From e0729fb3a417e57c6c20681dcf99552be6e0a65e Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 14 Dec 2021 17:08:58 +0100 Subject: [PATCH] Feat: solution du DS4 pour les 2nd --- 2nd/Evaluations/DS_2021-12-10/exercises.tex | 102 ++++++++++++++++++++ 2nd/Evaluations/DS_2021-12-10/sujet.pdf | Bin 194713 -> 203047 bytes 2nd/Evaluations/DS_2021-12-10/sujet.tex | 2 + 3 files changed, 104 insertions(+) diff --git a/2nd/Evaluations/DS_2021-12-10/exercises.tex b/2nd/Evaluations/DS_2021-12-10/exercises.tex index 68cdce0..cd4f013 100644 --- a/2nd/Evaluations/DS_2021-12-10/exercises.tex +++ b/2nd/Evaluations/DS_2021-12-10/exercises.tex @@ -54,6 +54,46 @@ \end{enumerate} \end{exercise} +\begin{solution} + \begin{enumerate}[label={\textbf{Partie \Alph*:}}] + \item + \begin{enumerate} + \item Univers $\Omega$ est composé des éléments suivants + \begin{itemize} + \item Garçon né à Villeouf + \item Garçon né à Bettedeville + \item Garçon né à Sacrévillage + \item Fille né à Villeouf + \item Fille né à Bettedeville + \item Fille né à Sacrévillage + \end{itemize} + \item Probabilités + \[ + P(A) = \frac{536}{1033} \qquad P(B) = \frac{21}{1033} \qquad P(C)= \frac{432}{1033} + \] + \end{enumerate} + \item + \begin{enumerate} + \item En notant $F$ une fille et $G$ un garçon. L'univers est + \[ + \Omega = \left\{ FFF, FFG, FGF, FGG, GFF, GFG, GGF, GGG \right\} + \] + \item Loi de probabilités + \begin{center} + \begin{tabular}{|c|*{8}{c|}} + \hline + Issues & FFF & FFG & FGF & FGG & GFF & GFG & GGF & GGG \\ + \hline + Probabilités & $\frac{1}{8}$ & $\frac{1}{8}$ & $\frac{1}{8}$ & $\frac{1}{8}$ & $\frac{1}{8}$ & $\frac{1}{8}$ & $\frac{1}{8}$ & $\frac{1}{8}$ \\ + \hline + \end{tabular} + \end{center} + \item La probabilités d'avoir deux filles est de $\frac{3}{8}$ + \item La probabilité d'avoir les deux ainés du même sexe est de $\frac{4}{8} = \frac{1}{2}$ + \end{enumerate} + \end{enumerate} +\end{solution} + \begin{exercise}[subtitle={Vecteurs}, step={1}, origin={Un livre}, topics={Vecteur hors repère}, tags={ Vecteurs }, points=4] \noindent \begin{minipage}{0.6\linewidth} @@ -92,6 +132,24 @@ \end{minipage} \end{exercise} +\begin{solution} + \begin{enumerate} + \item Vecteurs correspondant aux descriptions + \begin{enumerate} + \item $\vect{BC} = \vect{v} = \vect{DA}$ + \item $\vect{u} = \vect{CF} = \vect{ED}$ + \item $\vect{v}$ ou $\vect{BC}$ ou $\vect{DA}$ + \end{enumerate} + \item L'image est le point $F$. + \item + \begin{enumerate} + \item $\vect{ED} + \vect{DA} = \vect{EA}$ + \item $\vect{EF} + \vect{DE} = \vect{EC}$ + \item $2\vect{u} = \vect{BA}$ + \end{enumerate} + \end{enumerate} +\end{solution} + \begin{exercise}[subtitle={Géométrie}, step={1}, origin={Ma tête}, points=4, topics={ Démonstration}, tags={ Géométrie }] \begin{minipage}{0.5\linewidth} $ABCD$ est un quadrilatère. Ses diagonales se coupent en un point $O$. On nous dit de plus que @@ -116,6 +174,39 @@ \end{tasks} \end{exercise} +\begin{solution} + \begin{enumerate} + \item On sait que $ABCD$ est un quadrilatère, que $(AB)$ et $(CD)$ sont parallèles et que $(AD)$ et $(BC)$ sont parallèles. + + Or un parallélogramme est un quadrilatère qui a ses cotés opposées parallèles. + + Donc $ABCD$ est un parallélogramme. + + \item On sait que $ABCD$ est un parallélogramme. + + Or un parallélogramme a ses diagonales qui se coupent en leur milieu + + Donc $O$ est le milieu de $[BD]$ et donc $BD = 5$. + + On sait que $DA = 3$, $AB = 4$ et $DB = 5$ et donc que $DA^2 + AB^2 = 3^2 + 4^2 = 25$ et que $DB^2 = 5^2 = 25$ + + Or d'après le théorème de Pythagone + + On en conclu que $DAB$ est un triangle rectangle en $A$ + + + \item On sait que $ABCD$ est un parallélogramme et que $\widehat{DAB}$ est un angle droit. + + Or un parallélogramme qui a un angle droit est un rectangle. + + Donc $ABCD$ est un rectangle. + + Or un rectangle a ses diagonales qui ont la même longueur. + + Donc $AC = DB$. + \end{enumerate} +\end{solution} + \begin{exercise}[subtitle={QCM - questions flashs}, step={1}, origin={Ma tête}, points=5, topics={ }, tags={ QCM }] \emph{Pour chaque question, une seule des propositions est exacte. Une réponse exacte rapporte un point. Une réponse fausse, plusieurs réponses ou l'absence de réponse n'ajoutent ni ne retirent aucun point.\\ Inscrire sur la copie la référence de la question et la lettre de la réponse choisie.\\ @@ -179,3 +270,14 @@ \end{enumerate} \end{exercise} +\begin{solution} + \begin{enumerate} + \item c) + \item a) + \item a) + \item b) + \item c) + \end{enumerate} + +\end{solution} + diff --git a/2nd/Evaluations/DS_2021-12-10/sujet.pdf b/2nd/Evaluations/DS_2021-12-10/sujet.pdf index b5b5b13145a0d6e338fb880c64070ada63dd5203..1f01c27d39223dcd4ec91c5732814ef86d6c1b05 100644 GIT binary patch delta 60517 zcmZUYQ;aSQ(4@zerJEHI3l}?QiZK`!;8=Ge8Fvi1 zcTTfK5ky3!@nr-7-$DvO1V%g&!&+a8K&X&g1T38xL+8i0|KjEXJ`4iltPzg`5e!0q zoZrww1KsK&ao)^NGz#@CV=s*-29q{biUU#lYoPuxr=AmTw-j17lUQP67)G{KW5Uh* zP*4-kaG$|Am1-u^It#gs4Rv&Z6UEX+03i zV93gSkU%tk`RZPvqmbGV#T;uz+N&z)S3CiS2pG)(6WK3VUoej$e|nzq>5@*U@urpYQEaztvfcO#@Kx!For42`KJTY{oK{T1WgyOK{kO zI7)3G0NSG2J^W6!jD(+F>4W3r2#Nk}zZn;0axP`= 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b/2nd/Evaluations/DS_2021-12-10/sujet.tex @@ -22,6 +22,8 @@ Le barème est donné à titre indicatif, il pourra être modifié. \input{exercises.tex} \printcollection{banque} +\clearpage +\printsolutionstype{exercise} \end{document} %%% Local Variables: