tex
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4e/DS/4eC/10_milieux_stat/10_milieux_stat.tex
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\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classDS}
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\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
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% Title Page
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\titre{2}
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% \quatreC \quatreD \troisB \troisPro
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\classe{\quatreC}
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\date{16 octobre 2013}
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%\duree{1 heure}
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%\sujet{%{{infos.subj%}}}
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% DS DSCorr DM DMCorr Corr
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\typedoc{DS}
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\duree{1 heure}
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\begin{document}
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\maketitle
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Le barème est donné à titre indicatif, il pourra être modifié.
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\begin{Exo}[5]
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Charles a peur que son toit tombe. Il voudrait donc le renforcer avec une pièce de bois placée au milieu du toit. Il a fait le dessin suivant pour mieux se présenter le problème.
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\begin{minipage}{0.5\textwidth}
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\includegraphics[scale=0.3]{fig/charpente}
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\end{minipage}
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\begin{minipage}{0.5\textwidth}
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\begin{enumerate}[a.]
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\item Expliquer pourquoi $\left( AB \right)$ est parallèle à $\left( DE \right)$.
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\item Justifier que $D$ est le milieu de $[AC]$.
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\item Quel devra être la taille de la pièce de bois?
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\end{enumerate}
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\end{minipage}
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\end{Exo}
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\begin{Exo}[6]
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\textbf{Dans cet exercice, il est demandé de faire un schéma à chaque question et mettre en valeur les éléments dont la question parle.}
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$IJKL$ est un quadrilatère quelconque. $A, B, C$ et $D$ sont les milieux respectifs de $[IJ]$, $[JK]$,$[KL]$,$[LI]$
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\begin{enumerate}
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\item Démontrer que $(AB)$ est parallèle à $(IK)$.
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\item Démontrer que $(CD)$ est parallèle à $(IK)$.
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\item En déduire que $(AB)$ est parallèle à $(CD)$.
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\item Démontrer rapidement et de même façon que $(DA)$ est parallèle à $(CB)$.
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\item Quel est la nature du quadrilatère $ABCD$?
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\end{enumerate}
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\end{Exo}
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\begin{Exo}[4]
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Marie a tracé un triangle $ABC$ mais le point $C$ est en dehors de la feuille. Le points $I$ est le milieu de $[CB]$.
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\begin{minipage}{0.5\textwidth}
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\includegraphics[scale=0.2]{./fig/AB_C}
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\end{minipage}
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\begin{minipage}{0.5\textwidth}
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\begin{enumerate}
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\item Construire le point $J$ milieu de $[AB]$ en laissant les traits de construction.
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\item Énoncer le théorème qui vous a permis de faire cette construction.
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\end{enumerate}
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\end{minipage}
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\end{Exo}
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\begin{Exo}[5]
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On étudie les résultats d'une classe à un contrôle. Voici un tableau résumant les notes de cette classe.
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\begin{center}
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\begin{tabular}{|c|*{18}{c|}}
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\hline
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Valeurs & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 \\ \hline
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Effectifs & 1 & 0 & 0 & 2 & 1 & 1 & 2 & 2 & 2 & 1 & 0 & 5 & 2 & 2 & 2 & 0 & 0 & 1 \\ \hline
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\end{tabular}
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\end{center}
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\begin{enumerate}
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\item Combien y a-t-il d'élèves dans cette classe?
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\item Calculer la moyenne des notes de cette classe.
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\item Tracer un diagramme bâtons représentant les notes de cette classe (0.5cm pour une unité horizontalement et 2cm pour une unité verticalement).
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\end{enumerate}
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\end{Exo}
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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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4e/DS/4eC/10_milieux_stat/10_milieux_stat_rattr.pdf
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4e/DS/4eC/10_milieux_stat/10_milieux_stat_rattr.pdf
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4e/DS/4eC/10_milieux_stat/10_milieux_stat_rattr.tex
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4e/DS/4eC/10_milieux_stat/10_milieux_stat_rattr.tex
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\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classDS}
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\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
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% Title Page
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\titre{2}
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% \quatreC \quatreD \troisB \troisPro
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\classe{\quatreC}
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\date{11 novembre 2013}
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%\duree{1 heure}
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%\sujet{%{{infos.subj%}}}
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% DS DSCorr DM DMCorr Corr
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\typedoc{DS}
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\duree{1 heure}
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\begin{document}
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\maketitle
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Le barème est donné à titre indicatif, il pourra être modifié.
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\begin{Exo}[5]
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Charles a peur que son toit tombe. Il voudrait donc le renforcer avec une pièce de bois placée au milieu du toit( à la place de $[DE]$ ou de $[HG]$). Il a fait le dessin suivant pour mieux se présenter le problème.
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\begin{minipage}{0.5\textwidth}
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\includegraphics[scale=0.3]{fig/charpente}
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\end{minipage}
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\begin{minipage}{0.5\textwidth}
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\begin{enumerate}[a.]
