From 636d5e0ae2edd0359f2ac57df684e9e3edfcc784 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 14 Dec 2021 09:53:27 +0100 Subject: [PATCH] Feat: DS4 2nd --- 2nd/Evaluations/DS_2021-12-10/exercises.tex | 220 ++++++++++--------- 2nd/Evaluations/DS_2021-12-10/fig/dessin.jpg | Bin 0 -> 109232 bytes 2nd/Evaluations/DS_2021-12-10/sujet.pdf | Bin 91707 -> 194713 bytes 3 files changed, 118 insertions(+), 102 deletions(-) create mode 100644 2nd/Evaluations/DS_2021-12-10/fig/dessin.jpg diff --git a/2nd/Evaluations/DS_2021-12-10/exercises.tex b/2nd/Evaluations/DS_2021-12-10/exercises.tex index bd18ea4..68cdce0 100644 --- a/2nd/Evaluations/DS_2021-12-10/exercises.tex +++ b/2nd/Evaluations/DS_2021-12-10/exercises.tex @@ -1,3 +1,121 @@ +\begin{exercise}[subtitle={Probabilités}, step={1}, origin={Ma tête}, points=7, topics={ }, tags={ Probabilités }] + Dans cet exercice les parties sont indépendantes, elles peuvent être traité séparément. + \begin{enumerate}[label={\textbf{Partie \Alph*:}}] + \item \textbf{répartition géographique} + + On a relevé le sexe des enfants nés en février dans 3 communes différentes et on a noté les résultats. + + On considère l'expérience aléatoire qui consiste à tirer au hasard un enfant né en février dans une de ces trois communes. + + \hspace{-1cm} + \begin{minipage}{0.4\linewidth} + \begin{center} + \begin{tabular}{|c|c|c|c|} + \hline + Communes & Garçons & Filles & Total \\ + \hline + Villeouf & 432 & 456 & 888\\ + \hline + Betedeville & 11 & 10 & 21\\ + \hline + Sacrévillage & 54 & 70 & 124\\ + \hline + Total & 497 & 536 & 1033\\ + \hline + \end{tabular} + \end{center} + \end{minipage} + \hfill + \begin{minipage}{0.6\linewidth} + \begin{enumerate} + \item Déterminer l'univers de cette expérience aléatoire. + \item Calculer la probabilité des évènements suivants + \hspace{-1cm} + \begin{tasks}[label={\Alph*=}] + \task $\left\{ \mbox{ l'enfant est une fille} \right\}$ + \task $\left\{ \mbox{ l'enfant est né à Betedeville} \right\}$ + \task $\left\{ \mbox{ l'enfant est un garçon et il est né à Villeouf}\right\}$ + %\task $\left\{ \mbox{ l'enfant est une fille ou il est né à Sacrévillage} \right\}$ + \end{tasks} + \end{enumerate} + \end{minipage} + \item \textbf{fonder une famille} + + M.Dupont et Mme Dupont souhaitent avoir 3 enfants. Ils se sont renseignés, chaque enfants a autant de chance d'être un garçon qu'une fille. + + On associe ce souhait d'avoir 3 enfants à une expérience aléatoire où l'on s'intéressera au sexe des enfants. + \begin{enumerate} + \item En utilisant un arbre de probabilité, déterminer l'univers de cette expérience aléatoire. + \item Quelle est la loi de probabilité de cette expérience aléatoire? + \item Quelle est la probabilité pour que le couple ait 2 filles? + % \item Quelle est la probabilité que leur deuxième enfant soit un garçon? + \item