corrigés DMs, + activité 2nde + ESPE
authorDenise sur Titasmo <denise.maurice@normalesup.org>
Wed, 9 Mar 2016 17:47:23 +0000 (18:47 +0100)
committerDenise sur Titasmo <denise.maurice@normalesup.org>
Wed, 9 Mar 2016 17:47:23 +0000 (18:47 +0100)
19 files changed:
1ere/DM_6/arbre.pdf [new file with mode: 0644]
1ere/DM_6/arbre.svg [new file with mode: 0644]
1ere/DM_6/arbre2.pdf [new file with mode: 0644]
1ere/DM_6/arbre2.svg [new file with mode: 0644]
1ere/DM_6/dm6.tex
2nde/DM_5/dm5.tex
2nde/DM_5/dm5_corrige.pdf
2nde/DM_5/dm5_enonce.pdf
2nde/DM_5/exo2.ggb [new file with mode: 0644]
2nde/DM_5/exo2.pdf [new file with mode: 0644]
2nde/chapitre8_droites/act_parallele.pdf [new file with mode: 0644]
2nde/chapitre8_droites/act_parallele.tex [new file with mode: 0644]
2nde/chapitre8_droites/act_parallele_suite.pdf [new file with mode: 0644]
2nde/chapitre8_droites/act_parallele_suite.tex [new file with mode: 0644]
2nde/chapitre8_droites/actparallelles.ggb [new file with mode: 0644]
2nde/chapitre8_droites/actparallelles.pdf [new file with mode: 0644]
ESPE/TC_projets/scratch/Quizz ET.sb2 [new file with mode: 0644]
ESPE/TC_projets/seance3 [new file with mode: 0644]
header_a5.tex

diff --git a/1ere/DM_6/arbre.pdf b/1ere/DM_6/arbre.pdf
new file mode 100644 (file)
index 0000000..5a9b9cc
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diff --git a/1ere/DM_6/arbre.svg b/1ere/DM_6/arbre.svg
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index f353b65..932bb4a 100644 (file)
@@ -1,5 +1,6 @@
 \input{../../header.tex}
 
+
 \title{\vspace{-2cm}Classe de 1ere ES1 -- Devoir Maison numéro 6}
 \date{\vspace{-1.5cm}\dateoucorr{Pour le 10 mars}}
 
@@ -17,10 +18,17 @@ Deux clients entrent dans son restaurant, et on considère que leurs choix de pl
 
 \begin{enumerate}
 \item Réaliser un arbre pondéré correspondant à la situation. On pourra noter $C$ l'événement \og le client choisit la choucroute \fg, $R$ l'événement \og le client choisit la raclette \fg, $T$ l'événement \og le client choisit la tartiflette \fg.
+
+\includegraphics[width=10cm]{arbre.pdf}
+
 \item Quelle est la probabilité que les deux clients choisissent la raclette ?
-\item Quelle est la probabilité que les deux clients choisissent le même plat ? \reponse{0,38}
-\item Quelle est la probabilité qu'aucun client ne choisisse de choucroute ?
-\end{enumerate}
+\[ P(RR) = \frac{3}{10} \times \frac{3}{10} = 0,09 \]
+\item Quelle est la probabilité que les deux clients choisissent le même plat ? \reponse{
+\[ P( \text{\og deux fois le même plat \fg}) = P(\{RR; CC; TT \} ) = 0,09 + \frac{1}{5} \times \frac{1}{5} + \frac{1}{2} \times \frac{1}{2} = 0,09 + 0,04 + 0,25 = 0,38\]}
+\item Quelle est la probabilité qu'aucun client ne choisisse de choucroute ? \reponse{
+\[P(\text{\og aucune choucroute \fg}) = P(\{ RR; RT; TR; TT \}) = 0,09 + \frac{3}{10} \times \frac{1}{2} + \frac{1}{2} \times \frac{3}{10} + 0,25 = 0,09 + 0,15 + 0,15 + 0,15 = 0,54 \]
+}
+\end{enumerate} 
 
