From e8c04058b57d3f408f3cd5275184a84770c839fa Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 30 Aug 2022 09:04:04 +0200 Subject: [PATCH] Feat: ajoute les exercices techniques et les solutions pour 1E --- .../1E_proportion.pdf | Bin 24753 -> 28402 bytes .../all_exercises.pdf | Bin 0 -> 38312 bytes .../all_exercises.tex | 26 +++++ 2nd/01_Proportion_et_fractions/exercises.tex | 102 +++++++++++++++++- 2nd/01_Proportion_et_fractions/index.rst | 22 +++- 2nd/01_Proportion_et_fractions/solutions.pdf | Bin 0 -> 28093 bytes 2nd/01_Proportion_et_fractions/solutions.tex | 28 +++++ 7 files changed, 176 insertions(+), 2 deletions(-) create mode 100644 2nd/01_Proportion_et_fractions/all_exercises.pdf create mode 100644 2nd/01_Proportion_et_fractions/all_exercises.tex create mode 100644 2nd/01_Proportion_et_fractions/solutions.pdf create mode 100644 2nd/01_Proportion_et_fractions/solutions.tex diff --git a/2nd/01_Proportion_et_fractions/1E_proportion.pdf 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e5c6e3a..a868d2f 100644 --- a/2nd/01_Proportion_et_fractions/exercises.tex +++ b/2nd/01_Proportion_et_fractions/exercises.tex @@ -16,9 +16,52 @@ \begin{exercise}[subtitle={Techniques}, step={1}, origin={MEpC}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\trainMode}] + \begin{enumerate} + \item Sur 150 candidats à l'examen, 120 ont été admis. Calculer la proportion d'élèves admis. + \item Une urne contient 7 jetons noirs, 5 rouges et 10 vert. Calculer la proportion de jetons rouges. + \item Pour mieux orienter ses clients, un loueur de camping-car a demandé aux campings la nature des emplacements qu'ils proposent. Son gérant a mis les résultats dans le tableau suivant: + \begin{table}[htbp] + \centering + \begin{tabular}{|c|*{4}{c|}} + \hline + Camping & Les flots bleu & Cascade magique & Le tronc dégarni & La vallée plate\\ + \hline + Emplacements tentes & 25 & 0 & 30 & 50\\ + \hline + Emplacements Camping car & 0 & 10 & 40 & 100 \\ + \hline + Mobile Home & 10 & 5 & 5 & 50 \\ + \hline + \end{tabular} + \end{table} + \begin{enumerate} + \item Calculer la proportion de d'emplacement camping car pour chacun des emplacements. + \item Classer les campings en ordre croissant de la part qu'ils dédient aux camping cars. + \end{enumerate} + \end{enumerate} \end{exercise} +\begin{solution} + \begin{enumerate} + \item $\frac{120}{150} = \frac{4}{5} = 0.8 = 80\%$ + \item $\frac{5}{22} \approx 0.22 = 22\%$ + \item + + \begin{tabular}{|p{4cm}|*{4}{c|}} + \hline + Camping & Les flots bleu & Cascade magique & Le tronc dégarni & La vallée plate\\ + \hline + Proportion en fraction & $\frac{0}{35}$ & $\frac{10}{15}$ & $\frac{40}{75}$ & $\frac{100}{200}$ \\ + \hline + Proportion en décimal & 0 & 0.66 & 0.53 & 0.5 \\ + \hline + Classement & 4e & 1er & 2e & 3e \\ + \hline + \end{tabular} + \end{enumerate} +\end{solution} + \begin{exercise}[subtitle={Lancers francs (suite)}, step={1}, origin={MEpC}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\searchMode}] Sarah s'entraine encore chaque jour entre le 3 et 7 septembre. Sur l'ensemble des deux semaines, sa fréquence de réussite fluctue entre 55\% et 77\% (fréquence arrondis au centième). @@ -60,8 +103,65 @@ \end{center} \end{exercise} +\begin{solution} + \begin{tabular}{|*{4}{c|}} + \hline + Proportion & Fraction irréductible & Effectifs associés & Valeur décimale \\ + \hline + 10\% & $\frac{1}{10}$ & 10 pour 100, c'est comme 1 pour 10 & 0.1\\ + \hline + 20\% & $\frac{1}{5}$ & 20 pour 100, c'est comme 1 pour 5 & 0.2\\ + \hline + 25\% & $\frac{1}{4}$ & 25 pour 100, c'est comme 1 pour 4 & 0.25\\ + \hline + 33.3\% & $\frac{333}{1000}$ & 33.3 pour 100, c'est comme 333 pour 1000 & 0.333\\ + \hline + 50\% & $\frac{1}{2}$ & 50 pour 100, c'est comme 1 pour 2 & 0.5 \\ + \hline + 60\% & $\frac{3}{5}$ & 60 pour 100, c'est comme 3 pour 5 & 0.6 \\ + \hline + 66.7\% & $\frac{667}{1000}$ & 66.7 pour 100, c'est comme 667 pour 1000 & 0.667\\ + \hline + 75\% & $\frac{3}{4}$ & 75 pour 100, c'est comme 3 pour 4 & 0.75 \\ + \hline + 100\% & 1 & 100 pour 100, c'est comme 1 pour 1 & 1\\ + \hline + \end{tabular} +\end{solution} -\begin{exercise}[subtitle={Radars}, step={1}, origin={MEpC}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\projectMode}] +\begin{exercise}[subtitle={Techniques}, step={1}, origin={MEpC}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\trainMode}] + \begin{enumerate} + \item Calculer 20\% de 190. + \item Calculer les deux tiers de 126. + \item Donner le pourcentage 42\% sous forme de fraction irréductible puis sous forme décimale. + \item Donner le pourcentage 78\% sous forme de fraction irréductible puis sous forme décimale. + \item Dans un panier, il y a 5kg de course dont 1,5kg de légumes. Calculer la proportion de légumes sous forme de fraction, de pourcentage et décimale. + \item Dans un forêt, il y a 2300 arbres dont 1500 sont des sapins. Calculer la proportion de sapins sous forme de fraction, de pourcentage et décimale. + \item Dans un pot de crème fraiche de 400g, il y a écrit 30\% de matière grasse. Calculer la quantité de matière grasse dans ce pot. + \item Une usine produit environ \np{2 000 000} de clous par jours. 0,6\% sont non conformes. Calculer la quantité de clous non conformes. + \item Un professeur a rendez-vous avec 40\% des parents d'élèves, c'est à dire 14 parents. Combien d'élèves a ce professeur? + \item Les trois quart des recettes d'une entreprise se font par la vente de marchandises. Ces ventes ont représenté \np{150 000}\euro. Quelles sont les recettes de cette entreprise? + \item (*)Les élèves de 2nd représentent environ 24\% des élèves d'un lycée. Ils sont répartis en 5 classes de 30 élèves. Combien y a-t-il d'élèves dans le lycée? + \end{enumerate} +\end{exercise} + +\begin{solution} + \begin{enumerate} + \item $\frac{20}{100} \times 190 = 38$ + \item $\frac{2}{3} \times 126 = 84$ + \item $\frac{42}{100} = \frac{31}{50} = 0.42$ + \item $\frac{78}{100} = \frac{39}{50} = 0.78$ + \item $\frac{1,5}{5} = \frac{3}{10} = 0.3$ + \item $\frac{1500}{2300} = \frac{15}{23} \approx 0.65$ + \item $\frac{30}{100} \times 400 = 120$ + \item $\frac{0.6}{100} \times \np{2 000 000} = \np{12 000}$ + \item $ \frac{14}{0.4} = 35$ + \item $ \frac{150 000}{0.75} = 200 000$ + \item $ \frac{5\times 30}{0.24} = 625$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}, step={1}, origin={MEpC}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\groupMode}] Un radar de la sécurité routière prend en photo les véhicules en excès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule, on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. Le radar a pris des photos pendant l'été: diff --git a/2nd/01_Proportion_et_fractions/index.rst b/2nd/01_Proportion_et_fractions/index.rst index e3f2a42..9d8065c 100644 --- a/2nd/01_Proportion_et_fractions/index.rst +++ b/2nd/01_Proportion_et_fractions/index.rst @@ -2,7 +2,7 @@ Proportion et fractions ####################### :date: 2022-08-27 -:modified: 2022-08-27 +:modified: 2022-08-30 :authors: Benjamin Bertrand :tags: Statistiques, Fractions :category: 2nd @@ -41,9 +41,28 @@ Description de la séquence On reprend en grande partie la séquence 1 du livre Les Maths Ensemble et pour Chacun. +Tous les exercices de la séquence (ou presque) avec la correction des exercices techniques + +.. image:: ./all_exercises.pdf + :height: 200px + :alt: Solution des exercices techniques + +Juste les solution + +.. image:: ./solutions.pdf + :height: 200px + :alt: Juste les solutions + + + Étape 1: Fréquence/proportion et simplification de fractions ------------------------------------------------------------ +.. image:: ./1E_proportion.pdf + :height: 200px + :alt: Exercices de l'étape 1 + + Elaboration de la notion de proportion: exercice des lancers francs. 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+\title{Proportion et fractions - Solutions} +\date{août 2022} + + +\DeclareExerciseCollection{banque} +\xsimsetup{ + exercise/print=false, + solution/print=true, +} + +\pagestyle{empty} + + +\begin{document} + +\maketitle + +\input{exercises.tex} +%\printcollection{banque} +%\printsolutions{exercises} + +\end{document}