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4 Commits
ac5e40eed9
...
78f1174f07
| Author | SHA1 | Date | |
|---|---|---|---|
| 78f1174f07 | |||
| 71a2e48941 | |||
| e63845787c | |||
| 8f8402e55f |
@@ -1,6 +1,6 @@
|
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@@ -456,7 +466,7 @@
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2nd/05_Vecteurs_hors_repere/1B_vecteurs.pdf
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2nd/05_Vecteurs_hors_repere/1B_vecteurs.pdf
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2nd/05_Vecteurs_hors_repere/1B_vecteurs.tex
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2nd/05_Vecteurs_hors_repere/1B_vecteurs.tex
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|
||||
\documentclass[a4paper,10pt]{article}
|
||||
\usepackage{myXsim}
|
||||
|
||||
\author{Benjamin Bertrand}
|
||||
\title{Vecteurs hors repère - Cours}
|
||||
\date{novembre 2025}
|
||||
|
||||
\pagestyle{empty}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\maketitle
|
||||
|
||||
\section{Généralités}
|
||||
|
||||
\paragraph{Remarque:} suivant le contexte, on veut pouvoir avoir les outils mathématiques pour définir des \textbf{flèches}:
|
||||
\begin{itemize}
|
||||
\item En géométrie, si on a deux points $A$ et $B$, la flèche qui amène $A$ sur $B$.
|
||||
\item En physique, une flèche peut décrire une force.
|
||||
\item Le mouvement: des déplacements, des vitesses...
|
||||
\end{itemize}
|
||||
|
||||
\begin{definition}[ Vecteur ]
|
||||
\begin{minipage}{0.7\textwidth}
|
||||
Un \textbf{vecteur} $\vect{v}$ est l'objet mathématique qui modélise une \textbf{flèche}. Il est caractérisé par trois données:
|
||||
|
||||
\begin{itemize}
|
||||
\item Une \textbf{direction}: la pente de la droite qui porte la flèche
|
||||
\item Un \textbf{sens}: l'orientation de la flèche sur cette droite
|
||||
\item Une \textbf{norme}: la longueur de la flèche
|
||||
\end{itemize}
|
||||
|
||||
Il existe un vecteur particulier qui a une \textbf{norme} nulle: c'est le \textbf{vecteur nul} noté $\vect{0}$.
|
||||
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
\begin{tikzpicture}[scale=0.8]
|
||||
% Vecteur 1
|
||||
\draw[->, very thick, blue] (0,0) -- ++(2,1) node[midway, above, sloped] {$\vect{u}$};
|
||||
|
||||
% Vecteur 2
|
||||
\draw[->, very thick, red] (0.5,-0.5) -- ++(1,-1.5) node[midway, right] {$\vect{v}$};
|
||||
\end{tikzpicture}
|
||||
\end{minipage}
|
||||
\end{definition}
|
||||
|
||||
\begin{definition}[Vecteurs égaux]
|
||||
\begin{minipage}{0.7\textwidth}
|
||||
On dit que $\vect{u}$ et $\vect{v}$ sont deux vecteurs \textbf{égaux} si et seulement si ils ont
|
||||
\begin{itemize}
|
||||
\item la même direction
|
||||
\item le même sens
|
||||
\item la même norme
|
||||
\end{itemize}
|
||||
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\begin{tikzpicture}[scale=0.8]
|
||||
% Vecteur u
|
||||
\draw[->, very thick, blue] (0,0) -- ++(2,1) node[midway, above, sloped] {$\vect{u}$};
|
||||
|
||||
% Vecteur v (égal à u)
|
||||
\draw[->, very thick, blue] (0.5,-1.5) -- ++(2,1) node[midway, below, sloped] {$\vect{v}$};
|
||||
|
||||
% Vecteur u
|
||||
\draw[->, very thick, red] (5, 2) -- ++(1,-2) node[midway, above, sloped] {$\vect{w}$};
|
||||
|
||||
% Vecteur v (égal à u)
|
||||
\draw[->, very thick, red] (3,2) -- ++(1,-2) node[midway, below, sloped] {$\vect{x}$};
|
||||
\end{tikzpicture}
|
||||
\end{minipage}
|
||||
|
||||
\end{definition}
|
||||
|
||||
\begin{definition}[Vecteurs opposés]
|
||||
\begin{minipage}{0.7\textwidth}
|
||||
On dit que $\vect{u}$ et $\vect{v}$ sont deux vecteurs \textbf{opposés} si et seulement si ils ont
|
||||
\begin{itemize}
|
||||
\item la même direction
|
||||
\item le même sens
|
||||
\item la même norme
|
||||
\end{itemize}
|
||||
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\begin{tikzpicture}[]
|
||||
% Vecteur u
|
||||
\draw[->, very thick, blue] (3, 0) -- ++(2,1) node[midway, above, sloped] {$\vect{u}$};
|
||||
|
||||
% Vecteur v (opposé à u)
|
||||
\draw[->, very thick, blue] (3,2) -- ++(-2,-1) node[midway, below, sloped] {$\vect{v}$};
|
||||
\end{tikzpicture}
|
||||
\end{minipage}
|
||||
\end{definition}
|
||||
|
||||
\begin{definition}[Vecteurs translation]
|
||||
\begin{minipage}{0.7\textwidth}
|
||||
Soient $A$ et $B$ deux points.
|
||||
|
||||
Le vecteur $\vect{AB}$ modélise la \textbf{translation} qui transforme le point $A$ en le point $B$.
|
||||
|
||||
On dit que $B$ est \textbf{l'image} du point $A$ par la translation $\vect{AB}$.
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\begin{tikzpicture}
|
||||
% Point A
|
||||
\coordinate (A) at (0,0);
|
||||
\fill (A) circle (2pt) node[below left] {$A$};
|
||||
|
||||
% Point B
|
||||
\coordinate (B) at (2.5,1.5);
|
||||
\fill (B) circle (2pt) node[above right] {$B$};
|
||||
|
||||
% Vecteur AB
|
||||
\draw[->, very thick, blue] (A) -- (B) node[midway, above, sloped] {$\vect{AB}$};
|
||||
\end{tikzpicture}
|
||||
\end{minipage}
|
||||
\end{definition}
|
||||
|
||||
\paragraph{Exemples}:~
|
||||
|
||||
\noindent
|
||||
\begin{minipage}{0.55\textwidth}
|
||||
Sur le dessin ci-contre:
|
||||
\begin{enumerate}[leftmargin=*]
|
||||
\item Donner deux vecteurs égaux au vecteur $\vect{AB}$.
|
||||
|
||||
\vspace{1cm}
|
||||
|
||||
\item Donner un vecteur opposé au vecteur $\vect{CD}$.
|
||||
|
||||
\vspace{1cm}
|
||||
|
||||
\item Quelle est l'image du point $E$ par la translation $\vect{AB}$?
|
||||
|
||||
\vspace{1cm}
|
||||
|
||||
\item Quel vecteur modélise la translation qui transforme $C$ en $D$?
|
||||
|
||||
\vspace{1cm}
|
||||
\end{enumerate}
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.45\textwidth}
|
||||
\begin{tikzpicture}[scale=1.2]
|
||||
% Quadrillage
|
||||
%\draw[gray!30, step=1] (-0.5,-0.5) grid (5.5,4.5);
|
||||
|
||||
% Points
|
||||
\coordinate (A) at (0,1);
|
||||
\fill (A) circle (2pt) node[below left] {$A$};
|
||||
|
||||
\coordinate (B) at (2,3);
|
||||
\fill (B) circle (2pt) node[above] {$B$};
|
||||
|
||||
\coordinate (C) at (3,1);
|
||||
\fill (C) circle (2pt) node[below] {$C$};
|
||||
|
||||
\coordinate (D) at (6,2);
|
||||
\fill (D) circle (2pt) node[above right] {$D$};
|
||||
|
||||
\coordinate (E) at (1,0);
|
||||
\fill (E) circle (2pt) node[below] {$E$};
|
||||
|
||||
\coordinate (F) at (3,2);
|
||||
\fill (F) circle (2pt) node[right] {$F$};
|
||||
|
||||
\coordinate (G) at (4,0);
|
||||
\fill (G) circle (2pt) node[below] {$G$};
|
||||
|
||||
% Vecteurs avec points
|
||||
% \draw[->, very thick, blue] (A) -- (B) node[midway, left] {$\vect{AB}$};
|
||||
% \draw[->, very thick, red] (C) -- (D) node[midway, below right] {$\vect{CD}$};
|
||||
% \draw[->, very thick, green!60!black] (E) -- (F);
|
||||
% \draw[->, very thick, orange] (G) -- ++(2,2);
|
||||
|
||||
% Vecteurs sans points
|
||||
\draw[->, very thick, purple] (0.5,0) -- ++(2,2) node[midway, above] {$\vect{u}$};
|
||||
\draw[->, very thick, brown] (4.5,1) -- ++(0,2) node[midway, right] {$\vect{v}$};
|
||||
\end{tikzpicture}
|
||||
\end{minipage}
|
||||
|
||||
\afaire{Exemple à compléter}
|
||||
|
||||
\end{document}
|
||||
BIN
2nd/05_Vecteurs_hors_repere/2B_operations.pdf
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2nd/05_Vecteurs_hors_repere/2B_operations.pdf
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180
2nd/05_Vecteurs_hors_repere/2B_operations.tex
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2nd/05_Vecteurs_hors_repere/2B_operations.tex
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@@ -0,0 +1,180 @@
|
||||
\documentclass[a4paper,10pt]{article}
|
||||
\usepackage{myXsim}
|
||||
|
||||
\author{Benjamin Bertrand}
|
||||
\title{Vecteurs hors repère - Cours}
|
||||
\date{novembre 2025}
|
||||
|
||||
\pagestyle{empty}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\maketitle
|
||||
|
||||
\setcounter{section}{1}
|
||||
\section{Opérations}
|
||||
|
||||
\subsection*{Sommes de vecteurs}
|
||||
|
||||
\begin{definition}[Somme de vecteurs]
|
||||
\begin{minipage}{0.7\textwidth}
|
||||
Soient $\vect{u}$ et $\vect{v}$ deux vecteurs.
|
||||
|
||||
La \textbf{somme} $\vect{u} + \vect{v}$ est le vecteur obtenu en plaçant l'origine de $\vect{v}$ à l'extrémité de $\vect{u}$.
|
||||
|
||||
Le vecteur $\vect{u} + \vect{v}$ a pour origine celle de $\vect{u}$ et pour extrémité celle de $\vect{v}$.
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\begin{tikzpicture}[scale=1]
|
||||
% Vecteur u
|
||||
\draw[->, very thick, blue] (0,0) -- ++(2,0.5) node[midway, below] {$\vect{u}$};
|
||||
|
||||
% Vecteur v
|
||||
\draw[->, very thick, blue] (2,0.5) -- ++(1,1.5) node[midway, right] {$\vect{v}$};
|
||||
|
||||
% Somme u + v
|
||||
\draw[->, very thick, purple, dashed] (0,0) -- ++(3,2) node[midway, above, sloped] {$\vect{u} + \vect{v}$};
|
||||
\end{tikzpicture}
|
||||
\end{minipage}
|
||||
\end{definition}
|
||||
|
||||
\begin{propriete}[Relation de Chasles]
|
||||
\begin{minipage}{0.7\textwidth}
|
||||
Soient $A$, $B$ et $C$ trois points.
|
||||
|
||||
On a:
|
||||
\[\vect{AB} + \vect{BC} = \vect{AC}\]
|
||||
|
||||
Cette relation permet de simplifier des sommes de vecteurs en "chaînant" les points.
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\begin{tikzpicture}[scale=0.9]
|
||||
% Points
|
||||
\coordinate (A) at (0,0);
|
||||
\fill (A) circle (2pt) node[below left] {$A$};
|
||||
|
||||
\coordinate (B) at (2.5,2);
|
||||
\fill (B) circle (2pt) node[above] {$B$};
|
||||
|
||||
\coordinate (C) at (4,0.5);
|
||||
\fill (C) circle (2pt) node[right] {$C$};
|
||||
|
||||
% Vecteurs
|
||||
\draw[->, very thick, blue] (A) -- (B) node[midway, above, sloped] {$\vect{AB}$};
|
||||
\draw[->, very thick, red] (B) -- (C) node[midway, above, sloped] {$\vect{BC}$};
|
||||
\draw[->, very thick, purple, dashed] (A) -- (C) node[midway, below, sloped] {$\vect{AC}$};
|
||||
\end{tikzpicture}
|
||||
\end{minipage}
|
||||
\end{propriete}
|
||||
|
||||
\vspace{-0.5cm}
|
||||
\paragraph{Exemples}:~
|
||||
|
||||
\noindent
|
||||
\begin{minipage}{0.55\textwidth}
|
||||
Sur le dessin ci-contre:
|
||||
\begin{enumerate}[leftmargin=*]
|
||||
\item Construire le vecteur $\vect{u} + \vect{v}$.
|
||||
|
||||
\item Simplifier $\vect{AB} + \vect{BC} = $.
|
||||
\end{enumerate}
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.45\textwidth}
|
||||
\begin{tikzpicture}[scale=1.1]
|
||||
% Points
|
||||
\coordinate (A) at (0,0);
|
||||
\fill (A) circle (2pt) node[below left] {$A$};
|
||||
|
||||
\coordinate (B) at (2,0);
|
||||
\fill (B) circle (2pt) node[below right] {$B$};
|
||||
|
||||
\coordinate (C) at (2.5,2);
|
||||
\fill (C) circle (2pt) node[above right] {$C$};
|
||||
|
||||
\coordinate (D) at (0.5,2);
|
||||
\fill (D) circle (2pt) node[above left] {$D$};
|
||||
|
||||
% Segments du parallélogramme (en pointillés)
|
||||
\draw[gray, dashed] (A) -- (B) -- (C) -- (D) -- cycle;
|
||||
|
||||
% Vecteurs sans points
|
||||
\draw[->, very thick, purple] (4,0) -- ++(1.5,0.5) node[midway, below] {$\vect{u}$};
|
||||
\draw[->, very thick, brown] (4,1) -- ++(0.8,1.2) node[midway, right] {$\vect{v}$};
|
||||
\end{tikzpicture}
|
||||
\end{minipage}
|
||||
|
||||
\subsection*{Multiplication par un nombre}
|
||||
|
||||
\begin{propriete}[Multiplication d'un vecteur par un nombre]
|
||||
\begin{minipage}{0.65\textwidth}
|
||||
Soit $\vect{u}$ un vecteur et $k$ un nombre réel.