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\item Expliquer pourquoi $\left( AB \right)$ est parallèle à $\left( DE \right)$.
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\item Justifier que $D$ est le milieu de $[AC]$.
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\item Quel devra être la taille de la pièce de bois?
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\end{enumerate}
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\end{minipage}
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\end{Exo}
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\begin{Exo}[6]
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$ABCD$ est un quadrilatère quelconque. $E$ est le milieu de $[AD]$ et $F$ le milieu de $[CD]$. La droite passant par $E$ et parallèle à $(AB)$ coupe $(BD)$ en $P$.
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\begin{enumerate}
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\item Faire une figure en prenant bien soin de faire un quadrilatère \textbf{quelconque} et en la codant.
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\item Démontrer que $P$ est le milieu de $[BD]$.
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\item Démontrer que $(PF)$ et $(BC)$ sont parallèles.
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\end{Exo}
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\begin{Exo}[4]
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Marie a tracé un triangle $ABC$ mais les points $B$ et $C$ sont en dehors de la feuille. Le point $J$ est le milieu de $[CB]$.
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\begin{minipage}{0.5\textwidth}
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\includegraphics[scale=0.2]{./fig/triangle_cache.pdf}
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\end{minipage}
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\begin{minipage}{0.5\textwidth}
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\begin{enumerate}
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\item Construire les points $I$ et $K$ milieux, respectifs de $[AB]$ et de $[AC]$en laissant les traits de construction.
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\item Énoncer le théorème qui vous a permis de faire ces constructions.
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\end{enumerate}
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\end{minipage}
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\end{Exo}
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\begin{Exo}[5]
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Aujourd'hui à la cantine c'est petits pois. Tous les élèves décident de compter le nombre de petits pois et comparer leurs assiettes. Voici le tableau résumant le nombre de petits pois.
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\begin{center}
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\begin{tabular}{|c|*{9}{c|}}
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\hline
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Nombre de petits pois& 44 & 46 & 47 & 48 & 49 & 50 & 51 & 52 & 53 \\ \hline
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Effectifs & 1 & 2 & 1 & 4 & 8 & 3 & 1 & 2 & 3 \\ \hline
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\end{tabular}
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\end{center}
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\begin{enumerate}
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\item Quel est l'effectif total de cette série? Que signifie ce nombre?
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\item Calculer la moyenne du nombre de petits pois dans chaque assiette.
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\item Tracer le diagramme bâton représentant le nombre de petits pois dans chaque assiette pour cette table (1cm pour une unité horizontalement et 1cm pour une unité verticalement)
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\end{Exo}
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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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4e/DS/4eC/10_milieux_stat/10_milieux_stat_rattr_corr.pdf
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4e/DS/4eC/10_milieux_stat/10_milieux_stat_rattr_corr.pdf
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4e/DS/4eC/10_milieux_stat/10_milieux_stat_rattr_corr.tex
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4e/DS/4eC/10_milieux_stat/10_milieux_stat_rattr_corr.tex
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\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classDS}
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\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
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% Title Page
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\titre{2}
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% \quatreC \quatreD \troisB \troisPro
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||||
\classe{\quatreC}
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||||
\date{11 novembre 2013}
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%\duree{1 heure}
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||||
%\sujet{%{{infos.subj%}}}
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||||
% DS DSCorr DM DMCorr Corr
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||||
\typedoc{DSCorr}
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\duree{1 heure}
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\begin{document}
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\maketitle
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\begin{Exo}[5]
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\begin{enumerate}
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\item D'après le schéma, on sait que $\left( AB \right) $ est perpendiculaire à $\left( BE \right)$ et que $\left( DE \right)$ est perpendiculaire à $\left( BE \right)$. Or si deux droites sont perpendiculaires à une même troisième droite alors elles sont parallèles. Donc $\left( AB \right)$ est parallèle à $\left( DE \right)$.
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\item On sait que dans le triangle $ABC$, les droites $\left( AB \right)$ et $\left( DE \right)$ sont parallèles et que $E$ est le milieu de $\left[ BC \right]$. Donc d'après le théorème des milieux, $D$ est le milieu de $\left[ AC \right]$.
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\item La taille de la pièce de bois correspond à la longueur $DE$. On sait que $E$ est le milieu de $\left[ BC \right]$ et que $D$ est milieu de $\left[ AC \right]$ donc d'après le théorème des milieux,
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\begin{eqnarray*}
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DE = \frac{AB}{2} = \frac{5}{2} = 2.5m
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\end{eqnarray*}
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Donc $DE$ fait 2,5m.
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\end{enumerate}
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\end{Exo}
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\begin{Exo}[6]
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\begin{enumerate}
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\item \note{Faire le dessin}
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\item On sait que dans le triangle $ABD$la droite $\left( EP \right)$ est parallèle à $\left( AB \right)$ et que $E$ est le milieu de $\left[ AD \right]$. Donc d'après le théorème des milieux, $P$ est le milieu de $\left[ DB \right]$.
