From dcce2aff1b3fae926c81d69683d5af93578e548b Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 12 Jan 2023 10:18:00 +0100 Subject: [PATCH] =?UTF-8?q?Feat(2nd):=20premi=C3=A8res=20pierres=20pour=20?= =?UTF-8?q?un=20chapitre=20report=C3=A9?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 2nd/09_Racine_carre/1B_definition.pdf | Bin 0 -> 27815 bytes 2nd/09_Racine_carre/1B_definition.tex | 100 ++++++++++++++++++++++++ 2nd/09_Racine_carre/exercises.tex | 15 ++++ 2nd/09_Racine_carre/index.rst | 28 +++++++ 2nd/09_Racine_carre/plan_de_travail.tex | 44 +++++++++++ 2nd/09_Racine_carre/solutions.tex | 28 +++++++ 6 files changed, 215 insertions(+) create mode 100644 2nd/09_Racine_carre/1B_definition.pdf create mode 100644 2nd/09_Racine_carre/1B_definition.tex create mode 100644 2nd/09_Racine_carre/exercises.tex create mode 100644 2nd/09_Racine_carre/index.rst create mode 100644 2nd/09_Racine_carre/plan_de_travail.tex create mode 100644 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+\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Racine carre - Cours} +\date{janvier 2023} + +\pagestyle{empty} + +\begin{document} + +\maketitle + +\begin{definition}[La racine carré] + La \textbf{racine carré d'une nombre $a$}, noté $\sqrt{a}$, est le nombre \textbf{positif} qui mis au carré est égal à $a$. C'est à dire + + \[ + \sqrt{a} \geq 0 \qquad \qquad (\sqrt{a})^2 = a + \] +\end{definition} + +\paragraph{Exemples:} +\begin{multicols}{2} + \begin{itemize} + \item $\sqrt{4} = ...... $ car \dotfill + \item $\sqrt{25} = ...... $ car \dotfill + \item $\sqrt{1,6} = ...... $ car \dotfill + \item $\sqrt{4.41} = ...... $ car \dotfill + \item $\sqrt{2} = ...... $ car \dotfill + \end{itemize} +\end{multicols} + +\paragraph{Remarque:} On ne peut pas prendre la racine carrée d'un nombre négatif, car \dotfill +\bigskip + +\begin{propriete}[ Multiplication ou division ] + Règles de calculs pour la multiplication. Soit $a$ et $b$ deux nombres positifs. + + \[ + \sqrt{a}\times\sqrt{b} = \sqrt{a\times b} + \qquad \qquad + a\sqrt{b} = \sqrt{a^2\times b} + \qquad \qquad + \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} + \] + +\end{propriete} + +\begin{multicols}{2} + + \paragraph{Exemples:}~\\ + \noindent + Multplications + \begin{itemize} + \item $\sqrt{32}\times\sqrt{2} = $ + \item $\sqrt{27}\times\sqrt{3} = $ + \item $\sqrt{3}\times\sqrt{36}\times\sqrt{3} = $ + \item $\left( 6\sqrt{3} \right) = $ + \end{itemize} + Mise sous la forme $a\sqrt{b}$ (avec $b$ le plus petit possible) + \begin{itemize} + \item $\sqrt{72}=$ + \item $\sqrt{45} = $ + \item $3\sqrt{125} = $ + \end{itemize} + + \columnbreak + Démonstration de la formule $\sqrt{a}\times\sqrt{b} = \sqrt{a\times b}$ +\end{multicols} + + +\begin{propriete}[ Somme ] + + Soit $a$ et $b$ deux nombres positifs \textbf{non nuls}. + + \[ + \sqrt{a+b} < \sqrt{a}+ \sqrt{b} + \] +\end{propriete} + +\paragraph{Méthode pour additionner des racines carrés}~ + +\begin{multicols}{2} + \begin{itemize} + \item Écrire le nombre suivant sous la forme $a\sqrt{b}$ + \[ + A = 7\sqrt{5} + 9\sqrt{5} + \] + + \item Écrire le nombre suivant sous la forme $a\sqrt{b}$ + \[ + B = 2\sqrt{147} + 5\sqrt{12} - 3\sqrt{27} + \] + \end{itemize} + +\end{multicols} + + + +\end{document} diff --git a/2nd/09_Racine_carre/exercises.tex b/2nd/09_Racine_carre/exercises.tex new file mode 100644 index 0000000..0995e88 --- /dev/null +++ b/2nd/09_Racine_carre/exercises.tex @@ -0,0 +1,15 @@ +\begin{exercise}[subtitle={Simplification}, step={1}, origin={???}, topics={ Racine carre }, tags={ Racine carre }] + Simplifier les valeurs suivantes sans calculatrices + \begin{multicols}{4} + \begin{enumerate} + \item $\sqrt{25}$ + \item $\sqrt{7^2}$ + \item $(\sqrt{14})^2$ + \item + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + <++> +\end{solution} diff --git a/2nd/09_Racine_carre/index.rst b/2nd/09_Racine_carre/index.rst new file mode 100644 index 0000000..9149e9d --- /dev/null +++ b/2nd/09_Racine_carre/index.rst @@ -0,0 +1,28 @@ +Racine carre +############ + +:date: 2023-01-12 +:modified: 2023-01-12 +:authors: Benjamin Bertrand +:tags: Racine carre +:category: 2nd +:summary: Exercices techniques autour de la racine carré + + +Éléments du programme +===================== + +Contenus +-------- + +Capacités attendues +------------------- + +Commentaires +------------ + +Progression +=========== + +Étape 1: +-------- diff --git a/2nd/09_Racine_carre/plan_de_travail.tex b/2nd/09_Racine_carre/plan_de_travail.tex new file mode 100644 index 0000000..2c82209 --- /dev/null +++ b/2nd/09_Racine_carre/plan_de_travail.tex @@ -0,0 +1,44 @@ +\documentclass[a4paper,12pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Racine carre - Plan de travail} +\tribe{2nd} +\date{janvier 2023} + +\pagestyle{empty} + +\DeclareExerciseCollection{banque} +\xsimsetup{ +} + + +\begin{document} +\maketitle + +% Résumé + +\bigskip + +Savoir-faire de la séquence +\begin{itemize} + \item +\end{itemize} + +\bigskip + +Ordre des étapes à respecter + + +\section{} + +\listsectionexercises + + +\pagebreak + +\input{exercises.tex} +\printcollection{banque} + + +\end{document} diff --git a/2nd/09_Racine_carre/solutions.tex b/2nd/09_Racine_carre/solutions.tex new file mode 100644 index 0000000..ed9b3f9 --- /dev/null +++ b/2nd/09_Racine_carre/solutions.tex @@ -0,0 +1,28 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\usetikzlibrary{shapes.geometric} + +\author{Benjamin Bertrand} +\title{Racine carre - Solutions} +\tribe{2nd} +\date{janvier 2023} + +\DeclareExerciseCollection{banque} +\xsimsetup{ + exercise/print=false, + solution/print=true, +} + +\pagestyle{empty} + + +\begin{document} + +\maketitle + +\input{exercises.tex} +%\printcollection{banque} +%\printsolutions{exercises} + +\end{document}