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Feat: tous les exercices sur les droites

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Bertrand Benjamin 2022-03-23 10:26:50 +01:00
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2nd/16_Droites_dans_un_repère/exercises.tex
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\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}

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