|
||||
|
||||
Le vecteur $k \times \vect{u}$ est le vecteur qui a:
|
||||
\begin{itemize}
|
||||
\item La même \textbf{direction} que $\vect{u}$
|
||||
\item Le même \textbf{sens} que $\vect{u}$ si $k > 0$, le sens opposé si $k < 0$
|
||||
\item Une \textbf{norme} égale à $|k|$ fois celle de $\vect{u}$
|
||||
\end{itemize}
|
||||
|
||||
\textbf{Cas particuliers:}
|
||||
Si $k = 0$, alors $k \times \vect{u} = \vect{0}$
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\begin{tikzpicture}[scale=0.9]
|
||||
% Vecteur u
|
||||
\draw[->, very thick, blue] (0,0) -- ++(1.5,1) node[midway, above, sloped] {$\vect{u}$};
|
||||
|
||||
% Vecteur 2u
|
||||
\draw[->, very thick, green!60!black] (0,-0.8) -- ++(3,2) node[midway, below, sloped] {$2\vect{u}$};
|
||||
|
||||
% Vecteur -u
|
||||
\draw[->, very thick, red] (3,0) -- ++(-1.5,-1) node[midway, below, sloped] {$-\vect{u}$};
|
||||
|
||||
% Vecteur 0.5u
|
||||
\draw[->, very thick, orange] (4,-1) -- ++(0.75,0.5) node[midway, above, sloped] {$0{,}5\vect{u}$};
|
||||
\end{tikzpicture}
|
||||
\end{minipage}
|
||||
\end{propriete}
|
||||
|
||||
\vspace{-0.5cm}
|
||||
\paragraph{Exemples}:~
|
||||
|
||||
\noindent
|
||||
\begin{minipage}{0.55\textwidth}
|
||||
Sur le dessin ci-contre:
|
||||
\begin{enumerate}[leftmargin=*]
|
||||
\item Construire le vecteur $2\vect{u}$.
|
||||
|
||||
\item Construire le vecteur $-\vect{v}$.
|
||||
|
||||
\item Construire le point $E$ tel que $\vect{AE} = 3\vect{AB}$.
|
||||
\end{enumerate}
|
||||
\afaire{réaliser les exemples. Vous pouvez dessiner les vecteurs et les points sans respecter précisément le dessin}
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.45\textwidth}
|
||||
\begin{tikzpicture}[scale=1.1]
|
||||
% Points
|
||||
\coordinate (A) at (0,0);
|
||||
\fill (A) circle (2pt) node[below left] {$A$};
|
||||
|
||||
\coordinate (B) at (1.5,0.5);
|
||||
\fill (B) circle (2pt) node[above right] {$B$};
|
||||
|
||||
\coordinate (C) at (3,1);
|
||||
\fill (C) circle (2pt) node[above right] {$C$};
|
||||
|
||||
% Segments
|
||||
\draw[gray, dashed] (A) -- (C);
|
||||
|
||||
% Vecteurs sans points
|
||||
\draw[->, very thick, purple] (0,2) -- ++(1.2,1) node[midway, above, sloped] {$\vect{u}$};
|
||||
\draw[->, very thick, brown] (2.5,2.5) -- ++(0.5,1.5) node[midway, right] {$\vect{v}$};
|
||||
\end{tikzpicture}
|
||||
\end{minipage}
|
||||
|
||||
\end{document}
|
||||
BIN
2nd/05_Vecteurs_hors_repere/3B_parallelogramme.pdf
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2nd/05_Vecteurs_hors_repere/3B_parallelogramme.pdf
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128
2nd/05_Vecteurs_hors_repere/3B_parallelogramme.tex
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128
2nd/05_Vecteurs_hors_repere/3B_parallelogramme.tex
Normal file
@@ -0,0 +1,128 @@
|
||||
\documentclass[a4paper,10pt]{article}
|
||||
\usepackage{myXsim}
|
||||
|
||||
\author{Benjamin Bertrand}
|
||||
\title{Vecteurs hors repère - Cours}
|
||||
\date{novembre 2025}
|
||||
|
||||
\pagestyle{empty}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\maketitle
|
||||
|
||||
\setcounter{section}{2}
|
||||
\section{Parallélogramme}
|
||||
|
||||
\begin{propriete}[Caractérisation des parallélogrammes]
|
||||
Un quadrilatère $ABCD$ est un parallélogramme si et seulement si il vérifie l'une des propriétés suivantes:
|
||||
|
||||
\begin{multicols}{2}
|
||||
\begin{enumerate}
|
||||
\item Les côtés opposés sont \textbf{parallèles deux à deux}
|
||||
|
||||
\begin{center}
|
||||
\begin{tikzpicture}[scale=0.8]
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (B) at (3,0);
|
||||
\coordinate (C) at (4,2);
|
||||
\coordinate (D) at (1,2);
|
||||
|
||||
\draw (A) node[below left] {$A$} -- (B) node[below right] {$B$} -- (C) node[above right] {$C$} -- (D) node[above left] {$D$} -- cycle;
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
|
||||
\item Les côtés opposés ont \textbf{même longueur deux à deux}
|
||||
|
||||
\begin{center}
|
||||
\begin{tikzpicture}[scale=0.8]
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (B) at (3,0);
|
||||
\coordinate (C) at (4,2);
|
||||
\coordinate (D) at (1,2);
|
||||
|
||||
\draw (A) node[below left] {$A$} -- (B) node[below right] {$B$} -- (C) node[above right] {$C$} -- (D) node[above left] {$D$} -- cycle;
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
|
||||
\item Les angles opposés ont \textbf{même mesure deux à deux}
|
||||
|
||||
\begin{center}
|
||||
\begin{tikzpicture}[scale=0.8]
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (B) at (3,0);
|
||||
\coordinate (C) at (4,2);
|
||||
\coordinate (D) at (1,2);
|
||||
|
||||
\draw (A) node[below left] {$A$} -- (B) node[below right] {$B$} -- (C) node[above right] {$C$} -- (D) node[above left] {$D$} -- cycle;
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
|
||||
\item Les diagonales se coupent en \textbf{leur milieu}
|
||||
|
||||
\begin{center}
|
||||
\begin{tikzpicture}[scale=0.8]
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (B) at (3,0);
|
||||
\coordinate (C) at (4,2);
|
||||
\coordinate (D) at (1,2);
|
||||
\coordinate (O) at (2,1);
|
||||
|
||||
\draw (A) node[below left] {$A$} -- (B) node[below right] {$B$} -- (C) node[above right] {$C$} -- (D) node[above left] {$D$} -- cycle;
|
||||
\draw[dashed] (A) -- (C);
|
||||
\draw[dashed] (B) -- (D);
|
||||
|
||||
\fill (O) circle (2pt) node[below] {$O$};
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
\end{propriete}
|
||||
|
||||
|
||||
\begin{propriete}[Egalité des vecteurs et parallélogrammes]
|
||||
\begin{minipage}{0.65\textwidth}
|
||||
$ABCD$ est un parallélogramme si et seulement si $\vect{AB} = \vect{DC}$
|
||||
|
||||
\vspace{1cm}
|
||||
|
||||
\textbf{Remarque:} On peut aussi écrire $\vect{AD} = \vect{BC}$
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\begin{tikzpicture}[scale=1]
|
||||
\coordinate (A) at (0,0);
|
||||
\coordinate (B) at (2.5,0);
|
||||
\coordinate (C) at (3.5,2);
|
||||
\coordinate (D) at (1,2);
|
||||
|
||||
\draw (A) node[below left] {$A$} -- (B) node[below right] {$B$} -- (C) node[above right] {$C$} -- (D) node[above left] {$D$} -- cycle;
|
||||
|
||||
% Vecteurs
|
||||
% \draw[->, very thick, blue] (A) -- ++(2.5,0) node[midway, below] {$\vect{AB}$};
|
||||
% \draw[->, very thick, blue] (D) -- ++(2.5,0) node[midway, above] {$\vect{DC}$};
|
||||
\end{tikzpicture}
|
||||
\end{minipage}
|
||||
\end{propriete}
|
||||
|
||||
\paragraph{Exemples}:~
|
||||
|
||||
\noindent
|
||||
\begin{minipage}{0.55\textwidth}
|
||||
On suppose que les droites sont parallèles.