Quelle est la probabilité pour que les deux ainés (les deux enfants nés en premier) soient du même sexe? + \end{enumerate} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Vecteurs}, step={1}, origin={Un livre}, topics={Vecteur hors repère}, tags={ Vecteurs }, points=4] + \noindent + \begin{minipage}{0.6\linewidth} + \begin{enumerate} + \item À partir de la figure ci-contre trouver deux vecteurs correspondant aux descriptions suivantes + \begin{enumerate} + \item égal au vecteur $\vect{BC}$ + \item opposé à $\vect{FC}$ + \item même direction et même sens que $\vect{EF}$ + \end{enumerate} + \item Quelle est l'image du point $C$ par la translation de vecteur $\vect{u}$ + \item Donner un vecteur correspondant aux calculs suivants + \begin{tasks}(3) + \task $\vect{ED} + \vect{DA}$ + \task $\vect{EF} + \vect{ED}$ + \task $2\vect{u}$ + \end{tasks} + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.35\linewidth} + \begin{tikzpicture}[scale=1.2] + \draw (0, 0) grid (6, 6); + \draw (0, 0) rectangle (6, 6); + + \draw (4, 5) node {x} node [above right] {$A$}; + \draw (2, 1) node {x} node [below right] {$B$}; + \draw (4, 1) node {x} node [below right] {$C$}; + \draw (2, 5) node {x} node [below right] {$D$}; + \draw (1, 3) node {x} node [above right] {$E$}; + \draw (5, 3) node {x} node [above right] {$F$}; + + \draw [->, very thick] (1, 1) -- node [midway, left] {$\vect{u}$} ++(1, 2); + \draw [->, very thick] (1, 4) -- node [midway, below right] {$\vect{v}$} ++ (2, 0); + \end{tikzpicture} + \end{minipage} +\end{exercise} + +\begin{exercise}[subtitle={Géométrie}, step={1}, origin={Ma tête}, points=4, topics={ Démonstration}, tags={ Géométrie }] + \begin{minipage}{0.5\linewidth} + $ABCD$ est un quadrilatère. Ses diagonales se coupent en un point $O$. On nous dit de plus que + \begin{tasks}[style=itemize] + \task $(AB)$ et $(CD)$ sont parallèles + \task $(AD)$ et $(BC)$ sont parallèles + \task $AB=4$ + \task $DA=3$ + \task $OB = 2,5$ + \end{tasks} + Amine a réalisé la figure à main levée ci-contre. + \end{minipage} + \begin{minipage}{0.5\linewidth} + \includegraphics[scale=0.1]{./fig/dessin} + + \end{minipage} + + \begin{tasks} + \task Démontrer que $DABC$ est un parallélogramme. + \task Démontrer que $DAB$ est un triangle rectangle. + \task (bonus) Démontrer que $AC = DB$ + \end{tasks} +\end{exercise} + \begin{exercise}[subtitle={QCM - questions flashs}, step={1}, origin={Ma tête}, points=5, topics={ }, tags={ QCM }] \emph{Pour chaque question, une seule des propositions est exacte. Une réponse exacte rapporte un point. Une réponse fausse, plusieurs réponses ou l'absence de réponse n'ajoutent ni ne retirent aucun point.\\ Inscrire sur la copie la référence de la question et la lettre de la réponse choisie.\\ @@ -61,105 +179,3 @@ \end{enumerate} \end{exercise} - - -\begin{exercise}[subtitle={Probabilités}, step={1}, origin={Ma tête}, points=8, topics={ }, tags={ Probabilités }] - Dans cet exercice les parties sont indépendantes, elles peuvent être traité séparément. - \begin{enumerate} - \item \textbf{Partie A: fonder une famille} - - M.Dupont et Mme Dupont souhaitent avoir 3 enfants. Ils se sont renseignés, chaque enfants a autant de chance d'être un garçon qu'une fille. - - On associe ce souhait d'avoir 3 enfants à une expérience aléatoire où l'on s'intéressera au sexe des enfants. - \begin{enumerate} - \item En utilisant un arbre de probabilité, déterminer l'univers de cette expérience aléatoire. - \item Quelle est la loi de probabilité de cette expérience aléatoire? - \item Quelle est la probabilité pour que le couple ait 2 filles? - \item Quelle est la probabilité que leur deuxième enfant soit un garçon? - \item Quelle est la probabilité pour que les deux ainés (les deux enfants nés en premier) soient du même sexe? - \end{enumerate} - \item \textbf{Partie B: répartition géographique} - - On a relevé le sexe des enfants nés en février dans 3 communes différentes et on a noté les résultats. - - On considère l'expérience aléatoire qui consiste à tirer au hasard un enfant né en février dans une de ces trois communes. - - \hspace{-1cm} - \begin{minipage}{0.4\linewidth} - \begin{center} - \begin{tabular}{|c|c|c|c|} - \hline - Communes & Garçons & Filles & Total \\ - \hline - Villeouf & 432 & 456 & 888\\ - \hline - Betedeville & 11 & 10 & 21\\ - \hline - Sacrévillage & 54 & 70 & 124\\ - \hline - Total & 497 & 536 & 1033\\ - \hline - \end{tabular} - \end{center} - \end{minipage} - \hfill - \begin{minipage}{0.6\linewidth} - \begin{enumerate} - \item Déterminer l'univers de cette expérience aléatoire. - \item Calculer la probabilité des évènements suivants - \hspace{-1cm} - \begin{tasks}[label={\Alph*=}] - \task $\left\{ \mbox{ l'enfant est une fille} \right\}$ - \task $\left\{ \mbox{ l'enfant est né à Betedeville} \right\}$ - \task $\left\{ \mbox{ l'enfant est un garçon et il est né à Villeouf}\right\}$ - \task $\left\{ \mbox{ l'enfant est une fille ou il est né à Sacrévillage} \right\}$ - \end{tasks} - \end{enumerate} - \end{minipage} - \end{enumerate} -\end{exercise} - -\begin{exercise}[subtitle={Géométrie}, step={1}, origin={Ma tête}, points=7, topics={ Démonstration, Vecteurs }, tags={ Géométrie }] - On considère la figure géométrique suivante. Les deux parties peuvent être traitées de façon indépendantes. - - \begin{minipage}{0.5\linewidth} - \begin{tikzpicture}[scale=2.5] - \draw (0, 0) node [below left] {$A$} -- - (1, 0) node [below right] {$B$} -- - (1, 1) node [below right] {$C$} -- - (0, 1) node [below left] {$D$} -- - cycle; - - \draw (2, 3) node [left] {$E$} -- - (3, 3) node [below right] {$F$} -- - (3, 4) node [above right] {$G$} -- - (2, 4) node [above left] {$H$} -- - cycle; - - \draw (0, 1) -- (3, 4); - \draw (0, 0) -- (3, 3); - \end{tikzpicture} - \end{minipage} - \begin{minipage}{0.45\linewidth} - \begin{enumerate} - \item \textbf{Partie A: démonstration géométrique} - $ABCD$ et $EFGH$ sont deux carrés tels que $AB = EF$. $D$, $E$ et $G$ sont alignés. $A$, $C$ et $F$ sont alignés. $DCFE$ est un parallélogramme. - \begin{enumerate} - \item Démontrer que $(AB)$ est parallèle à $(HG)$ - \item Placer le point $P$ projeté orthogonal de $D$ sur $(FC)$ et le point $Q$ projeté orthogonal de $F$ sur $(DE)$. - \item \dure Démontrer que $DPFQ$ est un rectangle. \textit{(dans cette question tout début de démonstration sera valorisé)} - \end{enumerate} - \item \textbf{Partie B: vecteurs} - \begin{enumerate} - \item Déterminer deux vecteurs égaux à $\vect{AD}$. - \item En partant de $F$ et en faisant la translation (le chemin) - \[ - \vect{GH} + \vect{ED} + \vect{AB} - \] - où arrive-t-on? - \end{enumerate} - \end{enumerate} - \end{minipage} - -\end{exercise} - diff --git a/2nd/Evaluations/DS_2021-12-10/fig/dessin.jpg b/2nd/Evaluations/DS_2021-12-10/fig/dessin.jpg new file mode 100644 index 0000000000000000000000000000000000000000..7760173b039c3aa5b398e51895d3871c0c07e764 GIT binary patch literal 109232 zcmdqIbyybL_dYyGDkUJ@t)$Z3Eg^z*cXzj35f~;U|?W?2q4Q&hv zgheG@U4MV@T$G<*{ncwJAyIKb5E=j;5SVD2T0=Ys08=v?E8*9?iVBKK1kg(W8~_g> z0MG!1rna>O@2gkhz`x4T2ms0i0E5&wx&9UQ&jBbMU2APns0;LGrfp$m0{~zgAf3tH z#^Oc?{Q*ymWnc4ybRUpTpkr#L1JW}=I*E>{&W(P1_J{Rzf3HA$(E{Z#1m(KfgE?Rd%6YRt;O6{-Fd*5N{&}Qe zXk8YXR+>Lu;GpdTJv{)}%K!j)MF2qQ1As@$|FSO_5c*f&{sqJI6Z8MGkJpo+o`OGk zaPtci2+%Ji3?w831mq)VXeb!CM{sbkk6>Zp5s)9lBOoEb!ahcOjD+$86%`c@5gh~V z2?p{L)F;=C04xlo4van+7!q*Z4B&!#4a#>j`tAi91`_H4I0V?k>j?nnX8^2};6C{O zSc|~T>hWJ);(9%;w`oG~Uoael0M@6oRR5U{@ng_KrRrDzl@9y^L&1d|cVAw>e<2Y$ zp?BLXYCTIE{tM~&lq%K4_=EN(FzN9hSTNs<%_2Kzu+tqn724$g0%!DL>vBy$UreCVIm0i(R5bh7E8p5*M9l0G@@)_2U29XtYa?OTMQ(Fx4SSM!M_n8z~yN3 z=WJv+bjOc8eu5xL`rY|m{|yg7>gI7LI~xo=osLZ6`H6ZE>RRn_kB4K>rE>md-FdSj z(novMt^s#a)Awe2tGC{#GfoTlEP(hCE|V&E@-O?R0_J(K++e@ViOKrNdC++3li6Lj zA)hZ<^W%zAmu=qT12Vaz4#0jGS1I(3H!%k87) z6TE!1{2L!s`+Ep$Uh_PEwfT^A;>XVzRJ}OOwg`jYLuZ}aqX89r?v>@h%}c7DKgf`j zgXXijP}r#Dw*j{Gv~YT8RmN`RU+0O_&a-WhJpyi##zaPgEX2^J5C?v)DJ>kr%`DrIJ)@R~jD%)17XVAOm^ z0?U8A=zqg#I)1e{8=sw#?k_}u|j?>~7i93}TQXQnc$O6Gnn{to(O zA#KyhL14<1kE8UCzYjW$7gAF%LMHF~75^s%A)kxNje;=W;Tq_hj%Ha`fEi#Ly>MZU zkrSJ$^!S|t-Zb9>fbFlS3;VYW4lb^Z?y{q2U@xA|ZSJ%run z;a9?IBX%ZoLpR}Wo(HV$&ZmgmQ%V^%usJ!^>9GEOFaR(wOY*P{1`FZPs{P{Y?xD>b ztL+J063gMmzDYH+|LAeK-mU|kV^>gRXX@mX={wp#q{bab06!rpH-h8+n=2~JJ;=< z?}va`_=xdA92Ir8dz<_F3;W$`r%gKu94FRi_J^(uo#ipdD+CXcN7F zKYtS}@0I0RZ8I7a*eWZIQ1b$_HfMHL*R#K4pdXPV&SE+arVFv9YbngKd;C2J(xDRr zTd?1>ebiFYq*V(1{f-P);O1^54`mjpO)Kk9s_*uHxE)JxOyBn>o$t|PDZI3Par}Gk zch98cRw%Y!b9`F+Jpfucr@z7+nY4$Zs~X8F8`f+1dmKDKQQT(djb~AHxyIl9H#)Q+ z?f~s}D|Fj>n%1_;??=0D@OTqEEBABR;h!u3^(p&Y-6Ji4J0;AFji4#T)j2dxaZ!taQG|R zkLG%L0IU|~**x+uw|+>?A(Ql-1CXIb>~JnJrpF3ReDHXfdb;3S+CB5W1z*xAV45%m z-8DzDq1S_p_)$cUY>Mn^ZxCil zV{Z=h{8Rk~JCxZ20KUp7(sbWe;q{AaAb^a0whi}m%)2l&M$cb^!H5^wXYg$IU!2VwiAC=MtD6Ui?B8s~QCZ)aS^6jVNPBP?SN* zTvx9*`36Vyh;sN$uncT3?5iB!q6eIgEv{y9m`dst01&TJe!P76+f01$AUmqbfsLD6 zuNpMGz@Ud-8na!3vLGdB7VkyhX{E$AqP`Kp%Hqg>Ep`KwEW_{rS zfG_Ffgfotv-9Yc<(FWoSEl=7xZYe0G_owrvh9gi2y3MS3at-1J1nHEip5pAd^yv(7 zRcL*RzFb^NHa=S9W0RZr@gmG0B4Q_z<0&`TSB9(#lj8@?X0I;odNZH$4fMRTO z29i@|1UD%833ppP6Z>E--=`M~)_~)oh`js~ZKql?=wfoEpXPL~-=OXVJcyQx5ewT+ z2b6_qLR)+D=e$6O9fh5)jlTh*@)hZq;|jw&>aLQ%`qI!UxEoYYyTgt359UkKWsn8wj;JP}!Y7}E4=1GzmwOEV|J?x3E zKoLZEoUbaCa3Jk3vGkxcotfqVz*{-e-^ zkIY@iH|Gh$RQ#y3{o<&I6=D_uzW$ek%&f zd)8J>{&PypVXbjY-hh4ycp$v@sZzBhXmM*x_d^wD?k0lO%@~r$oP47qu(%?lj;B?E zgT~ek=0)E&N9K+CO9-pB(p{?e9s|IsN{(%3#LoajtTmUyPi=qIBGodY%su(WBJPmh ztUCo=kiW@%o=mWAe>-Tej6{hhD}6U12xXbvgZ7)!1TFa)bAvTT+303?fv#C>vE<0l zTjx*n=LV^TqRL7H08fdXr?GSR={iLk!FH|l0MWaiSfV?UoHA=K{tR#oMF~{Ut^U;S zH*mBodCk!P@VHy+iww+9ucb!{wrPn6X!IRsx)D#3*Ur}b^uu$-IBjps-ZOu;5a6%O z3+(AXYu451fR0eugzMn_Lf)s2#{&9&7`w32h8$a;)jdF}>@=x`CgW*7t*-`I04So=tw{R{z)`zG29dP=T)ps?2Z8ijpWXWA za{Uqq1}ZXk{NVHHh)E`iR8XmFEH#j8(!Gtt+ohSIc@BU#8_T7#PZ_74l`iPl&RiDoNL4_(3U1Zn2n=@e9 zLze?>IyFU$!u}sgaFYh^z!2=ONS#0a!35Sau|C&N@!Yymzo%|iXH3`0g_hiT035?j zQq%vlu7;41&+YnpcOsy>tt#X>+*OLKj~Z_C0N|==6CbXDiF^Cb4LlzT5-#OTzBRQ{ zqptzkDW+T(#@y-d+uRQrw+2bO zK+B0Y1!d0ny<{^SQZ!t#_=Ei7AY-X{tl`FsafwGZ%&s%euMb+(z;T)kPz?p&T{v*{ z&u)}o3q5XNe+l@KsYjkk%TEjfRt-OV|)Om(lA^7yI$ z+JIroJPR8A*%xpx1Xh2G7(*t}aaK?q8W*ABoGN|n7K)Ia2R{Ci#Op0I2asq3Z2t#Q8vE!(HRZ!LO&?0pU5 z%pKv0B}{BxP!edw-km-^-)WpNV3;Bis<$Kl1_J<;rYePKLqFBOHXH|gR8?WGKn~k= zO9s=_WinrD{T-0$xGH!JJi{%X@BqgK=NYv9(B^T&0$cg~Lbo&Kr+#DK$^*O%IhxL! zy8_Dsv4OczcYCqk(#M-K`~-Pl*JTLh06H3ASwn5g|7PCslQNPyLUy{9{8Rt60S6b} zABE)rmFgfgMjv9gN-wn#*9#9&T)0%-Wq?Yj7yz4po9vta_4Wn=@kVs-8u)}a_bbCs z1w1`dfN5Ldru3uoy{N<1jU~q|U%d$}eCV9LTNWOPtKUz~Eopid7+_l0_syVI70l>yEgo86n@3UyDK+k;%0eSfz z!}V%#CWFAxZy5ZyzWg~R8V5zTCneQ+plEsCY2h$UvUgz@fKJ7oa0wljSQec&fJ~@z z$s%T9v-`+hyFctV&!9q;433}DSfp1HHLL%Sp1JK82&_QP1Ts9-1LPo5YLBaOo%=>V68dvcb1mkQJW$ZMn59C2$Oh+ypJozhjqd|QZVT_Z} zWasyKfbVIe>OA|vF&$a7O1Dqc4qWA z`?bGaA(tTIAfsM=9?;}BHhuH4Kv?7V3>fQ{*$U%L1tOk=-BS3gVVfkMzuezje(#muh5CBfgL03hU^bR;%m z@8UzLmXR21;-2|i*kL1$QE%yr2ei17OcgC2_4q9c3~!M7%?SJ9w9sew4v0~tK$KUJ<-xQS2~aTz-?=L1TK4VG&-H+W_4(PigGj%h3(ZW>kUiYcH+`fNBLqZqpLnrMhq6 z$Y`I9@9(Hf#kDVN?0vVqqH&1V_r&-3ru}0^iaE(UXQgC%wL{w#8*MylYod(fN@{R@ zW&P})zV2nrvCpXk0N-R`tfqVK-G6Ic_D?So)uAX+yqgv-SR`J82hIDP@2<5i(QSom zjFr^wNXn2#Z7r=I*x!{r@O=EdV#fFm09-t+YH2&f<8R6CReUy%D}*F8TKOLu7GpSw zo=ri!KMwcSmR1j(IL8C>m2JE9=@QkMz9t;nU*5g(vhb(aZZfgc0DKISG7czd?o<8N za=EPSJJy_B$R~B@Y;d~a*pVap?>byeU-hWgv zT3s z>8P^&(s9f>Fd$#!3o#4+rAe+Up1`p1SU1gvM!vqf> zbN$eMzx|vkFo*MFy9p+@l#K+Kz&m})ot6Xh=-Vo*IkXrc`sK3zfW{PumYbeoy3`LFOlYY6%I!8C}{-iON0m46|? 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