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\item Dans le triangle $BCD$, on sait que $F$ est le milieu de $\left[ DC \right]$ et que $P$ est le milieu de $\left[ BD \right]$. Donc d'après le théorème des milieux, $\left( PF \right)$ est parallèle à $\left( BC \right)$.
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\end{enumerate}
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\end{Exo}
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\begin{Exo}[4]
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\begin{minipage}{0.5\textwidth}
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\includegraphics[scale=0.2]{./fig/triangle_cache.pdf}
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\end{minipage}
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\begin{minipage}{0.5\textwidth}
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Pour placer $I$ le milieu de $\left[ AB \right]$, nous allons utiliser le théorème des milieux. On sait que que dans un triangle, si une droite passe par le milieu d'un coté et est parallèle à un autre coté, alors elle va passer par le milieu du troisième coté. Donc si on trace la droite parallèle à $\left( AC \right)$ parssant par $J$, alors cette droite passera par le milieu de $\left[ AC \right]$.
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On peut faire de la même façon pour placer $K$.
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\end{minipage}
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\end{Exo}
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\begin{Exo}[5]
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Aujourd'hui à la cantine c'est petits pois. Tous les élèves décident de compter le nombre de petits pois et comparer leurs assiettes. Voici le tableau résumant le nombre de petits pois.
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\begin{center}
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\begin{tabular}{|c|*{9}{c|}}
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\hline
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Nombre de petits pois& 44 & 46 & 47 & 48 & 49 & 50 & 51 & 52 & 53 \\ \hline
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Effectifs & 1 & 2 & 1 & 4 & 8 & 3 & 1 & 2 & 3 \\ \hline
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\end{tabular}
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\end{center}
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\begin{enumerate}
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\item Calcul de l'effectif total:
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\begin{eqnarray*}
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1+ 0+ 2+ 1+ 4+ 8+ 3+ 1+ 2+ 3 = 25
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\end{eqnarray*}
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L'effectif total est de 25. Il y avait donc 25 élèves lors de ce repas.
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\item Calcul de la moyenne
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\begin{eqnarray*}
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\frac{44 \times 1 + 45 \times 0 + 46 \times 2 + 47 \times 1 + 48 \times 4 + 49 \times 8 + 50 \times 3 + 51 \times 1 + 52 \times 2 + 53 \times 3 }{25}
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&=& 49.24
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\end{eqnarray*}
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La moyenne est donc de 49,24 petit poids.
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\end{enumerate}
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\end{Exo}
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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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4e/DS/4eC/10_milieux_stat/fig/AB1.pdf
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4e/DS/4eC/10_milieux_stat/fig/AB1.pdf
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4e/DS/4eC/10_milieux_stat/fig/AB1.svg
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4e/DS/4eC/10_milieux_stat/fig/AB1.svg
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After Width: | Height: | Size: 11 KiB |
BIN
4e/DS/4eC/10_milieux_stat/fig/triangle_cache.pdf
Normal file
BIN
4e/DS/4eC/10_milieux_stat/fig/triangle_cache.pdf
Normal file
Binary file not shown.
33
4e/DS/4eC/10_milieux_stat/index.rst
Normal file
33
4e/DS/4eC/10_milieux_stat/index.rst
Normal file
@@ -0,0 +1,33 @@
|
||||
Notes sur 10 milieux stat
|
||||
#########################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: DS
|
||||
:category: 4e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers 10_milieux_stat_rattr.tex <10_milieux_stat_rattr.tex>`_
|
||||
|
||||
`Lien vers 10_milieux_stat_rattr_corr.pdf <10_milieux_stat_rattr_corr.pdf>`_
|
||||
|
||||
`Lien vers 10_milieux_stat.pdf <10_milieux_stat.pdf>`_
|
||||
|
||||
`Lien vers 10_milieux_stat.tex <10_milieux_stat.tex>`_
|
||||
|
||||
`Lien vers 10_milieux_stat_rattr_corr.tex <10_milieux_stat_rattr_corr.tex>`_
|
||||
|
||||
`Lien vers 10_milieux_stat_rattr.pdf <10_milieux_stat_rattr.pdf>`_
|
||||
|
||||
`Lien vers fig/triangle_cache.pdf <fig/triangle_cache.pdf>`_
|
||||
|
||||
`Lien vers fig/charpente.pdf <fig/charpente.pdf>`_
|
||||
|
||||
`Lien vers fig/AB1.pdf <fig/AB1.pdf>`_
|
||||
|
||||
`Lien vers fig/AB2.pdf <fig/AB2.pdf>`_
|
||||
|
||||
`Lien vers fig/AB_C.pdf <fig/AB_C.pdf>`_
|
||||
Reference in New Issue
Block a user