 Pour la Saint-Valentin, le gérant du restaurant propose de faire une formule pour deux personnes, à un prix unique quel que soit les plats choisis. Il sait que la choucroute lui coûte, à fabriquer, \ueur{5,50} par personne, la tartiflette \ueur{4,50} par personne, et la raclette \ueur{6} par personne. Pour ce menu spécial, et uniquement lorsque les deux amoureux ont choisi le même plat, les deux portions sont alors servies dans un même plat, et cela coûte au gérant \ueur{1} de moins sur le prix global des deux plats (par exemple, deux raclettes ne coûtent pas \ueur{12} mais \ueur{11}).
 
index 578fee0..cd02bce 100644 (file)
@@ -56,11 +56,37 @@ Dans le repère orthonormé $(O;I,J)$ d'unité \ucm{1}, on considère les points
 \vspace{-1.5em}
 \begin{enumerate}
 \item Faire une figure.
+\reponse{
+
+\includegraphics[width=9cm]{exo2.pdf}
+}
 \item Prouver que le triangle $ABC$ est rectangle.
+\reponse{On calcule :
+\[ AB = \sqrt{(6-0)^2 + (0-4)^2} = \sqrt{36 + 16} = \sqrt{52} = 2\sqrt{13}\]
+\[ AC = \sqrt{(6-1)^2 + (0-(-1))^2} = \sqrt{25 + 1} = \sqrt{26} \]
+\[ BC = \sqrt{(0-1)^2 + (4-(-1))^2} = \sqrt{1 + 25} = \sqrt{26}\]
+
+On a, d'une part $AB^2 = 52$.
+
+D'autre part, $AC^2 + BC^2 = 26 + 26 = 52$.
+
+Donc par la réciproque du théorème de Pythagore, le triangle $ABC$ est rectangle en $C$ (il est même rectangle isocèle puisque $AC=BC$).
+}
+
 \item On appelle $K$ le milieu du segment $[AB]$.
 \begin{enumerate}
 \item Calculer les coordonnées de $K$.
+\reponse{\[ x_K = \frac{6+0}{2} = 3 \qquad y_K = \frac{0+4}{2} = 2\]
+Donc $K(3; 2)$.}
+
 \item Prouver que $K$ appartient à la médiatrice de $[OC]$.
+\reponse{
+On calcule les distances $KO$ et $KC$ :
+\[ KO = \sqrt{(3-0)^2 + (2-0)^2} = \sqrt{9 + 4} = \sqrt{13} \]
+\[ KC = \sqrt{(3-1)^2 + (2-(-1))^2} = \sqrt{4 + 9} = \sqrt{13}\]
+On a $KO=KC$, donc $K$ est équidistant de $O$ et de $C$, ce qui veut dire qu'il est sur la médiatrice de $[0C]$.
+}
+
 \end{enumerate}
 
