From fa716381012704c2ad18781cc792f727d4230340 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Wed, 23 Mar 2022 10:26:50 +0100 Subject: [PATCH] Feat: tous les exercices sur les droites --- 2nd/16_Droites_dans_un_repère/exercises.tex | 85 +++++ 2nd/16_Droites_dans_un_repère/fig/bijoux.pdf | Bin 0 -> 13344 bytes 2nd/16_Droites_dans_un_repère/fig/bijoux.svg | 350 ++++++++++++++++++ .../plan_de_travail.pdf | Bin 50970 -> 66267 bytes 4 files changed, 435 insertions(+) create mode 100644 2nd/16_Droites_dans_un_repère/fig/bijoux.pdf create mode 100644 2nd/16_Droites_dans_un_repère/fig/bijoux.svg diff --git a/2nd/16_Droites_dans_un_repère/exercises.tex b/2nd/16_Droites_dans_un_repère/exercises.tex index 28d8c70..a6b4128 100644 --- a/2nd/16_Droites_dans_un_repère/exercises.tex +++ b/2nd/16_Droites_dans_un_repère/exercises.tex @@ -212,3 +212,88 @@ \end{multicols} \end{enumerate} \end{exercise} + +%%%%%%%%% +% systeme d'équations + +\begin{exercise}[subtitle={Bijoux}, step={5}, origin={Création}, topics={Droites dans un repère}, tags={Géométrie repérée}, mode={\searchMode}] + \begin{minipage}{0.5\linewidth} + On fabrique des bijoux à l'aide de triangles qui ont tous la même forme. Certains triangles sont en verre et les autres sont en métal. + + \bigskip + + Trois exemples de bijoux sont donnés ci-contre. Les triangles en verre sont représentés en blanc, ceux en métal en gris. + + \bigskip + + Tous les triangles de métal ont le même prix. Tous les triangles de verre ont le même prix. + + Le bijou 1 revient à 11€ et le bijou 2 revient à 8,15€. + + \begin{enumerate} + \item Comment peut on retrouver le prix du bijou 3? + \item Comment pourrait on calculer le prix de n'importe quel bijou? + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.4\linewidth} + \includegraphics[scale=0.6]{./fig/bijoux} + \end{minipage} +\end{exercise} + +\begin{exercise}[subtitle={Bilan}, step={5}, origin={Création}, topics={Droites dans un repère}, tags={Géométrie repérée}, mode={\groupMode}] + On note $x$ le prix d'un triangle de verre et $y$ le prix d'un triangle de métal. + \begin{enumerate} + \item Exprimer le prix du bijou 1 en fonction de $x$ et $y$. + \item Même question pour le bijoux 2. + \item À quoi ressemble les deux formules que vous avez obtenus? + \item Tracer ces deux droites dans un repère orthonormé. Que dire du point d'intersection? + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Système d'équations}, step={5}, origin={sesamaths}, topics={Droites dans un repère}, tags={Géométrie repérée}, mode={\trainMode}] + Résoudre les systèmes d'équations suivants + \begin{multicols}{3} + \begin{enumerate} + \item + \[ + \left\{ + \begin{aligned} + & 2x - y + 1 = 0\\ + & -3x + 4y - 2 = 0 + \end{aligned} + \right. + \] + \item + \[ + \left\{ + \begin{aligned} + & x - 3y + 4 = 0\\ + & 2x - 5y + 2 = 0 + \end{aligned} + \right. + \] + \item + \[ + \left\{ + \begin{aligned} + & 2x - 5y + 1 = 0\\ + & -3x + 4y - 2 = 0 + \end{aligned} + \right. + \] + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Kangourous et bisons}, step={5}, origin={???}, topics={Droites dans un repère}, tags={Géométrie repérée}, mode={\trainMode}] + Un troupeau de kangourous et de bisons se défoule dans le désert. On compte 178 pâtes qui touchent le sol et 116 oreilles. + + Combien ce troupeau compte-t-il de kangourous et de bisons? +\end{exercise} + +\begin{exercise}[subtitle={Tarif de groupe}, step={5}, origin={???}, topics={Droites dans un repère}, tags={Géométrie repérée}, mode={\trainMode}] + Deux groupes vont au ski. Le premier groupe est composé de 2 adultes et 3 enfants et a payé 73€ de forfait. Le deuxième groupe est composé de 14 adultes et 21 enfants et a payé 511€. + + Retrouver tous les prix du forfait adulte et ceux du forfait enfant possibles? +\end{exercise} diff --git a/2nd/16_Droites_dans_un_repère/fig/bijoux.pdf b/2nd/16_Droites_dans_un_repère/fig/bijoux.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3f909f5627c82ea1b2159a7ee14539aafe41ad0f GIT binary patch literal 13344 zcmdUWbzGF&*Ds=Uqmlvxf;7wkGl0_FEnP!*4BaJ-fFKP33mU1v&=+2(UGDUKcvAmNhc=5G;Ic5M$9H6zI6 zeSj59|LQ3JI;`v&KOe!cr%}#uM4uEa=-!UcjL(-Pdcaj^ckzd&L$M&~&on9D7~9Yd z*|@n*!>qVoBbBpLu6SSO(SH^H{DN^AeWUxs6SW9aoCjePX82DhOLxKw-xUnH=1KZY zv(+{5Y+XH;c@mV@tvS&L9J^PRXmxkdmoS`b1tE^g?-eJSd?H=4P{!JaeM(B9swZP~ z1sRJf>RDQnVNT&_Ege`C>?)tXRZRIk_MZcJ$xY-WN=UN1D!d8~*Y`)sHd4a=QYvm- ze#hrdCI_$|nu&>2K(L&Y)okKQf>&~WAty@F>I`UNO)KrXjKrGN1tQL3OCrXD|I=GsGGl>PIKxaK3sbP z45{r@ewTJw6@R*-Tie-`^R3*l=L~w9aBtk{00rYbTR~t6gDZY z0)&dGas_b;x!ml-4qW+!dNx}x-+tW_)tSBa{(i+O%UX)#0t@KG0=n-OSs!EyU_11> z4V)wAPqZHKAHW=rMnX 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