|
||||
|
||||
Trouver trois parallélogrammes et en déduire les égalités entre vecteurs.
|
||||
|
||||
\afaire{Résoudre l'exemple}
|
||||
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.45\textwidth}
|
||||
\includegraphics[scale=0.3]{./fig/paralleles.png}
|
||||
\end{minipage}
|
||||
|
||||
|
||||
\end{document}
|
||||
210
2nd/05_Vecteurs_hors_repere/exercises.tex
Normal file
210
2nd/05_Vecteurs_hors_repere/exercises.tex
Normal file
@@ -0,0 +1,210 @@
|
||||
\begin{exercise}[subtitle={Déplacement d'un ballon}, step={1}, origin={Camille Crespeau}, topics={ Vecteurs hors repère }, tags={ vecteurs }, mode={\searchMode}]
|
||||
Au fil des questions, il vous sera demandé de compléter le tableau suivant à la fin de l'exercice.
|
||||
\begin{enumerate}[label={\textbf{Partie \Alph*:}}, leftmargin=0.3cm, itemindent=*]
|
||||
\item Entrainement au tir au but
|
||||
|
||||
\begin{minipage}{0.55\textwidth}
|
||||
\begin{enumerate}[label={\arabic*.}, leftmargin=*]
|
||||
\item Ayla est située au point A, elle tente de marquer un but mais rate et envoie le ballon en E. Représenter ce déplacement par une flèche allant de A vers E. On note ce déplacement $\vect{AE}$ (prononcer “vecteur A E”).
|
||||
\item Ayla se positionne en C ; elle fait exactement le même tir que le précédent et le ballon suit le même déplacement. Représenter son point d’arrivée D, puis le déplacement effectué par le ballon par une flèche. A-t-elle marqué ?
|
||||
\end{enumerate}
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.4\textwidth}
|
||||
\includegraphics[scale=0.2]{./fig/tir_but.png}
|
||||
\end{minipage}
|
||||
\begin{enumerate}[label={\arabic*.}, leftmargin=*]
|
||||
\setcounter{enumii}{2}
|
||||
\item Pour que son ballon arrive dans le but, en B, avec le même geste, d’où Ayla doit-elle tirer ? Placer le point F correspondant puis représenter le déplacement du ballon.
|
||||
\item Comparer les trois flèches tracées ; lister leurs points communs et leurs différences. (tableau des notations à compléter)
|
||||
\item En restant en A, combien de fois plus loin aurait dû aller le ballon pour qu’il arrive en B au lieu d’arriver en E ? Tracer de déplacement. (tableau des notations à compléter)
|
||||
\item Pour permettre à Ayla de marquer à partir du point C, représenter le déplacement du ballon s’il allait deux fois plus loin que son tir vers D. Il arrive en G.
|
||||
\end{enumerate}
|
||||
\item Entrainement aux passes
|
||||
|
||||
\begin{minipage}{0.55\textwidth}
|
||||
\textbf{A}yla est au point A, \textbf{C}olin est au point C, \textbf{F}atima en F, \textbf{D}enis en D, \textbf{E}liot en E. Le \textbf{B}ut est atteint en B.
|
||||
\begin{enumerate}[label={\arabic*.}, leftmargin=*]
|
||||
\setcounter{enumii}{6}
|
||||
\item L'entraîneur veut que l’équipe s’exerce à faire des passes ; il demande à Ayla de passer la balle à Colin, qui tirera dans le But. Représenter l'enchaînement de déplacements suivis par le ballon à l’aide de flèches. (tableau des notations à compléter)
|
||||
\end{enumerate}
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.4\textwidth}
|
||||
\includegraphics[scale=0.2]{./fig/passes.png}
|
||||
\end{minipage}
|
||||
|
||||
\begin{enumerate}[label={\arabic*.}, leftmargin=*]
|
||||
\setcounter{enumii}{7}
|
||||
\item Tracer au moins deux autres déplacements du ballon correspondant à une passe de A yla pour atteindre le But. Chacun d’eux correspond finalement à un déplacement du ballon de A vers B . (tableau des notations à compléter)
|
||||
\end{enumerate}
|
||||
Eliot fait une passe à Fatima qui refait une passe à E liot.
|
||||
\begin{enumerate}[label={\arabic*.}, leftmargin=*]
|
||||
\setcounter{enumii}{8}
|
||||
\item Tracer les deux déplacements correspondants et donner leurs notations. Décrire ces déplacements et les comparer : qu’ont-ils en commun ? Qu’ont-ils de différent ? (tableau des notations à compléter)
|
||||
\item Que dire du déplacement total après la succession de ces deux déplacements ? (tableau des notations à compléter)
|
||||
\end{enumerate}
|
||||
\end{enumerate}
|
||||
|
||||
\paragraph{Tableau des notations}
|
||||
\begin{center}
|
||||
\begin{tabular}{|c|*{2}{p{7cm}|}}
|
||||
\hline
|
||||
Questions n° & Déplacements & Notation mathématiques \\
|
||||
\hline
|
||||
1 & Déplacement de A vers E & $\vect{AE}$ \\
|
||||
\hline
|
||||
4 & & \\
|
||||
\hline
|
||||
5 & & \\
|
||||
\hline
|
||||
7 & & \\
|
||||
\hline
|
||||
8 & & \\
|
||||
\hline
|
||||
9 & & \\
|
||||
\hline
|
||||
10 & & \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
\end{exercise}
|
||||
|
||||
|
||||
\begin{exercise}[subtitle={Manipulation de vecteurs}, step={1}, origin={Camille Crespeau}, topics={ Vecteurs hors repère }, tags={ vecteurs }, mode={\trainMode}]
|
||||
\begin{minipage}{0.5\textwidth}
|
||||
L'exercice se base sur les points et vecteurs représentés sur l'image ci-contre.
|
||||
\begin{enumerate}[leftmargin=*]
|
||||
\item Déterminer des vecteurs correspondants aux descriptions suivantes
|
||||
\begin{enumerate}
|
||||
\item égal au vecteur $\vect{AB}$
|
||||
\item opposé à $\vect{CD}$
|
||||
\end{enumerate}
|
||||
\item Placer les points $E$, $F$, $G$ et $H$, images du point $A$ par les translations de vecteurs
|
||||
\begin{multicols}{2}
|
||||
\begin{enumerate}
|
||||
\item $\vect{w}$
|
||||
\item $\vect{v}$
|
||||
\item $\vect{p}$
|
||||
\item $\vect{m}$
|
||||
\end{enumerate}
|
||||
|
||||
\end{multicols}
|
||||
\item Placer les points $I$, $J$, $K$ et $L$, images du point $A$ par les translations de vecteurs
|
||||
\begin{multicols}{2}
|
||||
\begin{enumerate}
|
||||
\item $\vect{r}$
|
||||
\item $\vect{u}$
|
||||
\item $\vect{w}$
|
||||
\item $\vect{m}$
|
||||
\end{enumerate}
|
||||
|
||||
\end{multicols}
|
||||
\end{enumerate}
|
||||
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.45\textwidth}
|
||||
\includegraphics[scale=0.25]{./fig/points_vecteurs.png}
|
||||
\end{minipage}
|
||||
\end{exercise}
|
||||
|
||||
\begin{exercise}[subtitle={Somme de vecteurs}, step={2}, origin={Camille Crespeau}, topics={ Vecteurs hors repère }, tags={ vecteurs }, mode={\trainMode}]
|
||||
Dans chacun des cas suivants, construire un représentant du vecteur $\vect{u}+\vect{v}$
|
||||
|
||||
\includegraphics[scale=0.3]{./fig/somme_vect.png}
|
||||
\end{exercise}
|
||||
|
||||
\begin{exercise}[subtitle={Équilibre des forces}, step={2}, origin={Camille Crespeau}, topics={ Vecteurs hors repère }, tags={ vecteurs }, mode={\trainMode}]
|
||||
Dans les dessins ci-dessous des forces ont été modélisées par des vecteurs.
|
||||
|
||||
Placer un dernier vecteur force pour équilibrer le système (c'est à dire pour que la somme des forces soit nulle). Il est possible que vous deviez sortir du cadre.
|
||||
|
||||
\begin{multicols}{3}
|
||||
\begin{tikzpicture}[scale=0.6]
|
||||
\tkzInit[xmin=-4,xmax=4,xstep=1,
|
||||
ymin=-4,ymax=4,ystep=1]
|
||||
\tkzGrid
|
||||
\draw (0, 0) node {x} node[below left] {$0$};
|
||||
\draw[->, very thick] (0, 0) -- (-1, 2) node[below left, midway] {$\vec{F_1}$};
|
||||
\draw[->, very thick] (0, 0) -- (3, 1) node[above, midway] {$\vec{F_2}$};
|
||||
\draw[->, very thick] (0, 0) -- (2, -2) node[right, midway] {$\vec{F_3}$};
|
||||
\end{tikzpicture}
|
||||
\columnbreak
|
||||
|
||||
\begin{tikzpicture}[scale=0.6]
|
||||
\tkzInit[xmin=-4,xmax=4,xstep=1,
|
||||
ymin=-4,ymax=4,ystep=1]
|
||||
\tkzGrid
|
||||
\draw (0, 0) node {x} node[below left] {$0$};
|
||||
\draw[->, very thick] (0, 0) -- (-1, 1) node[below left, midway] {$\vec{F_1}$};
|
||||
\draw[->, very thick] (0, 0) -- (3, -1) node[above, midway] {$\vec{F_2}$};
|
||||
\draw[->, very thick] (0, 0) -- (2, -2) node[right, midway] {$\vec{F_3}$};
|
||||
\end{tikzpicture}
|
||||
\columnbreak
|
||||
|
||||
\begin{tikzpicture}[scale=0.6]
|
||||
\tkzInit[xmin=-4,xmax=4,xstep=1,
|
||||
ymin=-4,ymax=4,ystep=1]
|
||||
\tkzGrid
|
||||
\draw (0, 0) node {x} node[below left] {$0$};
|
||||
\draw[->, very thick] (0, 0) -- (-1, -2) node[below left, midway] {$\vec{F_1}$};
|
||||
\draw[->, very thick] (0, 0) -- (2, 1) node[below, midway] {$\vec{F_2}$};
|
||||
\draw[->, very thick] (0, 0) -- (1, 2) node[left, midway] {$\vec{F_3}$};
|
||||
\draw[->, very thick] (0, 0) -- (1, -2) node[right, midway] {$\vec{F_4}$};
|
||||
\end{tikzpicture}
|
||||
\end{multicols}
|
||||
\end{exercise}
|
||||
|
||||
\begin{exercise}[subtitle={Avec des triangles}, step={2}, origin={Camille Crespeau}, topics={ Vecteurs hors repère }, tags={ vecteurs }, mode={\trainMode}]
|
||||
\begin{minipage}{0.65\textwidth}
|
||||
La figure ci-contre est compsée de triangles équilatéraux. Identifier un vecteur correspondants aux calculs suivants
|
||||
\begin{multicols}{3}
|
||||
\begin{enumerate}[leftmargin=*]
|
||||
\item $\vect{AB}+\vect{BD} $
|
||||
\item $\vect{BC} + \vect{CF} + \vect{FE}$
|
||||
\item $3\vect{AC}$
|
||||
\item $-2\vect{HI}$
|
||||
\item $\frac{1}{2} \vect{BI}$
|
||||
\item $\vect{BC} + \vect{FI}$
|
||||
\item $2\vect{DE} + \vect{FI}$
|
||||
\item (*) $\frac{1}{3} \vect{AJ} + 2\vect{JI}$
|
||||
\item (*) $\frac{-1}{2} \vect{DF} + \frac{1}{2}\vect{JH}$
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\includegraphics[scale=0.25]{./fig/triangles.png}
|
||||
\end{minipage}
|
||||
\end{exercise}
|
||||
|
||||
\begin{exercise}[subtitle={Parallélogramme}, step={3}, origin={Camille Crespeau}, topics={ Vecteurs hors repère }, tags={ vecteurs }, mode={\searchMode}]
|
||||
\begin{enumerate}
|
||||
\item En s'aidant du quadrillage de votre cahier, tracer un parallélogramme $ABCD$.
|
||||
\item Citer toutes les propriétés des parallélogrammes.
|
||||
\item Identifier les vecteurs égaux sur votre figure.
|
||||
\end{enumerate}
|
||||
\end{exercise}
|
||||
|
||||
|
||||
\begin{exercise}[subtitle={Vrai/faux}, step={3}, origin={Camille Crespeau}, topics={ Vecteurs hors repère }, tags={ vecteurs }, mode={\trainMode}]
|
||||
Pour chacune des propositions suivantes, la propriété est fausse. Proposer un contre-exemple pour expliquer en quoi elle est fausse puis proposer une correction.
|
||||
\begin{enumerate}
|
||||
\item Si $ABCD$ est un parallélogramme alors $\vect{AB} = \vect{CD}$.
|
||||
\item Si $\vect{AB} = \vect{BC}$ alors $A$ est le milieu de $[BC]$.
|
||||
\item Si $AB = BC$ alors $B$ est le milieu de $[AC]$.
|
||||
\item Si $(AB) // (BC)$ alors $\vect{AD} = \vect{BC}$.
|
||||
\end{enumerate}
|
||||
\end{exercise}
|
||||
|
||||
|
||||
\begin{exercise}[subtitle={Problème}, step={3}, origin={Camille Crespeau}, topics={ Vecteurs hors repère }, tags={ vecteurs }, mode={\trainMode}]
|
||||
Soient $E$, $F$ et $I$ trois points non alignés du plan.
|
||||
\begin{enumerate}
|
||||
\item Construire le point $G$ tel que $\vect{EI} = \vect{IG}$.
|
||||
\item Construire le point $H$ tel que $\vect{FI} = \vect{IH}$.
|
||||
\item Quelle est la nature du quadrilatère $EFGH$?
|
||||
\item Que peut-on en déduire sur les vecteurs $\vect{FG}$ et $\vect{EH}$?
|
||||
\end{enumerate}
|
||||
\end{exercise}
|
||||
BIN
2nd/05_Vecteurs_hors_repere/fig/paralleles.png
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2nd/05_Vecteurs_hors_repere/fig/paralleles.png
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|
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2nd/05_Vecteurs_hors_repere/fig/passes.png
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2nd/05_Vecteurs_hors_repere/fig/passes.png
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|
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2nd/05_Vecteurs_hors_repere/fig/points_vecteurs.png
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|
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2nd/05_Vecteurs_hors_repere/fig/somme_vect.png
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|
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2nd/05_Vecteurs_hors_repere/fig/tir_but.png
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2nd/05_Vecteurs_hors_repere/fig/tir_but.png
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|
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2nd/05_Vecteurs_hors_repere/fig/triangles.png
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2nd/05_Vecteurs_hors_repere/fig/triangles.png
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|
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76
2nd/05_Vecteurs_hors_repere/index.rst
Normal file
76
2nd/05_Vecteurs_hors_repere/index.rst
Normal file
@@ -0,0 +1,76 @@
|
||||
Vecteurs hors repère
|
||||
####################
|
||||
|
||||
:date: 2025-11-03
|
||||
:modified: 2025-11-03
|
||||
:authors: Benjamin Bertrand
|
||||
:tags: vecteurs
|
||||
:category: 2nd
|
||||
:summary: Découverte des vecteurs, manipulation et opérations
|
||||
|
||||
|
||||
Éléments du programme
|
||||
=====================
|
||||
|
||||
Contenus
|
||||
--------
|
||||
|
||||
- Vecteur MM' associé à la translation qui transforme M en M'. Direction, sens et norme.
|
||||
- Égalité de deux vecteurs. Notation. Vecteur nul.
|
||||
- Somme de deux vecteurs en lien avec l’enchaînement des translations. Relation de Chasles.
|
||||
- Produit d’un vecteur par un nombre réel. Colinéarité de deux vecteurs.
|
||||
|
||||
Capacités attendues
|
||||
-------------------
|
||||
|
||||
- Représenter géométriquement des vecteurs.
|
||||
- Construire géométriquement la somme de deux vecteurs.
|
||||
|
||||
Commentaires
|
||||
------------
|
||||
|
||||
Progression
|
||||
===========
|
||||
|
||||
Plan de travail
|
||||
|
||||
.. image:: ./plan_de_travail.pdf
|
||||
:height: 200px
|
||||
:alt: Plan de travail de la séquence
|
||||
|
||||
|
||||
Étape 1: Découverte de la notion de vecteur
|
||||
-------------------------------------------
|
||||
|
||||
Déplacement d'un ballon: premières manipulation des vecteurs à travers le déplacement de ballons. On y apprend à enchainer les vecteurs, le vecteur nul et les vecteurs opposés.
|
||||
|
||||
Lecture du bilan 1
|
||||
|
||||
.. image:: ./1B_vecteur.pdf
|
||||
:height: 200px
|
||||
:alt: Définition d'un vecteur
|
||||
|
||||
Exercices techniques
|
||||
|
||||
Étape 2: Opération sur les vecteurs
|
||||
-----------------------------------
|
||||
|
||||
Cours: les opérations sur des vecteurs
|
||||
|
||||
.. image:: ./2B_operations.pdf
|
||||
:height: 200px
|
||||
:alt: Bilan sur les opérations sur les vecteurs
|
||||
|
||||
Exercices techniques
|
||||
|
||||
|
||||
Étape 3: Vecteurs et parallélogrammes
|
||||
-------------------------------------
|
||||
|
||||
Cours: liens entre vecteurs et parallélogrammes.
|
||||
|
||||
.. image:: ./3B_parallelogramme.pdf
|
||||
:height: 200px
|
||||
:alt: Bilan sur les parallélogrammes et les vecteurs
|
||||
|
||||
Exercices techniques durs de démonstrations.
|
||||
BIN
2nd/05_Vecteurs_hors_repere/plan_de_travail.pdf
Normal file
BIN
2nd/05_Vecteurs_hors_repere/plan_de_travail.pdf
Normal file
Binary file not shown.
50
2nd/05_Vecteurs_hors_repere/plan_de_travail.tex
Normal file
50
2nd/05_Vecteurs_hors_repere/plan_de_travail.tex
Normal file
@@ -0,0 +1,50 @@
|
||||
\documentclass[a4paper,12pt]{article}
|
||||
\usepackage{myXsim}
|
||||
|
||||
\author{Benjamin Bertrand}
|
||||
\title{Vecteurs hors repère - Plan de travail}
|
||||
\tribe{2nd}
|
||||
\date{novembre 2025}
|
||||
|
||||
\pagestyle{empty}
|
||||
|
||||
\DeclareExerciseCollection{banque}
|
||||
\xsimsetup{
|
||||
}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\maketitle
|
||||
|
||||
% Résumé
|
||||
|
||||
\bigskip
|
||||
|
||||
Savoir-faire de la séquence
|
||||
\begin{itemize}
|
||||
\item Représenter géométriquement des vecteurs.
|
||||
\item Construire géométriquement la somme de deux vecteurs.
|
||||
\item Faire des calculs avec des vecteurs avec un point de vue géométrique
|
||||
\item Utiliser le lien entre égalité de vecteurs et parallélogrammes
|
||||
\end{itemize}
|
||||
|
||||
\bigskip
|
||||
|
||||
\section{Découverte des vecteurs}
|
||||
|
||||
\listsectionexercises
|
||||
|
||||
\section{Opérations sur les vecteurs}
|
||||
\listsectionexercises
|
||||
|
||||
\section{Parallélogramme}
|
||||
\listsectionexercises
|
||||
|
||||
\bigskip
|
||||
\hline
|
||||
|
||||
\input{exercises.tex}
|
||||
\printcollection{banque}
|
||||
|
||||
|
||||
\end{document}
|
||||
28
2nd/05_Vecteurs_hors_repere/solutions.tex
Normal file
28
2nd/05_Vecteurs_hors_repere/solutions.tex
Normal file
@@ -0,0 +1,28 @@
|
||||
\documentclass[a4paper,10pt]{article}
|
||||
\usepackage{myXsim}
|
||||
|
||||
\usetikzlibrary{shapes.geometric}
|
||||
|
||||
\author{Benjamin Bertrand}
|
||||
\title{Vecteurs hors repère - Solutions}
|
||||
\tribe{2nd}
|
||||
\date{novembre 2025}
|
||||
|
||||
\DeclareExerciseCollection{banque}
|
||||
\xsimsetup{
|
||||
exercise/print=false,
|
||||
solution/print=true,
|
||||
}
|
||||
|
||||
\pagestyle{empty}
|
||||
|
||||
|
||||
\begin{document}
|
||||
|
||||
\maketitle
|
||||
|
||||
\input{exercises.tex}
|
||||
%\printcollection{banque}
|
||||
%\printsolutions{exercises}
|
||||
|
||||
\end{document}
|
||||
BIN
2nd/Questions_flashs/P2/QF_S45-1.pdf
Normal file
BIN
2nd/Questions_flashs/P2/QF_S45-1.pdf
Normal file
Binary file not shown.
82
2nd/Questions_flashs/P2/QF_S45-1.tex
Executable file
82
2nd/Questions_flashs/P2/QF_S45-1.tex
Executable file
@@ -0,0 +1,82 @@
|
||||
\documentclass[14pt]{classPres}
|
||||
\usepackage{tkz-fct}
|
||||
|
||||
\author{}
|
||||
\title{}
|
||||
\date{}
|
||||
|
||||
\begin{document}
|
||||
\begin{frame}{Questions flashs}
|
||||
\begin{center}
|
||||
\vfill
|
||||
2nd
|
||||
\vfill
|
||||
30 secondes par calcul
|
||||
\vfill
|
||||
\tiny \jobname
|
||||
\end{center}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Calcul 1}
|
||||
% développer
|
||||
Développer et réduire l'expression suivante
|
||||
\[
|
||||
A = (3 - x)(2x + 1)
|
||||
\]
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Calcul 2}
|
||||
% Evolution
|
||||
Une robe coûte 150\euro. Elle est soldée à -30\%. Quel est son nouveau prix?
