From 4ca89eb8e8c3049205453d048fbe2e93e898de35 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Mon, 11 Oct 2021 09:25:05 +0200 Subject: [PATCH] Feat: correction du devoir --- 2nd/Evaluations/DS_2021-10-11/exercises.tex | 64 +++++++++++++++++--- 2nd/Evaluations/DS_2021-10-11/sujet.pdf | Bin 52762 -> 79225 bytes 2nd/Evaluations/DS_2021-10-11/sujet.tex | 4 ++ 3 files changed, 58 insertions(+), 10 deletions(-) diff --git a/2nd/Evaluations/DS_2021-10-11/exercises.tex b/2nd/Evaluations/DS_2021-10-11/exercises.tex index 08eff6e..d1df609 100644 --- a/2nd/Evaluations/DS_2021-10-11/exercises.tex +++ b/2nd/Evaluations/DS_2021-10-11/exercises.tex @@ -6,31 +6,54 @@ \hline Sports & 2010 & 2015 & 2020 \\ \hline - Musculation & 60 & & 100 \\ + Musculation & 60 & & 100 \\ \hline - Natation & & & 55\\ + Natation & 90 & 115 & 55\\ \hline - Cyclisme & 90 & & 52\\ + Cyclisme & 25 & & 52\\ \hline - Athlétisme & 150 & 88 & 43\\ + Athlétisme & & & 43\\ \hline - Total & 325 & 300 & 250\\ + Total & 325 & 300 & 250\\ \hline \end{tabular} \end{center} - Les questions suivantes sont indépendantes vous pouvez les traiter dans l'ordre que vous souhaitez. + Les questions suivantes sont indépendantes vous pouvez les traiter dans l'ordre que vous souhaitez. Vos valeurs seront arrondis à l'unité. \begin{enumerate} - \item Calculer le nombre de personnes qui on fait de la natation en 2010. - \item En 2015, 15\% des adhérents faisaient de la musculation. Calculer le nombre d'inscrit en musculation en 2015. + \item Calculer le nombre de personnes qui ont fait de la athlétisme en 2010. + \item En 2015, 29,33\% des adhérents faisaient de la athlétisme. Calculer le nombre d'inscrit en athlétisme en 2015. \item Entre 2010 et 2015, le nombre d'inscrits à la musculation a baissé de 25\% tandis que le nombre d'inscrits en cyclisme a augmenté de 108\%. Déterminer les valeurs manquantes de 2015. - \item Calculer la proportion d'inscrits en musculation en 2020. - \item Calculer le taux d'évolution du nombre total d'inscrits en athlétisme entre 2010 et 2015 puis entre 2015 et 2020. Les résultats seront donnés en pourcentage arrondis à l'unité. + \item Calculer la proportion d'inscrits en musculation en 2020. Vous donnerez une réponse en pourcentage. + \item Calculer le taux d'évolution du nombre total d'inscrits en natation entre 2010 et 2015 puis entre 2015 et 2020. Les résultats seront donnés en pourcentage arrondis à l'unité. \item (Dure) Le président du club se rappelle que le nombre total d'inscrit avait augmenté de 30\% entre 2005 et 2010. Combien y avait-il d'inscrits en 2005? \end{enumerate} \end{exercise} +\begin{solution} + \begin{enumerate} + \item Athlétisme en 2010: $325 - (60 + 25 + 90) = 150$ + \item Inscrit en athlétisme en 2015: $300 \times \frac{29.33}{100} = 88$ + \item + \begin{itemize} + \item Inscrits en musculation: $60 \times (1 - \frac{25}{100}) = 45$ + \item Inscrits en cyclisme: $150 \times (1 + \frac{108}{100}) = 52$ + \item Inscrits en athlétisme: $300 - (45 + 52 + 115) = 88$ + \end{itemize} + \item Proportion en musculation en 2020: $\frac{100}{250} = 0.4 = 40\%$ + \item + \begin{itemize} + \item De 2010 à 2015: $\frac{115 - 90}{90} \approx 0.27 = 27\%$ + \item De 2015 à 2020 $\frac{43 - 115}{115} \approx -0.62 = - 62\%$ + \end{itemize} + \item Pour aller de 2005 à 2010, le nombre d'inscrits a été multiplié par $1+\frac{30}{100} = 1.3$ donc pour passer de 2010 à 2005 cette quantité a été divisée par 1,3. + \[ + 325 \div 1.3 = 250 + \] + \end{enumerate} +\end{solution} + \begin{exercise}[subtitle={Calculs avec les fractions}, step={1}, origin={Le chapeau}, topics={Calculs}, tags={Fractions}, points=6] Calculer les quantités suivantes et donner le résultat sous forme de fraction irréductible. \vfill @@ -51,6 +74,24 @@ \end{enumerate} \end{exercise} +\begin{solution} + \begin{enumerate}[label={\Alph*}] + \item $= \dfrac{4}{15} + \dfrac{21}{15} = \dfrac{25}{15} = \dfrac{5}{3}$ + \vfill + \item $= \dfrac{4}{6} - \dfrac{7}{4} = \dfrac{8}{12} -\dfrac{21}{12} = \dfrac{-13}{12}$ + \vfill + \item $= 3 - \dfrac{5}{8} = \dfrac{24}{8} - \dfrac{5}{8} = \dfrac{19}{8}$ + \vfill + \item $= \dfrac{1}{a} + \dfrac{4}{3a} = \dfrac{3}{3a} + \dfrac{4}{3a} = \dfrac{7}{3a}$ + \vfill + + \item $= \dfrac{9}{10} \times 5 = \dfrac{9 \times 5}{10} = \dfrac{9 \times 5}{2 \times 5} = \dfrac{9}{2}$ + \vfill + \item $= \dfrac{16}{21} \times \dfrac{6}{10} = \dfrac{16 \times 6}{21 \times 10} = \dfrac{2 \times 8 \times 3\times 2}{3 \times 7 \times 2 \times 5} = \dfrac{16}{35}$ + \vfill + \end{enumerate} +\end{solution} + \begin{exercise}[subtitle={Lecture de graphiques}, step={1}, origin={Le chapeau}, topics={Calculs}, tags={Fractions}, points=6] On a représenté ci-contre la fonction $f$ pour $x$ allant -5 à 5. @@ -98,3 +139,6 @@ \end{minipage} \end{exercise} +\begin{solution} +\end{solution} + diff --git a/2nd/Evaluations/DS_2021-10-11/sujet.pdf b/2nd/Evaluations/DS_2021-10-11/sujet.pdf index 0f6afdd0cbda3f45422ca9bb59097da2b142565d..507a21a5a72d77ee938047c91310f5d852690ca3 100644 GIT binary patch delta 58750 zcmZsiQ*;b$lY#={U`sTHpaxFqX#d?9MfJ-y?87!CA3Q(%fI)%i5WvzR2j$2)9BM!&h%jZ% zqmCh0aQnJY^;MRSEa0OP7z9t7qSQXoT+(0aUrR->5Zv1R#zeJanqWfHLus`fhnR4? zb$J~V1h&83eIH*JD&ZbUS&7$wlt#k_Q_LjAOVOrp)z;56ya01geT2!)oSw_y6dltT z%Sc&SexANhg1eLwZ1NazjqAI3z6bsa`6It@&Tsq zBU+ef{foT-XA4&Ob4c~TuzANCG}aJF!tISl%iTe$ z{1U;q{O`F}n=b8^_%pGtY+1euO~WgyZ(-k6-YjC~42dH~d1Zc14I_L4Mo)FN4u^(v zRe;k<``)#Ew8&4D{fjGpA5Cw4lBD-8XRcQd!G)pnLkHi)ecY##6)LyU}Rm#jtDy`yXwHDe!jwX^v~_>350jL)+yGQxDOk zqHkt_-17r 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a/2nd/Evaluations/DS_2021-10-11/sujet.tex b/2nd/Evaluations/DS_2021-10-11/sujet.tex index 41800e6..6b80b6d 100644 --- a/2nd/Evaluations/DS_2021-10-11/sujet.tex +++ b/2nd/Evaluations/DS_2021-10-11/sujet.tex @@ -23,6 +23,10 @@ Le barème est donné à titre indicatif, il pourra être modifié. \input{exercises.tex} \printcollection{banque} + +\newpage + +\printsolutionstype{exercise} \end{document} %%% Local Variables: