From a88ee14831eb0c3f2b4763863921929c1ee09fae Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 8 Feb 2022 09:37:03 +0100 Subject: [PATCH] Feat: plan de travail sur les multiples et diviseurs --- 4e/12_Arithmetique/1B.tex | 14 --- 4e/12_Arithmetique/exercises.tex | 133 +++++++++++++++++++++++-- 4e/12_Arithmetique/plan_de_travail.pdf | Bin 35194 -> 43013 bytes 4e/12_Arithmetique/plan_de_travail.tex | 4 + 4e/12_Arithmetique/solutions.pdf | Bin 0 -> 26229 bytes 4e/12_Arithmetique/solutions.tex | 2 +- 6 files changed, 128 insertions(+), 25 deletions(-) delete mode 100644 4e/12_Arithmetique/1B.tex create mode 100644 4e/12_Arithmetique/solutions.pdf diff --git a/4e/12_Arithmetique/1B.tex b/4e/12_Arithmetique/1B.tex deleted file mode 100644 index 92b21fd..0000000 --- a/4e/12_Arithmetique/1B.tex +++ /dev/null @@ -1,14 +0,0 @@ -\documentclass[a4paper,10pt]{article} -\usepackage{myXsim} - -\author{Benjamin Bertrand} -\title{Arithmetique - Cours} -\date{2022-02-01} - -\pagestyle{empty} - -\begin{document} - -\maketitle - -\end{document} diff --git a/4e/12_Arithmetique/exercises.tex b/4e/12_Arithmetique/exercises.tex index db721d0..3d63db6 100644 --- a/4e/12_Arithmetique/exercises.tex +++ b/4e/12_Arithmetique/exercises.tex @@ -35,18 +35,33 @@ Je n'aime pas gaspiller et je ne veux donc pas de reste. Combien de paquet de chaque dois-je acheter? Combien de sandwichs vais-je pouvoir me faire? \end{exercise} -\begin{exercise}[subtitle={Diviseurs}, step={2}, origin={Création}, topics={Arithmétique}, tags={arithmétique}, mode={\faIcon{search}}] - \begin{enumerate} - \item Déterminer tous les diviseurs des nombres suivants - - \[ - 4 \qquad 10 \qquad 21 \qquad 46 \qquad 64 \qquad 77 - \] - \item Trouver un nombre qui a exactement 4 diviseurs. - \item Trouver quatre nombres qui ont exactement 2 diviseurs. - \end{enumerate} +\begin{exercise}[subtitle={Multiples et diviseurs}, step={2}, origin={Création}, topics={Arithmétique}, tags={arithmétique}, mode={\faIcon{book}}] + Recopier le cours: \textbf{Multiples et diviseurs} \end{exercise} +\begin{solution} + \subsection*{Multiples et diviseurs} + + \begin{definition} + \begin{itemize} + \item On dit qu'un nombre, $a$, est un \textbf{diviseur} d'un autre, $b$, quand $b$ peut être partagé en $a$ parts (on dit que la division euclidienne de $a$ par $b$ n'a pas de reste) + \item On dit qu'un nombre, $a$, un \textbf{multiple} d'un autre, $b$, quand on peut multiplier $a$ pour obtenir $b$. + \end{itemize} + \end{definition} + + \paragraph{Exemples:} + \begin{itemize} + \item 2 est un \textbf{diviseur} de 10 car \dotfill \\[0.5cm] + \item 3 n'est pas un \textbf{diviseur} de 10 car \dotfill \\[0.5cm] + \item Les diviseurs de 10 sont \dotfill \\[1cm] + + \item 8 est un \textbf{multiple} de 4 car \dotfill \\[0.5cm] + \item 10 est un \textbf{multiple} de 2 car \dotfill \\[0.5cm] + \item 10 n'est pas un \textbf{multiple} de 3 car \dotfill \\[0.5cm] + \item 10 n'est pas un \textbf{multiple} de 20 car \dotfill \\[0.5cm] + \end{itemize} +\end{solution} + \begin{exercise}[subtitle={Vrai/faux}, step={2}, origin={Création}, topics={Arithmétique}, tags={arithmétique}, mode={\faIcon{tools}}] Déterminer plus expliquer si les phrases suivantes sont vraies. \begin{multicols}{2} @@ -78,3 +93,101 @@ \end{exercise} +\begin{exercise}[subtitle={Diviseurs}, step={3}, origin={Création}, topics={Arithmétique}, tags={arithmétique}, mode={\faIcon{search}}] + \begin{enumerate} + \item Déterminer tous les diviseurs des nombres suivants + + \[ + 4 \qquad 10 \qquad 21 \qquad 46 \qquad 64 \qquad 77 + \] + \item Trouver un nombre qui a exactement 4 diviseurs. + \item Trouver quatre nombres qui ont exactement 2 diviseurs. + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Nombres premiers}, step={3}, origin={Création}, topics={Arithmétique}, tags={arithmétique}, mode={\faIcon{book}}] + Recopier le cours: \textbf{Nombres premiers} +\end{exercise} + +\begin{solution} + \subsection*{Nombres premiers} + + \begin{definition}[Nombres premiers] + On dit qu'un nombre est un \textbf{nombre premier} quand il n'a que deux diviseurs 