From 9417318a9ed644156d66de6196884425fc23305c Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 29 Mar 2022 11:52:20 +0200 Subject: [PATCH] =?UTF-8?q?Feat:=20d=C3=A9but=20du=20plan=20de=20travail?= =?UTF-8?q?=20sur=20le=20tableur?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../exercises.tex | 110 +++++++++++++++++- .../fig/enclos.png | Bin 0 -> 35340 bytes .../fig/euler.png | Bin 0 -> 88707 bytes .../plan_de_travail.pdf | Bin 0 -> 156647 bytes .../plan_de_travail.tex | 27 +++-- 5 files changed, 120 insertions(+), 17 deletions(-) create mode 100644 4e/13_Tableur_et_calcul_litteral/fig/enclos.png create mode 100644 4e/13_Tableur_et_calcul_litteral/fig/euler.png create mode 100644 4e/13_Tableur_et_calcul_litteral/plan_de_travail.pdf diff --git a/4e/13_Tableur_et_calcul_litteral/exercises.tex b/4e/13_Tableur_et_calcul_litteral/exercises.tex index ef3c48e..2f916b4 100644 --- a/4e/13_Tableur_et_calcul_litteral/exercises.tex +++ b/4e/13_Tableur_et_calcul_litteral/exercises.tex @@ -1,7 +1,107 @@ -\begin{exercise}[subtitle={<++>}, step={1}, origin={<++>}, topics={ Tableur et calcul litteral }, tags={ tableur, calcul littéral }] - <++> +\begin{exercise}[subtitle={Distance d'arrêt}, step={1}, origin={???}, topics={ Tableur et calcul litteral }, tags={ tableur, calcul littéral }] + La distance d’arrêt pour un automobiliste est la distance qu'il parcourt entre le moment où il voit un obstacle et le moment où il s’arrête après avoir freiné. + La distance d'arrêt, notée $D$, depend de la vitesse du conducteur $V$ et de son état: + \begin{itemize} + \item Pour un conducteur lucide: + \[D = V\div 6 + 0,007\times V^2\] + \item Pour un conducteur peu lucide: + \[D = V\div 2 + 0,007\times V^2\] + \end{itemize} + \begin{enumerate} + \item Complète le tableau suivant en écrivant les calculs sur ton cahier. + + \hspace{-0.7cm} + \begin{tabular}{|m{3.5cm}|*{5}{p{1.3cm}|}} + \hline + Vitesse $V$ en km/h & 50 & 90 & 100 & 110 & 130 \\ + \hline + Distance $D$ d'arrêt pour le conducteur lucide & & & & & \\ + \hline + Distance $D$ d'arrêt pour le conducteur peu lucide & & & & & \\ + \hline + \end{tabular} + \item Un conducteur roule à 100 km/h. Un obstacle surgit à 100 m de lui. Pourra-t-il s’arrêter à temps ? + \item Un conducteur lucide veut pouvoir s’arrêter en 10 mètres au maximum. Détermine la vitesse qu’il ne doit pas dépasser. + \item \faIcon{table} Reproduire le tableau sur le tableau en listant toutes les vitesses de 0 à 130km/h. Puis y calculer les distance de freinage. + \end{enumerate} \end{exercise} -\begin{solution} - <++> -\end{solution} +\begin{exercise}[subtitle={La formule d'Euler}, step={2}, origin={???}, topics={ Tableur et calcul litteral }, tags={ tableur, calcul littéral }] + Le but de ce problème est d'arriver à prouver un résultat concernant les prismes droits + + \begin{center} + \includegraphics[scale=0.4]{./fig/euler} + \end{center} + \begin{enumerate} + \item Completer le tableau ci-dessous pour les prismes 1 à 6 + + \hspace{-1cm} + \begin{tabular}{|c|*{5}{p{2.9cm}|}} + \hline + Prisme N° & Nombre de sommets par base (n) & Nombre de sommets (s) & Nombre d'arêtes (a) & Nombre de faces (f) & calculer $$s+f-a = $$ \\ + \hline + 1 & & & & & \\ + \hline + 2 & & & & & \\ + \hline + 3 & & & & & \\ + \hline + 4 & & & & & \\ + \hline + 5 & & & & & \\ + \hline + 6 & & & & & \\ + \hline + \rowcolor{tabular} + 7 & & & & & \\ + \hline + \rowcolor{tabular} + 10 & & & & & \\ + \hline + \rowcolor{tabular} + 100 & & & & & \\ + \hline + \end{tabular} + \item Conjecturer des liens entre les colonnes et les lignes. + \item À partir des vos conjectures, calculer les valeurs des trois dernières lignes. + \item Quelle conjecture peut-on faire sur la dernière colonne. + \item Démontrer cette conjecture avec le calcul littéral. + \item \faIcon{table} Reproduire le tableau avec un tableur et faire calculer les valeurs des colonnes pour tous les prismes du numéro 1 à 100. + \end{enumerate} +\end{exercise} +\begin{exercise}[subtitle={Facture}, step={3}, origin={???}, topics={ Tableur et calcul litteral }, tags={ tableur, calcul littéral }] + Voici les tarifs d'un camping pour l'été 2013 + + \begin{center} + \begin{tabular}{|*{3}{m{4cm}|}} + \hline + \multicolumn{3}{|c|}{\textbf{Par nuitée}} \\ + \hline + Adulte: 8\euro (à partir de 7ans) & Voiture: 3\euro & Emplacement: 4\euro \\ + \hline + \multicolumn{3}{|c|}{Les enfants de moins de 7 ans paient la moitié du tarif adulte.} \\ + \hline + \end{tabular} + \end{center} + \begin{enumerate} + \item Une famille composée de deux parents et de deux enfants de 3ans et de 8ans séjourne au camping avec une voiture du 6juillet au 15 juillet. Quel est le montant total à payer par cette famille? + \item \faIcon{table} Le gérant du camping prépare un fichier de tableur pour pouvoir donner rapidement des factures à ses clients au moment du paiement. Reproduit le tableau et complète le pour que le montant à payer soit calculé automatiquement pour n'importe quelle famille. + \end{enumerate} +\end{exercise} + + + + +\begin{exercise}[subtitle={Enclos}, step={4}, origin={???}, topics={ Tableur et calcul litteral }, tags={ tableur, calcul littéral }] + \begin{minipage}{0.6\linewidth} + Dans son garage, Jean a trouvé 21m de grillage. \\ + Il décide de l'utiliser pour faire un enclos rectangulaire. Afin d'obtenir un enclos encore plus grand, il veut utiliser le mur du jardin qui formera un côté. Le grillage formera les 3 autres. + \end{minipage} + \hfill + \begin{minipage}{0.3\linewidth} + \includegraphics[scale=0.8]{./fig/enclos} + \end{minipage} + + Comment placer les poteaux pour avoir un enclos le plus grand possible? + +\end{exercise} diff --git a/4e/13_Tableur_et_calcul_litteral/fig/enclos.png b/4e/13_Tableur_et_calcul_litteral/fig/enclos.png new file mode 100644 index 0000000000000000000000000000000000000000..b43f5cd959ea97c2d2e537c902daf378336d9929 GIT binary patch literal 35340 zcmXtg2RxQ-*f)|Qo2(>R*<_`=LiXO-J9}kkD`amElD)|$dvB6W_TD=yE4+vAd*A2h zQQf)6b)M&O9RGC{C@(99g+YdagoK18AugW#MSMQkZ|;G|3}W{&oP4s?>R`wh}>I3e}GQ-lu{Rc79JvX5K(gw`e0>c zWbJ??WM`!BU}Q-7(agb=QcOZdUiC9JF%l9bl7#SEW#_4#2KDH~P20!rwYA@C|2EXR ze&8Z&{)FV;MvCT75KFHv)vd3Imu~6*!F~0~!cFQEgUg@#mp}2Gy7B&#NO1CHmgJZg`Yni*(N{(yza;q6b|{(W)%Kh}SaMn9dXQdPG$fojMk0aLa+_U*j2Sj=4 znP=V54qg4`)eysBxpu;oqgRoI)5}&7SsO>khkPjmn*wnzIu}#A>ou$hwG&t8tLdLV 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