From 29d3ac9439041b8a087022e7a5aa0914d39206db Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Wed, 23 May 2018 14:38:10 +0300 Subject: [PATCH] DS6 pour les 302 --- 3e/DS/DS_18_05_29/AirePerim/fig/figures.jpg | Bin 0 -> 44621 bytes .../DS_18_05_29/AirePerim/fig/plan_salon.jpg | Bin 0 -> 28242 bytes 3e/DS/DS_18_05_29/AirePerim/subject.tex | 49 +++++++++++++++ 3e/DS/DS_18_05_29/DS_18_05_30.pdf | Bin 0 -> 240427 bytes 3e/DS/DS_18_05_29/DS_18_05_30.tex | 54 ++++++++++++++++ 3e/DS/DS_18_05_29/Geometrie/fig/figures.jpg | Bin 0 -> 44621 bytes 3e/DS/DS_18_05_29/Geometrie/subject.tex | 17 +++++ 3e/DS/DS_18_05_29/Pgm/subject.tex | 50 +++++++++++++++ 3e/DS/DS_18_05_29/Proba/fig/plateau.jpg | Bin 0 -> 36899 bytes 3e/DS/DS_18_05_29/Proba/subject.tex | 42 +++++++++++++ 3e/DS/DS_18_05_29/Statistiques/subject.tex | 59 ++++++++++++++++++ 3e/DS/DS_18_05_29/Tache_complexe/fig/vase.jpg | Bin 0 -> 54023 bytes 3e/DS/DS_18_05_29/Tache_complexe/subject.tex | 26 ++++++++ 13 files changed, 297 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/dev/null +++ b/3e/DS/DS_18_05_29/AirePerim/subject.tex @@ -0,0 +1,49 @@ +% origin: Métropole septembre 2017 +% theme: Aire et périmètre + +Monsieur Chapuis souhaite changer le carrelage et les plinthes\footnote{Une plinthe est un élément décoratif de faible hauteur fixé au bas des murs le long du sol.} dans le salon de son appartement. Pour cela il doit acheter des carreaux, de la colle et des plinthes en bois qui seront clouées. Il dispose des documents suivants : + +\begin{center} + Document 1 : \textbf{plan}, la pièce correspond à la partie grisée + + \includegraphics[scale=1.5]{./fig/plan_salon} +\end{center} + +\begin{center} + \begin{tabularx}{\linewidth}{|X|p{0.4cm}|X|}\cline{1-1}\cline{3-3} + \multicolumn{1}{|c|}{Document 2} &&\multicolumn{1}{|c|}{Document 3}\\ + \textbf{Carrelage} &&\textbf{Colle pour le carrelage}\\ + Taille d'un carreau : 50 cm $\times$ 50 cm&&\\ + Epaisseur d'un carreau : 0,9 cm &&Conditionnement: sac de 25 kg\\ + Conditionnement: 1,25 m$^2$ par boîte &&Rendement (aire que l'on peut coller) : 4 m$^2$ par sac\\ + Prix : 19,95 \euro{} par boîte &&Prix : 22 \euro{} le sac\\ + \textbf{Plinthe} &&\textbf{Paquet de clous pour les plinthes}\\ + Forme: rectangulaire de longueur 1~m &&Prix: 5,50 \euro{} le paquet\\ + Vendue à l'unité &&\\ + Prix: 2,95 \euro{} la plinthe en bois &&\\ \cline{1-1}\cline{3-3} + \end{tabularx} +\end{center} + +\begin{enumerate} + \item + \begin{enumerate} + \item En remarquant que la longueur GD est égale à 7~m, déterminer l'aire du triangle BCH. + \item Montrer que l'aire de la pièce est 32 m$^2$. + \end{enumerate} + \item Pour ne pas manquer de carrelage ni de colle, le vendeur conseille à monsieur Chapuis de prévoir une aire supérieure de 10\,\% à l'aire calculée à la question 1. + + Monsieur Chapuis doit acheter des boîtes entières et des sacs entiers. + + Déterminer le nombre de boîtes de carrelage et le nombre de sacs de colle à acheter. + \item Le vendeur