 \end{enumerate}
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diff --git a/2nde/DM_5/exo2.ggb b/2nde/DM_5/exo2.ggb
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diff --git a/2nde/chapitre8_droites/act_parallele.pdf b/2nde/chapitre8_droites/act_parallele.pdf
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diff --git a/2nde/chapitre8_droites/act_parallele.tex b/2nde/chapitre8_droites/act_parallele.tex
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index 0000000..5444de5
--- /dev/null
@@ -0,0 +1,24 @@
+\input{../../header_a5.tex}
+
+\begin{document}
+\begin{enumerate}
+\item Dans le repère orthonormé ci-dessous, lire les coordonnées des points $A$, $B$, $C$, $D$.
+
+\includegraphics[width=\textwidth]{actparallelles.pdf}
+\item Montrer que $ABCD$ est un parallélogramme (voir chapitre 2).
+\item Déterminer les équations des droites $(AD)$ et $(BC)$. Qu'ont-elles en commun ?
+\item Compléter la conjecture suivante : \emph{\og Deux droites d'équations $y=ax+b$ et $y=a'x+b'$ sont parallèles si et seulement si... \fg}
+\item Vérifier cette conjecture sur les droites $(AB)$ et $(CD)$ (parallèles), puis sur les droites $(AB)$ et $(AD)$ (sécantes).
+
+\emph{Vous pouvez essayer cette question si vous ne trouvez pas la conjecture. Au besoin, essayez d'autres droites !}
+
+\item Que dire de la position relative de deux droites d'équation $x=c$ et $x=c'$ ? \emph{Au besoin, aidez-vous d'exemples, puis formulez une conjecture et si possible, démontrez la.}
+
+\item Que dire de la position relative d'une droite d'équation $x=c$ et $y=ax+b$ ? \emph{Même conseil que pour la question précécente.}
+
+\item * Vers une démonstration de la première conjecture (pour ceux qui ont terminé et aiment les défis) : demander la suite !
+
+\end{enumerate}
+
+
+\end{document}
diff --git a/2nde/chapitre8_droites/act_parallele_suite.pdf b/2nde/chapitre8_droites/act_parallele_suite.pdf
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--- /dev/null
@@ -0,0 +1,30 @@
+\input{../../header_a5.tex}
+
+\begin{document}
+On souhaite démontrer la propriété suivante : deux droites d'équations $y=ax+b$ et $y=a'x+b'$ sont parallèles si et seulement si $a=a'$. Voici un raisonnement à compléter (n'hésitez pas à faire une figure approximative !) :
+
+\bigskip
+Soient deux droites $\D : y=ax+b$ et $\D' : y'=a'x+b'$. On considère les points $A$, $B$, $C$, $D$ tels que $A$ soit le point d'abscisse $0$ de $\D$, $B$ le point d'abscisse $1$ de $\D$, $C$ le point d'abscisse $1$ de $\D'$ et $D$ le point d'abscisse $0$ de $\D'$.
+
+Les coordonnées de ces points sont donc : 
+
+\vspace{2cm}
+
+On sait que les droites $(AD)$ et $(BC)$ sont parallèles, car... \dotfill
+\lignepoint
+\lignepoint
+
+On est donc ramenés à montrer la propriété suivante : les droites $(AB)$ (c'est-à-dire $\D$) et $(CD)$ (c'est-à-dire $\D'$) sont parallèles, si et seulement si le quadrilatère $ABCD$ \dotfill
+\lignepoint
+
+Les coordonnées de  $K$, milieu de $[AC]$ sont :
+
+\vspace{1cm}
+
+Les coordonnées de $L$, milieu de $[BD]$ sont :
+
+\vspace{1cm}
+
+On a donc $(AB) // (CD)$ si et seulement si $K=L$, c'est-à-dire...
+
+\end{document}
diff --git a/2nde/chapitre8_droites/actparallelles.ggb b/2nde/chapitre8_droites/actparallelles.ggb
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diff --git a/ESPE/TC_projets/scratch/Quizz ET.sb2 b/ESPE/TC_projets/scratch/Quizz ET.sb2
new file mode 100644 (file)
index 0000000..76bd64b
Binary files /dev/null and b/ESPE/TC_projets/scratch/Quizz ET.sb2 differ
diff --git a/ESPE/TC_projets/seance3 b/ESPE/TC_projets/seance3
new file mode 100644 (file)
index 0000000..b81e443
--- /dev/null
@@ -0,0 +1,39 @@
+Programmation et LEGO MINDSTORM
+
+Défis par groupe, fiches avec ces défis (2 séances)
+
+Après des groupes par niveau mais deux disciplines mélangées --> défi ?
+
+séance d'après : défi complexe à réaliser
+
+Dernière séance : présentation de tout.
+
+----------------
+LEGO :
+
+branchement en USB, on uploade le programme sur le mini ordi bloc.
+4 prises de chaque côté
+-> moteurs à brancher (ABCD)
+-> capteurs à brancher (1234) : bouton contact, capteur luminosité/couleur, capteur distance, gyroscope
+Connecteurs de téléphone entre deux
+
+Bouton central <-> bouton play sur le logiciel
+
+Instructions :
+Vert : moteurs et output
+orange : structures conditionnelles et boucles
+jaune : capteurs
+rouge : données & traitement
+bleu : avancé
+cyan : ?
+
+mettre le prog sur le robot : flèche verte et poum (et il le lance). Le relancer avec le bouton central du robot
+
+
+
+-----
+
+Faire un tour = x secondes = y tours de roue
+1512 pour un tour, 4,2 tour
+
+avancer : 17.7 cm par tour de roue
index 1620ee1..eed42ea 100644 (file)
 \end{array}
 \right.
 }}
+
+\newcommand\lignepoint{{
+
+~\dotfill
+
+\smallskip
+
+}}