1 et lui même. + \end{definition} + + \paragraph{Exemples:} + \begin{itemize} + \item Les diviseurs de 5 sont: \dotfill \\[1cm] + Donc 5 est \qquad \textit{un nombre premier \qquad / \qquad pas un nombre premier} + \item Les diviseurs de 10 sont: \dotfill \\[1cm] + Donc 10 est \qquad \textit{un nombre premier \qquad / \qquad pas un nombre premier} + \item Les diviseurs de 32 sont: \dotfill \\[1cm] + Donc 32 est \qquad \textit{un nombre premier \qquad / \qquad pas un nombre premier} + \end{itemize} +\end{solution} + +\begin{exercise}[subtitle={Crible d'Eratosthène}, step={3}, origin={Création}, topics={Arithmétique}, tags={arithmétique}, mode={\faIcon{search}}] + \newcommand{\numInBox}[1]{% + \framebox{\parbox[][14pt][b]{1.2em}{% + \centering% + #1% + }}% + } + + \newcounter{clig} + \newcounter{ccol} + \newcounter{cligmax} + \newcounter{ccolmax} + \newcounter{csym} + \newcommand{\range}[3]{% + % #1 min, #3 nbr ligne, #4 nbr col + \setcounter{clig}{0}% Mise à zéro des compteurs de ligne + \setcounter{ccol}{0}% et de colonne + \setcounter{cligmax}{#2}% arguments 3 et 4 pour fixer + \setcounter{ccolmax}{#3}% le nombre max de colonnes et de lignes + \whiledo{\value{clig}<\value{cligmax}}{% + \setcounter{ccol}{0}% remise à zéro du compteur de colonne + \whiledo{\value{ccol}<\value{ccolmax}}{% + % on calcule le numéro du symbole + \setcounter{csym}{% + \value{clig}*\value{ccolmax}+\value{ccol}+#1} + \numInBox{\thecsym} + \stepcounter{ccol}% + }% on passe à la colonne suivante + \stepcounter{clig}% on passe à la ligne suivante + % on saute une ligne , sauf à la fin + \ifthenelse{\value{clig}<\value{cligmax}}{\\}{}% + }} + On cherche à découvrir une famille de nombres aux propriétés très particulières, \textbf{les nombres premiers}. + + \begin{minipage}{0.5\linewidth} + \begin{center} + \range{1}{10}{10} + \end{center} + \end{minipage} + \begin{minipage}{0.5\linewidth} + + + \Ovalbox{% + \begin{minipage}{0.9\textwidth} + \hspace{0.2cm} + \textbf{Algorithme du Crible} + \begin{itemize} + \item Sélectionner un nombre. + \item S'il n'est pas barré, l'entourer. + \item Barrer tous les multiples de ce nombre. + \end{itemize} + \end{minipage} + } + + \begin{enumerate} + \item Appliquer cet algorithme à 2. + \item Appliquer cet algorithme à 3. + \item Appliquer cet algorithme à 4. + \item Appliquer cet algorithme aux autres nombres dans l'ordre croissant. + \item Faire la liste de tous les nombres entourés. Ce sont tous les nombres premiers inférieur à 100. + \item Écrire une phrase expliquant ce qui lie tous ces nombres. + \end{enumerate} + \end{minipage} +\end{exercise} diff --git a/4e/12_Arithmetique/plan_de_travail.pdf b/4e/12_Arithmetique/plan_de_travail.pdf index 70233ea67f05d63e2282ab71ad162cfd9af8515f..1ba07391142a7ae5a4eaa2ab289856250fae1a3f 100644 GIT binary patch delta 30710 zcmbSyV{m0%*KImR$9B@OZQHgxw$mH_!9F->qA9@2~sgRIM{= z&UNSIMARe(3y$9pMx@QvHb2AhPjynb} z*Y{sTzPEjx?Hv^5o4|9QhkSu3>Kw?T2m17UJeR!rPSR)n(d4oXIEXXR3kvFk&0l z>Jz*jE~Roy{u0w5lIc(im%hSgx)DYV(6K{CPAw=T31Yz)GPOpWGeuS~JMKEzyS2

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a/4e/12_Arithmetique/plan_de_travail.tex b/4e/12_Arithmetique/plan_de_travail.tex index bea291b..07ada01 100644 --- a/4e/12_Arithmetique/plan_de_travail.tex +++ b/4e/12_Arithmetique/plan_de_travail.tex @@ -37,6 +37,10 @@ Savoir-faire de la séquence \listsectionexercises +\section{Nombres premiers} + +\listsectionexercises + \pagebreak \input{exercises.tex} diff --git a/4e/12_Arithmetique/solutions.pdf b/4e/12_Arithmetique/solutions.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2126ef84e01e6e6a41abe369d5f5bea2a2d521ca GIT binary patch literal 26229 zcmce;1CVU(k~Q46ZQHhOyZf|l+qP}nw%w<3+O}W&16I(N9a{@+I z0zN*1|9n6>IXjvd*g(0jFTl?zP|WNC0f2u2-a?t!8vlQ1{=EC^{@MRr`QH}@$GyzfS1N&^42w8CeW3Mo*$)Vs>xdJZ^-$YUu4VUNTR+(lv2W?Y<}#GZ}o{!%Kpzv ztV;1@yJ5njm2U%fWjmkG22alpPsiJtU@i4CQkHmq)$M@4gTQhW)>)RZ1t;0#W~cGp zlnRp^FG@%#OMLStKLb$ww(sNCsuicY6q*2i&@J0xDoQN#e5l`gsVQ^HuU{>+Dgz9w zyH3isy?sA5!ljqZ$L29WClAe%-QH25KffKGd`Jp}343gFbJYuSlaUWqgn@EweLt7H 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