recommande aussi de prendre une marge de 10\,\% sur la longueur des plinthes. + + Déterminer le nombre total de plinthes que monsieur Chapuis doit acheter pour faire le tour de la pièce. + + On précise qu'il n'y a pas de plinthe sur la porte. + \item Quel est le montant de la dépense de monsieur Chapuis, sachant qu'il peut se contenter d'un paquet de clous ? Arrondir la réponse à l'euro près. +\end{enumerate} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: diff --git a/3e/DS/DS_18_05_29/DS_18_05_30.pdf b/3e/DS/DS_18_05_29/DS_18_05_30.pdf new file mode 100644 index 0000000000000000000000000000000000000000..51ef7c92ad14d4c5ff9c26c13f42c78539af0c42 GIT binary patch literal 240427 zcmb5V1z1*1_b5`OCKxsr2P(tC`H~9RY z_dVaa&UMbxYv#9NX3wmdS+n-`mR3z#mX(u@7nOEqerOq$kCKDZ*}@)GSQwRE+1kn0 z<0&O4CpQ=69ig(z+CB5IcB5pMeP-@qEp2V-Y-NoqDvIjv;bv{_i0Zvkr8n-j%7?#x z$XpvOph?y0jV6?QioY@9U(UmrCWai1k;J;wTv?QjMEhdX??exhcB*3S+c}HsAbxw8<)d z=rDLGi?gAbwz2YSUvv)mcCDqVz@cY~)rewmJYa_=x+%qSidLI-Iw%*top_pPuT(W< zQGnGvu5{Z+{9vi806h^k-BnHy!KPH5SfMIEF>JX7Ze!!J2`fRD;Zqw2HE+1a16f+8 z1XQa^|CvwSsyv3(fnI$Bzt|t%c6R#|7BM2xJ~k-%9>g7|*i244kBOMo?3|@ny_w+o zI`ev~`y@2Fz2HTcfxj`pWebnYp@d_i|0H?Fs>{&-YGQ=EIe-!!&u-+C@iaM(fjTwU z?~jR@L&Fm2Xesgt^A_>1D3^`7GB_U~B*?12Jv$6}`QdlOgMkmya?m)f@&+V%rQ~{e zeRaIfbIX4HGspECZJrzVu21AYhc^tqUC<;evtwNrm-d`$Yj?Qo{~&a>c+bJ8`W~g* 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ci-dessous. Elles ne sont pas dessinées en vraie grandeur. + +Pour chacune d'elles, déterminer la longueur AB au millimètre près. + +\textbf{Dans cet exercice, on n'attend pas de démonstration rédigée. Il suffit d'expliquer brièvement le raisonnement suivi et de présenter clairement les calculs.} + +\begin{center} + \includegraphics[scale=1.5]{./fig/figures} +\end{center} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: diff --git a/3e/DS/DS_18_05_29/Pgm/subject.tex b/3e/DS/DS_18_05_29/Pgm/subject.tex new file mode 100644 index 0000000..87883c3 --- /dev/null +++ b/3e/DS/DS_18_05_29/Pgm/subject.tex @@ -0,0 +1,50 @@ +% origin: Pondichery mai 2018 +% theme: Programme de calculs, tableur + +\begin{tabularx}{\linewidth}{|X|X|}\hline + Programme A &Programme B\\ + \qquad$\bullet~~$ Choisir un nombre &\qquad$\bullet~~$Choisir un nombre\\ + \qquad$\bullet~~$ Soustraire 3 &\qquad$\bullet~~$ Calculer le carré de ce nombre\\ + \qquad$\bullet~~$ Calculer le carré du résultat obtenu&\qquad$\bullet~~$Ajouter le triple du nombre de départ\\ + &\qquad$\bullet~~$Ajouter 7\\ \hline +\end{tabularx} + +\medskip + +\begin{enumerate} + \item Corinne choisit le nombre 1 et applique le programme A. + + Expliquer en détaillant les calculs que le résultat du programme de calcul est 4. + \item Tidjane choisit le nombre $- 5$ et applique le programme B. Quel résultat obtient-il ? + \item Lina souhaite regrouper le résultat de chaque programme à l'aide d'un tableur. Elle crée la feuille de + calcul ci-dessous. Quelle formule, copiée ensuite à droite dans les cellules C3 à H3, a-t-elle saisie