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Calcul 3}
|
||||
% Inversion formule
|
||||
\vfill
|
||||
On rappelle la formule $U = R\times I$.
|
||||
|
||||
\vfill
|
||||
|
||||
On donne les valeurs $U = 12V$ et $R = 2\Omega$.
|
||||
|
||||
\vfill
|
||||
|
||||
Calculer la valeur de $I$.
|
||||
|
||||
\vfill
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Calcul 4}
|
||||
% Equation graphique
|
||||
Déterminer graphiquement $f(x) \geq 3$
|
||||
\begin{center}
|
||||
\begin{tikzpicture}[scale=0.8]
|
||||
\tkzInit[xmin=-5,xmax=5,xstep=1,
|
||||
ymin=-3,ymax=5,ystep=1]
|
||||
\tkzGrid
|
||||
\tkzAxeXY
|
||||
\draw[very thick, color=red] plot [smooth,tension=0.5] coordinates{%
|
||||
(-5, 0)
|
||||
(-4, 0.5)
|
||||
(-3, 1)
|
||||
(-2, 2)
|
||||
(-1, 3)
|
||||
(0, 4)
|
||||
(1, 5)
|
||||
(2, 4)
|
||||
(3, 3)
|
||||
(4, 2)
|
||||
(5, 1)
|
||||
};
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Fin}
|
||||
\begin{center}
|
||||
On retourne son papier.
|
||||
\end{center}
|
||||
\end{frame}
|
||||
|
||||
|
||||
\end{document}
|
||||
BIN
2nd/Questions_flashs/P2/QF_S45-2.pdf
Normal file
BIN
2nd/Questions_flashs/P2/QF_S45-2.pdf
Normal file
Binary file not shown.
82
2nd/Questions_flashs/P2/QF_S45-2.tex
Executable file
82
2nd/Questions_flashs/P2/QF_S45-2.tex
Executable file
@@ -0,0 +1,82 @@
|
||||
\documentclass[14pt]{classPres}
|
||||
\usepackage{tkz-fct}
|
||||
|
||||
\author{}
|
||||
\title{}
|
||||
\date{}
|
||||
|
||||
\begin{document}
|
||||
\begin{frame}{Questions flashs}
|
||||
\begin{center}
|
||||
\vfill
|
||||
2nd
|
||||
\vfill
|
||||
30 secondes par calcul
|
||||
\vfill
|
||||
\tiny \jobname
|
||||
\end{center}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Calcul 1}
|
||||
% développer
|
||||
Développer et réduire l'expression suivante
|
||||
\[
|
||||
A = (2 + 5x)(1 - x)
|
||||
\]
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Calcul 2}
|
||||
% Evolution
|
||||
Une usine produit 15 tonnes. Sa production augmente de 5\%.
|
||||
|
||||
Combien cette usine produit-elle après l'augmentation?
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Calcul 3}
|
||||
% Inversion formule
|
||||
\vfill
|
||||
On rappelle
|
||||
|
||||
\includegraphics[scale=0.5]{./fig/poids.png}
|
||||
|
||||
\vfill
|
||||
|
||||
Calculer la masse $m$ pour un objet dont le poids, $P$, est de $10N$ sur terre ($g = 9,6N.kg^{-1}$)
|
||||
|
||||
\vfill
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Calcul 4}
|
||||
% Equation graphique
|
||||
Déterminer graphiquement $f(x) \leq 2$
|
||||
\begin{center}
|
||||
\begin{tikzpicture}[scale=0.8]
|
||||
\tkzInit[xmin=-5,xmax=5,xstep=1,
|
||||
ymin=-3,ymax=5,ystep=1]
|
||||
\tkzGrid
|
||||
\tkzAxeXY
|
||||
\draw[very thick, color=red] plot [smooth,tension=0.5] coordinates{%
|
||||
(-5, 5)
|
||||
(-4, 4)
|
||||
(-3, 2)
|
||||
(-2, 1)
|
||||
(-1, 2)
|
||||
(0, 3)
|
||||
(1, 3)
|
||||
(2, 4)
|
||||
(3, 3)
|
||||
(4, 4)
|
||||
(5, 3)
|
||||
};
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Fin}
|
||||
\begin{center}
|
||||
On retourne son papier.
|
||||
\end{center}
|
||||
\end{frame}
|
||||
|
||||
|
||||
\end{document}
|
||||
BIN
2nd/Questions_flashs/P2/QF_S45-3.pdf
Normal file
BIN
2nd/Questions_flashs/P2/QF_S45-3.pdf
Normal file
Binary file not shown.
102
2nd/Questions_flashs/P2/QF_S45-3.tex
Executable file
102
2nd/Questions_flashs/P2/QF_S45-3.tex
Executable file
@@ -0,0 +1,102 @@
|
||||
\documentclass[14pt]{classPres}
|
||||
\usepackage{tkz-fct}
|
||||
|
||||
\author{}
|
||||
\title{}
|
||||
\date{}
|
||||
|
||||
\begin{document}
|
||||
\begin{frame}{Questions flashs}
|
||||
\begin{center}
|
||||
\vfill
|
||||
2nd
|
||||
\vfill
|
||||
30 secondes par calcul
|
||||
\vfill
|
||||
\tiny \jobname
|
||||
\end{center}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Calcul 1}
|
||||
% développer
|
||||
Développer et réduire l'expression suivante
|
||||
\begin{multicols}{2}
|
||||
\[
|
||||
A = (4 - 2x)(10x + 1)
|
||||
\]
|
||||
|
||||
\[
|
||||
B = (5 + 3x)(2 - 3x)
|
||||
\]
|
||||
\end{multicols}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Calcul 2}
|
||||
% Evolution
|
||||
\begin{multicols}{2}
|
||||
Une usine produit 35 tonnes. Sa production diminue de 7\%.
|
||||
|
||||
Une usine produit 40 tonnes. Sa production diminue de 3\%.
|
||||
\end{multicols}
|
||||
Combien cette usine produit-elle après cette évolution?
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Calcul 3}
|
||||
% Inversion formule
|
||||
\vfill
|
||||
On rappelle la formule $U = R\times I$.
|
||||
|
||||
\vfill
|
||||
|
||||
\begin{multicols}{2}
|
||||
On donne les valeurs $U = 12V$ et $I = 5A$.
|
||||
|
||||
On donne les valeurs $U = 220V$ et $I = 10A$.
|
||||
\end{multicols}
|
||||
|
||||
\vfill
|
||||
|
||||
Calculer la valeur de $R$.
|
||||
|
||||
\vfill
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Calcul 4}
|
||||
% Equation graphique
|
||||
Déterminer graphiquement
|
||||
\begin{multicols}{2}
|
||||
$f(x) \leq -1$
|
||||
|
||||
$f(x) \geq 1$
|
||||
\end{multicols}
|
||||
\begin{center}
|
||||
\begin{tikzpicture}[scale=0.8]
|
||||
\tkzInit[xmin=-5,xmax=5,xstep=1,
|
||||
ymin=-3,ymax=4,ystep=1]
|
||||
\tkzGrid
|
||||
\tkzAxeXY
|
||||
\draw[very thick, color=red] plot [smooth,tension=0.5] coordinates{%
|
||||
(-5, -0)
|
||||
(-4, -0)
|
||||
(-3, 1)
|
||||
(-2, 2)
|
||||
(-1, 3)
|
||||
(0, 2)
|
||||
(1, 1)
|
||||
(2, -1)
|
||||
(3, -2)
|
||||
(4, -1)
|
||||
(5, 0)
|
||||
};
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Fin}
|
||||
\begin{center}
|
||||
On retourne son papier.
|
||||
\end{center}
|
||||
\end{frame}
|
||||
|
||||
|
||||
\end{document}
|
||||
BIN
2nd/Questions_flashs/P2/fig/concentration.png
Normal file
BIN
2nd/Questions_flashs/P2/fig/concentration.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 24 KiB |
BIN
2nd/Questions_flashs/P2/fig/energie_cinetique.png
Normal file
BIN
2nd/Questions_flashs/P2/fig/energie_cinetique.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 28 KiB |
BIN
2nd/Questions_flashs/P2/fig/energie_elec.png
Normal file
BIN
2nd/Questions_flashs/P2/fig/energie_elec.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 62 KiB |
BIN
2nd/Questions_flashs/P2/fig/gravitation.png
Normal file
BIN
2nd/Questions_flashs/P2/fig/gravitation.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 251 KiB |
BIN
2nd/Questions_flashs/P2/fig/poids.png
Normal file
BIN
2nd/Questions_flashs/P2/fig/poids.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 56 KiB |
BIN
2nd/Questions_flashs/P2/fig/tension.png
Normal file
BIN
2nd/Questions_flashs/P2/fig/tension.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 82 KiB |
@@ -1,6 +1,6 @@
|
||||
<mxfile host="Electron" agent="Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) draw.io/27.0.9 Chrome/134.0.6998.205 Electron/35.7.5 Safari/537.36" version="27.0.9">
|
||||
<mxfile host="Electron" agent="Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) draw.io/28.2.5 Chrome/138.0.7204.251 Electron/37.5.1 Safari/537.36" version="28.2.5">
|
||||
<diagram name="Page-1" id="V1xW8uQNRNiIfV4cWiHY">
|
||||
<mxGraphModel dx="831" dy="2460" grid="1" gridSize="10" guides="1" tooltips="1" connect="1" arrows="1" fold="1" page="1" pageScale="1" pageWidth="827" pageHeight="1169" math="0" shadow="0">
|
||||
<mxGraphModel dx="1673" dy="1038" grid="1" gridSize="10" guides="1" tooltips="1" connect="1" arrows="1" fold="1" page="1" pageScale="1" pageWidth="827" pageHeight="1169" math="0" shadow="0">
|
||||
<root>
|
||||
<mxCell id="0" />
|
||||
<mxCell id="1" parent="0" />
|
||||
@@ -187,272 +187,284 @@
|
||||
<mxCell id="BBVUVwuMvon4YT-9Sltr-72" value="Coef binomiaux" style="text;strokeColor=none;fillColor=none;align=left;verticalAlign=middle;spacingLeft=4;spacingRight=4;overflow=hidden;points=[[0,0.5],[1,0.5]];portConstraint=eastwest;rotatable=0;whiteSpace=wrap;html=1;" parent="BBVUVwuMvon4YT-9Sltr-70" vertex="1">
|
||||
<mxGeometry y="60" width="140" height="30" as="geometry" />
|
||||
</mxCell>
|
||||
<mxCell id="CNFhG9bgBrck8LtLg0sj-2" value="" style="shape=table;startSize=0;container=1;collapsible=0;childLayout=tableLayout;fontSize=16;" vertex="1" parent="1">
|
||||
<mxCell id="CNFhG9bgBrck8LtLg0sj-2" value="" style="shape=table;startSize=0;container=1;collapsible=0;childLayout=tableLayout;fontSize=16;" parent="1" vertex="1">
|
||||
<mxGeometry x="40" y="1050" width="1480" height="1029" as="geometry" />
|
||||
</mxCell>
|
||||
<mxCell id="CNFhG9bgBrck8LtLg0sj-3" value="" style="shape=tableRow;horizontal=0;startSize=0;swimlaneHead=0;swimlaneBody=0;strokeColor=inherit;top=0;left=0;bottom=0;right=0;collapsible=0;dropTarget=0;fillColor=none;points=[[0,0.5],[1,0.5]];portConstraint=eastwest;fontSize=16;" vertex="1" parent="CNFhG9bgBrck8LtLg0sj-2">
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</mxCell>
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</root>
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</mxGraphModel>
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</diagram>
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|
Before Width: | Height: | Size: 233 KiB After Width: | Height: | Size: 220 KiB |
@@ -11,10 +11,10 @@ general:
|
||||
|
||||
# Configuration des classes/niveaux
|
||||
classes:
|
||||
- id: "1G_EnsSci"
|
||||
- id: "1G spec"
|
||||
display_name: "Première Générale Enseignement Scientifique math"
|
||||
directory: "1G_EnsSci"
|
||||
- id: "1G_math"
|
||||
- id: "1G math"
|
||||
display_name: "Première Générale spé math"
|
||||
directory: "1G_math"
|
||||
- id: "2nd"
|
||||
|
||||
@@ -12,7 +12,12 @@ import yaml
|
||||
import questionary
|
||||
from questionary import Choice
|
||||
|
||||
from .common_widgets import select_date_with_calendar, format_date_short, select_tags, normalize_filename
|
||||
from .common_widgets import (
|
||||
select_date_with_calendar,
|
||||
format_date_short,
|
||||
select_tags,
|
||||
normalize_filename,
|
||||
)
|
||||
|
||||
# Configuration des messages
|
||||
MESSAGES = {
|
||||
@@ -80,7 +85,7 @@ class SequenceCreator:
|
||||
existing_sequences.append(item.name)
|
||||
|
||||
existing_sequences.sort()
|
||||
next_number = len(existing_sequences) + 1
|
||||
next_number = len(existing_sequences) # + 1
|
||||
|
||||
return existing_sequences, next_number
|
||||
|
||||
@@ -299,4 +304,3 @@ def main():
|
||||
|
||||
if __name__ == "__main__":
|
||||
main()
|
||||
|
||||
|
||||
27
tools/skeleton/eval/solution.tex
Normal file
27
tools/skeleton/eval/solution.tex
Normal file
@@ -0,0 +1,27 @@
|
||||
\documentclass[a4paper,12pt]{article}
|
||||
\usepackage{myXsim}
|
||||
|
||||
% Title Page
|
||||
\title{${name} \hfill Solution}
|
||||
\tribe{${tribe}}
|
||||
\date{${date_short}}
|
||||
\duree{${duration}}
|
||||
% Tags: ${tags}
|
||||
|
||||
\DeclareExerciseCollection[step=1]{banque}
|
||||
\xsimsetup{
|
||||
exercise/print=false,
|
||||
solution/print=true,
|
||||
}
|
||||
|
||||
\begin{document}
|
||||
\maketitle
|
||||
|
||||
\input{exercises.tex}
|
||||
%\printcollection{banque}
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
@@ -2,7 +2,7 @@
|
||||
\usepackage{myXsim}
|
||||
|
||||
% Title Page
|
||||
\title{ ${name} \hfill ${subname}}
|
||||
\title{${name}}
|
||||
\tribe{${tribe}}
|
||||
\date{${date_short}}
|
||||
\duree{${duration}}
|
||||
|
||||
@@ -27,9 +27,6 @@ Savoir-faire de la séquence
|
||||
|
||||
\bigskip
|
||||
|
||||
Ordre des étapes à respecter
|
||||
|
||||
|
||||
\section{}
|
||||
|
||||
\listsectionexercises
|
||||
|
||||
Reference in New Issue
Block a user