From c9ca195edff24bd9da280186e8c750ff7a832d2c Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Mon, 7 Feb 2022 10:17:42 +0100 Subject: [PATCH] Feat: simplification ex1 --- 2nd/Evaluations/DS_2022-02-07/exercises.tex | 40 +++++++++++++++----- 2nd/Evaluations/DS_2022-02-07/sujet.pdf | Bin 37033 -> 36967 bytes 2nd/Evaluations/DS_2022-02-07/sujet.tex | 6 +-- 3 files changed, 34 insertions(+), 12 deletions(-) diff --git a/2nd/Evaluations/DS_2022-02-07/exercises.tex b/2nd/Evaluations/DS_2022-02-07/exercises.tex index b44b082..d212f43 100644 --- a/2nd/Evaluations/DS_2022-02-07/exercises.tex +++ b/2nd/Evaluations/DS_2022-02-07/exercises.tex @@ -8,8 +8,8 @@ \[ A(-3; 0) \qquad B(-1; 4) \qquad C(3;2) \] - \item Calculer les distances $AB$, $BC$ et $AC$. - \item En déduire la nature du triangle $ABC$. + \item Démontrer que $AB = \sqrt{20}$ et que $AC = \sqrt{40}$. + \item On admet que $BC = \sqrt{20}$ (vous n'avez pas à le calculer). En déduire la nature du triangle $ABC$. \item Calculer les coordonnées du point $E$ milieu du segment $[AC]$. \item Démontrer que les diagonales du quadrilatère $ABCD$ se coupent en leur milieu. \item Démontrer à partir des résultats des questions précédentes qua $ABCD$ est un carré. @@ -24,6 +24,31 @@ \end{minipage} \end{exercise} +\begin{solution} + \begin{enumerate} + \item ~ + \begin{tikzpicture} + \repere{-5}{5}{-5}{5} + \draw (1, -2) node {x} node [ below left ] {$D$}; + \draw (-3, 0) node {x} node [ below left ] {$A$}; + \draw (-1, 4) node {x} node [ below left ] {$B$}; + \draw (3, 2) node {x} node [ below left ] {$C$}; + \end{tikzpicture} + \item + Distance $AB$ + \[ + AB = \sqrt{(x_A - x_B)^2 + (y_A - y_B)^2} = \sqrt{(-3 - (-1))^2 + (0 - 4)^2} = \sqrt{4 + 16} = \sqrt{20} + \] + Distance $AC$ + \[ + AC = \sqrt{(x_A - x_C)^2 + (y_A - y_C)^2} = \sqrt{(-3 - 3)^2 + (0 - 2)^2} = \sqrt{36 + 4} = \sqrt{40} + \] + Distance $BC$ + \[ + BC = \sqrt{(x_B - x_C)^2 + (y_B - y_C)^2} = \sqrt{(-1 - 3)^2 + (4 - 2)^2} = \sqrt{16 + 4} = \sqrt{20} + \] + \end{enumerate} +\end{solution} \begin{exercise}[subtitle={Nombre d'écrans}, step={1}, origin={Création}, topics={ Statistiques }, tags={ Moyenne, médiane }, points=7] % Statistiques @@ -96,12 +121,9 @@ \end{multicols} \end{enumerate} - \item Tracer le tableau de signe des fonctions suivantes en passant par la résolution d'une inéquation - \begin{multicols}{2} - \begin{enumerate} - \item $f(x) = 5x - 25$ - \item $g(x) = 10 + 2x$ - \end{enumerate} - \end{multicols} + \item Tracer le tableau de signe de la fonction suivante en passant par la résolution d'une inéquation + \[ + f(x) = 5x - 25 + \] \end{enumerate} \end{exercise} diff --git a/2nd/Evaluations/DS_2022-02-07/sujet.pdf b/2nd/Evaluations/DS_2022-02-07/sujet.pdf index 6b3483de96bb5a20c94c10e5b51e16db57f7834c..44be8dd57c71eb693d54f4c460110b5d7d88bd85 100644 GIT binary patch delta 22278 zcmZs?Q;?ud&^6e$ZQHgv({}f?t!Yi$PjlL~&1u`VZQC~Y{l5Ko_h#!VFHU7fMMhM` 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