dans + la cellule B3 ? + + \begin{center} + \begin{tabularx}{\linewidth}{|>{\columncolor[gray]{0.85}}c|l|*{7}{>{\centering \arraybackslash}X|}}\hline + \multicolumn{2}{|l|}{B2}&\multicolumn{7}{l|}{=(B1$-3$) \verb+^+ + 2}\\ \hline + \rowcolor[gray]{0.85}&A&B&C&D&E&F&G&H\\ \hline + 1&Nombre de départ &$- 3$ &$- 2$ &$- 1$ &0 &1 &2 &3\\ \hline + 2&Résultat du programme A &36 &25 &16 &9 &4 &1 &0\\ \hline + 3&Résultat du programme B &7 &5 &5 &7 &11 &17 &25\\ \hline + \end{tabularx} + \end{center} + + \item Zoé cherche à trouver un nombre de départ pour lequel les deux programmes de calcul donnent le + même résultat. Pour cela, elle appelle $x$ le nombre choisi au départ et exprime le résultat de chaque programme de calcul en fonction de $x$. + \begin{enumerate} + \item Montrer que le résultat du programme A en fonction de $x$ peut s'écrire sous forme développée et + réduite: $x^2 - 6x + 9$, + \item Écrire le résultat du programme B. + \item Existe-t-il un nombre de départ pour lequel les deux programmes donnent le même résultat ? + + Si oui, lequel ? + \end{enumerate} +\end{enumerate} + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: diff --git a/3e/DS/DS_18_05_29/Proba/fig/plateau.jpg b/3e/DS/DS_18_05_29/Proba/fig/plateau.jpg new file mode 100644 index 0000000000000000000000000000000000000000..074c0e0de2210d32f038bda0785b6b7d1e577820 GIT binary patch literal 36899 zcmb4qby!tR7wJejfKb8fo~_S42iix@ zKKE%=)U@(F zOj%S+|Dl1It%I|Rvy6^+ke6eim6P*5L?;k@0s=B(GG0nb-g^pS3itlM>ADZVM}r{(C03g%8U5}<$v4!4;CXX(^X?3 z&?y3?G&(G@!3=n+J3V~;3A9lwEcbBf7?@G7_@r?0`cm9 zg|(bL2m~9^_TZkpfe7{=3TD&3_hA}9b141mR(1`W8yzfL)rUK!=pVbkb*up?V?6+z z%YrKpK@d#~_zeIQ*)&Q_Z{a^>Fk1@Khf|QN=90aU;oQ^nx>Z8f&J79@(spmTzvZ?r zN!c2R(NOhuZ$xM;^y9a>J7@z%a_mWv!&~;Y#2;ml^+mut81lzAB4jb%tXmx#(&t@N z25GCOx9n{x5B6~LNQk^;K@UO(leEl-BLILF^G+9_(Y$ccx?yh%S&p&Kx9=!VPkJMQ zqzkd!dWvfF-68-;6ETI|Ovm2_w4@cc>N{Ayl{Yf1CogVwtO-q^3O5R0vfx$#mS{@O z!6COCN^mnX0zr<4DQ_jjNG10{1U}-4;H?AzknFOi3uSLP`e)J400>#EH#dOfE$Dh9 zg|Zo2Beb~D{vC|BW&j|Ty>Yew_b~w3iFpt>ZZm3h8)#d#U=LtOqZT<0pr-LUPu+A8 zAP^mSJ81CPQh6sWUZ6}2jN;?9U`av%Aa7jEyLlK@JfY%0 z4=Q6Jl%>s|T)TaX=1?geSij6Wg7B?dyE&L$JfvWM9CGbf^Mym$?Y_55M*;QM_?C#wtY8)0|4j-buIvz z4r>-<0NV*OK>%%MwhcIUz=qg>5|ALrlN4YB1nFfc76AYrni68QA_pArYXVf7YHi}6 zibfN?T>=gQr%B~!V1*#Gr~tnkux3cw1A<6H3I=dyy`{3#v;h>^W^Pc37R~wzF;5UH zN9^K%RxL#SZa$&`Fqyei4_0VVkTMAXV4r;MTns?-N`zy;ZitoduYx+*lLR5;ScEZx zyjivI5Ou5^w=AMgbkw5b1R!gtApk5pN@(*K0Em$Fnn8^;xj;h&0Hwp*wnP{Ll6g2$ zW}+D&g5(RL79m8aFm~$s^bPLki7Wswfi6dyJma4I2=F`%y8}j0C~Q_+9m)n%vYaP29>zTW`|AEa18wc zL;yOC&4Qr<5@dWN4V(NFL^N1zMLeWI%$AWYOiklLdP>bw~=Z1CU@;u9&g_vRI~2R1v5LN5(q*{DKz*P&TAC0KnQS zxe79upx9K1u-HKIS+#m;fdIY=n9I#VqQaoB@8-rWLNtIV-=&5F<(%lW zH{5W%aSrI9VuA9=Zg6-UiDAV&Jt&$rB11)x95!sd2Z$zACF~lFr#}!406>`*+^L+B zZl(}GQ{m5>rRf2n&&D&h^G?Ax!3q@Kna0u^ScPLWF`H8~?Sk#eirF!}Wgp$P2gpCm zgL@7N{FdD?Az1^1LN1eqqNyGX^u+lLn{%5u<~gWX0?HidX(*e#AqjILVujt%ROZe! 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z3j{KuJDksrf_?LSvu$9$aH3D&MVEe;uX(-fNAsv(&-Td^(DLhE^O%fHqpJ2+MZ#Rg Kzd%@jjsG9Aot8}i literal 0 HcmV?d00001 diff --git a/3e/DS/DS_18_05_29/Proba/subject.tex b/3e/DS/DS_18_05_29/Proba/subject.tex new file mode 100644 index 0000000..c85174f --- /dev/null +++ b/3e/DS/DS_18_05_29/Proba/subject.tex @@ -0,0 +1,42 @@ +% origin: Pondichery mai 2018 +% theme: Probabilité + +\noindent +\parbox{0.58\linewidth}{ + On considère un jeu composé d'un plateau tournant et d'une boule. Représenté ci-contre, ce plateau comporte 13 cases numérotées de 0 à 12. + + \smallskip + + On lance la boule sur le plateau, La boule finit par s'arrêter + au hasard sur une case numérotée. + + \smallskip + + La boule a la même probabilité de s'arrêter sur chaque case. + + \smallskip + + \begin{enumerate} + \item Quelle est la probabilité que la boule s'arrête sur la case + numérotée 8 ? + \item Quelle est la probabilité que le numéro de la case sur + lequel la boule s'arrête soit un nombre impair ? + \end{enumerate} +} +\hfill +\parbox{0.38\linewidth}{ + \includegraphics[scale=0.9]{./fig/plateau} +} +\begin{enumerate} \setcounter{enumi}{2} + \item Quelle est la probabilité que le numéro de la case sur + laquelle la boule s'arrête soit un nombre premier ? + \item Lors des deux derniers lancers, la boule s'est arrêtée à chaque fois sur la case numérotée 9. + + A-t-on maintenant plus de chances que la boule s'arrête sur la case numérotée 9 plutôt que sur la case + numérotée 7 ? Argumenter à l'aide d'un calcul de probabilités. +\end{enumerate} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: diff --git a/3e/DS/DS_18_05_29/Statistiques/subject.tex b/3e/DS/DS_18_05_29/Statistiques/subject.tex new file mode 100644 index 0000000..82f1f2e --- /dev/null +++ b/3e/DS/DS_18_05_29/Statistiques/subject.tex @@ -0,0 +1,59 @@ +% origin: Pondichery septembre 2017 +% theme: Statistiques, tableur, Raisonnement + +Sur une feuille de calcul, on a reporté le classement des dix premiers pays, par le +nombre de médailles, aux Jeux Olympiques de Rio en 2016. +\begin{center} + \begin{tabularx}{\linewidth}{|>{\columncolor[gray]{0.85}}c|c|c|*{4}{>{\centering \arraybackslash}X|}}\hline + \rowcolor[gray]{0.85}&A &B &C &D &E &F\\ \hline + 1&Rang &Pays &Or &Argent &Bronze &Total\\ \hline + 2&1 &Etats-Unis &46 &37 &38 &121\\ \hline + 3&2 &Grande Bretagne&27 &23 &17 &67\\ \hline + 4&3 &Chine &26 &18 &26 &70\\ \hline + 5&4 &Russie &19 &18 &19 &56\\ \hline + 6&5 &Allemagne &17 &10 &15 &42\\ \hline + 7&6 &Japon &12 &8 &21 &41\\ \hline + 8&7 &France &10 &18 &14 &42\\ \hline + 9&8 &Corée du Sud &9 &3 &9 &21\\ \hline + 10&9 &Italie &8 &12 &8 &28\\ \hline + 11& 10 &Australie &8 &11 &10 &29\\ \hline + \end{tabularx} +\end{center} + +\medskip + +\begin{enumerate} + \item Quelle formule, parmi les trois proposées, a été saisie dans la cellule F2 de + cette feuille de calcul, avant qu'elle soit étirée vers le bas ? + \begin{center} + \begin{tabularx}{\linewidth}{|*{3}{>{\centering \arraybackslash}X|}}\hline + Formule A &Formule B &Formule C\\ \hline + $=46+37+38$ &=MOYENNE(C2 :\:E2) &=C2+D2+E2\\ \hline + \end{tabularx} + \end{center} + + \item On observe la série des nombres de médailles d'or de ces dix pays. + \begin{enumerate} + \item Quelle est l'étendue de cette série ? + \item Quelle est la moyenne de cette série ? + \item Quelle est la médiane de cette série ? + \end{enumerate} + \item Quel est le pourcentage de médailles d'or remportées par la France par rapport + à son nombre total de médailles ? Arrondir le résultat au dixième de \,\%. + \item Le classement aux Jeux Olympiques s'établit selon le nombre de médailles d'or + obtenues et non selon le nombre total de médailles. Pour cette raison, la France + avec 42 médailles se retrouve derrière le Japon qui n'en a que 41. En observant + l'Italie et l'Australie, établir la règle de classement en cas d'égalité sur le nombre + de médailles d'or. + \item Un journaliste sportif propose une nouvelle procédure pour classer les pays: + chaque médaille d'or rapporte 3 points, chaque médaille d'argent rapporte 2 + points et chaque médaille de bronze rapporte 1 point. Dans ces conditions, la + France dépasserait-elle le Japon ? +\end{enumerate} + + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: diff --git a/3e/DS/DS_18_05_29/Tache_complexe/fig/vase.jpg b/3e/DS/DS_18_05_29/Tache_complexe/fig/vase.jpg new file mode 100644 index 0000000000000000000000000000000000000000..04e232f32a81864633a69555124b41f3c738ec83 GIT binary patch literal 54023 zcmeFZbzGFq8!x;|cP%Z_UDDkwy&zqJ(v6Y|STsvX*Rph{v|!S(lyn+^h+u*sprW38 z0R{a%KJWRR&w1ZJ-gAcMvpX~QHP>8o&G(9#dwqV){#XQ&X{&3ggTO%H2lInKKfZ$? zsy>dkevS^zS6uyEm^HL?^?xjYR6%5fL?lE6WF*8S6y#(OT5ft;YHC_xHjdNWGNSTw z(xOt5N}5)BN>DR3Nhy6#1G5Wu&MwXhy550a4gpq<&h}^~U~&oyS}NKz^z>)!Risqx z|LgLj6GV=O@d5J{CYT(AK@P?w2mj~>(SyJsOkf3|BhReL(PI9z=u* z24Rq4l7T?r=d8!0{%2~LwIm4yJt?Cg5LpUC?&(kp8xRPi!sXAQ1SR=Oe%c@qW=gUO zg-w7uP{n8y9>q2s!>1Jhh^sH~CFkVHT%y#|8zIq&5TRHyPlazc7{~~cQRL<#bJMj~ zEeZ*HSlJ5g$LkA$(Z>a>-{PD^JrEHZ?XtGGNHvIC;xy#Y_nT~)@(-pQhaWsHoIja5wBDFjJ+mb6g8 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--git a/3e/DS/DS_18_05_29/Tache_complexe/subject.tex b/3e/DS/DS_18_05_29/Tache_complexe/subject.tex new file mode 100644 index 0000000..8850b98 --- /dev/null +++ b/3e/DS/DS_18_05_29/Tache_complexe/subject.tex @@ -0,0 +1,26 @@ +% origin: Métropole juin 2017 +% theme: Tache complexe, Volumes + + +Antoine crée des objets de décoration avec des vases, des billes et de l'eau colorée. + +Pour sa nouvelle création, il décide d'utiliser le vase et les billes ayant les caractéristiques suivantes : + +\begin{center} + \includegraphics[scale=1.7]{./fig/vase} +\end{center} + +Il met 150 billes dans le vase. Peut-il ajouter un litre d'eau colorée sans risquer le débordement ? + +\smallskip + +\paragraph{Rappels} +\begin{itemize} + \item Volume de la boule est donné par la formule : $\dfrac{4}{3}\times \pi \times \text{rayon}^3$ + \item Convertir des L en $cm^3$: $1L = 1000cm^3$ +\end{itemize} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: