ménage git
authorDenise sur Titasmo <denise.maurice@normalesup.org>
Fri, 5 Feb 2016 11:01:40 +0000 (12:01 +0100)
committerDenise sur Lya <sekhmet@lya>
Thu, 18 Feb 2016 09:32:30 +0000 (10:32 +0100)
182 files changed:
1ere/DM_5/dm5.tex
1ere/DM_5/dm5_corrige.pdf
1ere/DM_5/dm5_enonce.pdf
1ere/DST_5/capturecourbe.png [new file with mode: 0644]
1ere/DST_5/dst5.tex [new file with mode: 0644]
1ere/DST_5/dst5_corrige.pdf [new file with mode: 0644]
1ere/DST_5/dst5_enonce.pdf [new file with mode: 0644]
1ere/DST_5/exoparabole.ggb [new file with mode: 0644]
1ere/DST_5/exoparabole.pdf [new file with mode: 0644]
1ere/calcul_mental/tableausigne.pdf [new file with mode: 0644]
1ere/calcul_mental/tableausigne.tex [new file with mode: 0644]
1ere/chapitre5_probas/chap5.pdf
1ere/chapitre5_probas/chap5.tex
1ere/chapitre5_probas/chap5_page3.pdf [new file with mode: 0644]
1ere/chapitre5_probas/exo59p204.pdf [new file with mode: 0644]
1ere/chapitre5_probas/exo59p204.tex [new file with mode: 0644]
1ere/chapitre6_derivee/activite_derivee.pdf [new file with mode: 0644]
1ere/chapitre6_derivee/activite_derivee.tex [new file with mode: 0644]
1ere/chapitre6_derivee/chap6.pdf [new file with mode: 0644]
1ere/chapitre6_derivee/chap6.tex [new file with mode: 0644]
1ere/chapitre6_derivee/courbe1.pdf [new file with mode: 0644]
1ere/chapitre6_derivee/courbe1.svg [new file with mode: 0644]
1ere/mathematiques_ES_L_term.pdf [new file with mode: 0644]
2nde/AP/liste_eleves_AP.ods [new file with mode: 0644]
2nde/AP/seances
2nde/DST_6/dst6.tex [new file with mode: 0644]
2nde/DST_6/dst6_A_corrige.pdf [new file with mode: 0644]
2nde/DST_6/dst6_A_enonce.pdf [new file with mode: 0644]
2nde/DST_6/dst6_B_corrige.pdf [new file with mode: 0644]
2nde/DST_6/dst6_B_enonce.pdf [new file with mode: 0644]
2nde/DST_6/exo3.ggb [new file with mode: 0644]
2nde/DST_6/repere.ggb [new file with mode: 0644]
2nde/DST_6/repere.pdf [new file with mode: 0644]
2nde/DST_6/reperea.ggb [new file with mode: 0644]
2nde/DST_6/reperea.pdf [new file with mode: 0644]
2nde/DST_6/repereb.ggb [new file with mode: 0644]
2nde/DST_6/repereb.pdf [new file with mode: 0644]
2nde/calcul_mental/boiteamoustaches.png [new file with mode: 0644]
2nde/calcul_mental/boitemoustache.pdf [new file with mode: 0644]
2nde/calcul_mental/boitemoustache.tex [new file with mode: 0644]
2nde/calcul_mental/coeffdir.pdf [new file with mode: 0644]
2nde/calcul_mental/coeffdir.tex [new file with mode: 0644]
2nde/calcul_mental/signe1deg.pdf [new file with mode: 0644]
2nde/calcul_mental/signe1deg.tex [new file with mode: 0644]
2nde/chapitre6_fct_affines/enigme.pdf [new file with mode: 0644]
2nde/chapitre6_fct_affines/enigme.tex [new file with mode: 0644]
2nde/chapitre6_fct_affines/enigme_2pages.pdf [new file with mode: 0644]
2nde/chapitre7_echantillonnage/TI1.png [new file with mode: 0644]
2nde/chapitre7_echantillonnage/TI2.png [new file with mode: 0644]
2nde/chapitre7_echantillonnage/TI3.png [new file with mode: 0644]
2nde/chapitre7_echantillonnage/TP_donnees.pdf [new file with mode: 0644]
2nde/chapitre7_echantillonnage/TP_donnes.ods [new file with mode: 0644]
2nde/chapitre7_echantillonnage/TP_donnes.pdf [new file with mode: 0644]
2nde/chapitre7_echantillonnage/TP_echantillon.pdf [new file with mode: 0644]
2nde/chapitre7_echantillonnage/TP_echantillon.tex [new file with mode: 0644]
2nde/chapitre7_echantillonnage/TP_echantillon_2pages.pdf [new file with mode: 0644]
2nde/chapitre7_echantillonnage/chap7.pdf [new file with mode: 0644]
2nde/chapitre7_echantillonnage/chap7.tex [new file with mode: 0644]
2nde/chapitre7_echantillonnage/donnees_recolter.pdf [new file with mode: 0644]
2nde/chapitre7_echantillonnage/exorevision.pdf [new file with mode: 0644]
2nde/chapitre7_echantillonnage/exorevision.tex [new file with mode: 0644]
2nde/chapitre7_echantillonnage/exorevision_2pages.pdf [new file with mode: 0644]
2nde/chapitre7_echantillonnage/graphiqueTP.pdf [new file with mode: 0644]
2nde/chapitre7_echantillonnage/graphiqueTP.tex [new file with mode: 0644]
2nde/chapitre7_echantillonnage/resultTP.png [new file with mode: 0644]
2nde/chapitre7_echantillonnage/resultsTP.odc [new file with mode: 0644]
2nde/chapitre7_echantillonnage/resultsTP.pdf [new file with mode: 0644]
2nde/ficheprep_11-02.pdf [new file with mode: 0644]
2nde/ficheprep_11-02.tex [new file with mode: 0644]
2nde/liste_eleves.ods
2nde/manuel_sesamath/2SP2/2SP2/images/aurium_Ant.eps [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/images/logo_hospital_small.eps [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/images/roulette-wheel_small.eps [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2/inc_2SP2_affaire_castaneda_sourcetex.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2/inc_2SP2_appr_Simulation_IC_sourcetex.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2/inc_2SP2_appr_Simulation_IF_sourcetex.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2/inc_2SP2_appr_abaque2_sourcetex.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2/inc_2SP2_appr_grippe_sourcetex.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2/inc_2SP2_appr_opticien_sourcetex.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2/inc_2SP2_appr_publicite_sourcetex.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2/inc_2SP2_elections_sourcetex.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2/inc_2SP2_surbooking_sourcetex.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2/inc_SP2_TP4_sourcetex.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2_acti.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2_appr.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2_base.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2_cours.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2_fin.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2_mental.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2_mental.tex.backup [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2_pagedegarde.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2_qcm.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_2SP2_tp.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/2SP2/inc_chapitre_2SP2.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/MS2_2SP2_chapitrecomplet.cor [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/MS2_2SP2_chapitrecomplet.dvi [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/MS2_2SP2_chapitrecomplet.pdf [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/MS2_2SP2_chapitrecomplet.ps [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/MS2_2SP2_chapitrecomplet.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/commande.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-AE-SP2-1.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-AE-SP2-2.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-ExoBase-SP2-1.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-ExoBase-SP2-18.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-ExoBase-SP2-2.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-ExoBase-SP2-3.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-ExoBase-SP2-4.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-ExoBase-SP2-40.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-ExoBase-SP2-5.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-ExoBase-SP2-6.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-ExoBase-SP2-7.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-QCM-SP2-55.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-QCM-SP2-56.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-QCM-SP2-57.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-QCM-SP2-58.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-QCM-SP2-59.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-QCM-SP2-60.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-QCM-SP2-61.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-QCM-SP2-62.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-QCM-SP2-63.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-QCM-SP2-64.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/corrections/corr-QCM-SP2-65.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/patch.tex [new file with mode: 0644]
2nde/manuel_sesamath/2SP2/sesamathbook.cls [new file with mode: 0644]
ESPE/TC_projets/Quizz ET.sb2 [new file with mode: 0644]
ESPE/TC_projets/culturegev0.sb2 [new file with mode: 0644]
ESPE/TC_projets/culturegev1.1.sb2 [new file with mode: 0644]
ESPE/TC_projets/culturegev1.2.sb2 [new file with mode: 0644]
ESPE/TC_projets/culturegev1.sb2 [new file with mode: 0644]
ESPE/TC_projets/culturegev2.sb2 [new file with mode: 0644]
ESPE/TC_projets/scratch/0000000.png [new file with mode: 0644]
ESPE/TC_projets/scratch/1.png [new file with mode: 0644]
ESPE/TC_projets/scratch/10.png [new file with mode: 0644]
ESPE/TC_projets/scratch/11.png [new file with mode: 0644]
ESPE/TC_projets/scratch/12.png [new file with mode: 0644]
ESPE/TC_projets/scratch/13.png [new file with mode: 0644]
ESPE/TC_projets/scratch/14.png [new file with mode: 0644]
ESPE/TC_projets/scratch/15.png [new file with mode: 0644]
ESPE/TC_projets/scratch/2.png [new file with mode: 0644]
ESPE/TC_projets/scratch/3.png [new file with mode: 0644]
ESPE/TC_projets/scratch/4.png [new file with mode: 0644]
ESPE/TC_projets/scratch/5.png [new file with mode: 0644]
ESPE/TC_projets/scratch/6.png [new file with mode: 0644]
ESPE/TC_projets/scratch/7.png [new file with mode: 0644]
ESPE/TC_projets/scratch/8.png [new file with mode: 0644]
ESPE/TC_projets/scratch/9.png [new file with mode: 0644]
ESPE/TC_projets/scratch/BRAVO.png [new file with mode: 0644]
ESPE/TC_projets/scratch/culturegev0-2.sb2 [new file with mode: 0644]
ESPE/TC_projets/scratch/perdu.png [new file with mode: 0644]
ESPE/TC_projets/scratch/règles scratch jeu.txt [new file with mode: 0644]
ESPE/TC_projets/scratch/un-autre-monde.png [new file with mode: 0644]
ESPE/TC_projets/seance1 [moved from ESPE/projetpourlaclasse/seance1 with 100% similarity]
ESPE/TC_projets/seance2 [new file with mode: 0644]
ccprofst2.pdf [new file with mode: 0644]
dossier_inspec/1ere_dms.pdf [new file with mode: 0644]
dossier_inspec/1ere_dsts.pdf [new file with mode: 0644]
dossier_inspec/1ere_interros.pdf [new file with mode: 0644]
dossier_inspec/2nde_dms.pdf [new file with mode: 0644]
dossier_inspec/2nde_dsts.pdf [new file with mode: 0644]
dossier_inspec/2nde_interros.pdf [new file with mode: 0644]
dossier_inspec/IMPRESSION_CDT_1ere.pdf [new file with mode: 0644]
dossier_inspec/IMPRESSION_CDT_2nde.pdf [new file with mode: 0644]
dossier_inspec/cours_2nde/TI1.png [new file with mode: 0644]
dossier_inspec/cours_2nde/TI2.png [new file with mode: 0644]
dossier_inspec/cours_2nde/TI3.png [new file with mode: 0644]
dossier_inspec/cours_2nde/boitemoustache.pdf [new file with mode: 0644]
dossier_inspec/cours_2nde/chap7.pdf [new file with mode: 0644]
dossier_inspec/cours_2nde/enigme.pdf [new file with mode: 0644]
dossier_inspec/cours_2nde/exorevision.pdf [new file with mode: 0644]
dossier_inspec/cours_2nde/ficheprep_11-02.pdf [new file with mode: 0644]
dossier_inspec/cours_2nde/pagelivre.png [new file with mode: 0644]
dossier_inspec/notes_1ere_T1.pdf [new file with mode: 0644]
dossier_inspec/notes_1ere_T2.pdf [new file with mode: 0644]
dossier_inspec/notes_2nde_T1.pdf [new file with mode: 0644]
dossier_inspec/notes_2nde_T2.pdf [new file with mode: 0644]
dossier_inspec/progression_1ere.odt [new file with mode: 0644]
dossier_inspec/progression_1ere.pdf [new file with mode: 0644]
dossier_inspec/progression_2nde.ods [new file with mode: 0644]
dossier_inspec/progression_2nde.pdf [new file with mode: 0644]
dossier_inspec/script [new file with mode: 0644]
header.tex
planning surveillance.pdf [new file with mode: 0644]

index 3d3ad478b635be5324a63d0d74102c7c3c2f690a..cad089240915ef2e7cf26b32c08f6a12c944359a 100644 (file)
@@ -20,6 +20,26 @@ En utilisant la méthode de votre choix, déterminer l'expression de $f$.
 
 \emph{Laissez les traces de vos démarches, même (et surtout) si elles n'ont pas abouti.}
 
+\reponse{Une possibilité est d'abord de repérer le sommet : $S(-2; 1)$. On sait donc que $f$ est de a forme :
+\[ f(x) = a(x+2)^2 + 1\]
+
+Pour trouver $a$, on peut utiliser un point particulier "qui tombe juste". Par exemple, $(-5; -2)$. Cela donne donc :
+\begin{eqnarray*}
+& & f(-5) = -2 \\
+&\equi & a(-5+2)^2 + 1 = -2 \\
+& \equi & a\times (-3)^2 + 1 = -2 \\
+&\equi & a = \frac{-3}{9} = -\frac{1}{3}
+\end{eqnarray*}
+
+On a trouvé $a<0$, et on voit bien que la parabole est tournée vers le bas donc le signe (au moins) est cohérent.
+
+Donc \cadrem{f(x) = -\frac{1}{3}(x+2)^2 +1 = -\frac{1}{3}x^2 - \frac{4}{3}x - \frac{1}{3}}
+
+Autre méthode : choisir trois points à coordonnées entières, par exemple $(-2, 1)$, $(-5, -2)$, $(1, -2)$, et écrire les relations qu'elles donnent : $f(-2) = 1$, $f(-5) = -2$, $f(1) = -2$. On obtient alors un système de trois équations à trois inconnes ($a$, $b$, $c$), qu'on peut résoudre.
+
+Il y a encore plein de manières de faire...
+}
+
 
 \section{Inéquations du second degré}
 
@@ -32,11 +52,51 @@ On souhaite résoudre l'inéquation
 \[
 \frac{x^2 + 3x -4}{-2x^2 + x} \geq 0
 \]
+\reponse{
+\begin{eqnarray*}
+& & \frac{3x^2 + 2x - 4}{-2x^2 + x} \geq - 1 \\
+& \equi & frac{3x^2 + 2x - 4}{-2x^2 + x} + 1 \geq 0 \\
+& \equi & frac{3x^2 + 2x - 4}{-2x^2 + x} + \frac{-2x^2 + x}{-2x^2 + x} \geq 0 \\
+& \equi & \frac{3x^2 + 2x - 4 + -2x^2 + x}{-2x^2 + x} \geq 0 \\
+& \equi & \frac{x^2 +3x -4}{-2x^2 + x} \geq 0 
+\end{eqnarray*}
+}
 \item Chercher les racines du polynôme du numérateur (que vous pouvez appeler $N(x)$), puis celles du dénominateur ($D(x)$). En déduire les valeurs interdites au passage.
+
+\reponse{Racines du numérateur :
+\[\Delta = 3^2 -4 \times (-4) = 25\]
+Deux racines :
+\[x_1 = \frac{-3 + 5}{2} = 1 \qquad x_2 = \frac{-3 -5}{2} = -4\]
+
+Racines du dénominateur :
+\[ \Delta = 1\]
+Deux racines :
+\[x_1 = \frac{-1 + 1}{-4} = 0 \qquad x_2 = \frac{-1-1}{-4} = \frac{1}{2}\]
+
+Les valeurs interdites sont donc $0$ et $1/2$.
+}
 \item Dresser un tableau de signe avec le numérateur et le dénominateur, et en déduire le signe de l'expression à l'aide de la règle du signe du quotient (n'hésitez pas à utiliser la calculatrice ou un logiciel pour vérifier la cohérence du tableau de signe). Pour rappel, une valeur interdite s'indique par une double barre dans un tableau de signe.
+
+\reponse{
+
+\variations
+x & \mI & & -4 & & 0 & & 1/2 & & 1 & & \pI \\
+N(x) & \ga{+} & \z & - & \l & - & \l & - & \z & \dr{+} \\
+D(x) & \ga- & \l & - & \z & + & \z & - & \l & \dr- \\
+\frac{N(x)}{D(x)} & \ga- & \z & + & \bb & - & \bb & + & \z & \dr- \\
+\fin
+
+Explications : le signe de $N(x)$ et de $D(x)$ est "standard". Ensuite pour celui du quotient, on applique la règle des signes, qui est la même que pour le produit, à l'exception des "zéros" : le quotient "0/quelque chose" donne 0, alors que le quotient "quelque chose/0" n'est pas défini (d'où la double barre).
+
+}
+
 \item Conclure sur l'ensemble solution de l'inéquation.
 
-\reponse{$[-4; 0[ \cup ]1/2; 1]$.}
+\reponse{ On lit alors quels sont les intervalles où le quotient est positif ou nul : 
+\cadrem{\Sol = [-4; 0[ \cup ]1/2; 1]}
+
+On pense à inclure $-4$ et $1$ puisqu'en ces valeurs, le quotient est égal à $0$ (et on cherche un résultat positif \emph{ou nul}), par contre on pense à exclure $0$ et $1/2$, puisque ce sont des valeurs interdites.
+}
 \end{enumerate}
 
 \end{document}
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+\input{../../header.tex}
+
+\title{\vspace{-1.5cm}Devoir sur table numéro 5 -- classe de 1\iere ES1 \vspace{-1.5cm}}
+\date{\dateoucorr{13/02/2016}}
+
+\begin{document}
+
+\maketitle
+\nomprenom
+%\bigskip
+
+\chapoDST{Probas :
+
+\bigskip
+
+Second degré :
+
+\bigskip
+
+Fonctions : 
+
+\bigskip
+
+}
+
+\section{Probabilités : loi et espérance (4,5)}
+Une usine fabrique des produits qui peuvent avoir $0$, $1$, $2$ ou $3$ défauts. Un produit donné a $10~\%$ de chances d'avoir un défaut, $4~\%$ d'en avoir deux  et $1~\%$ d'en avoir trois. $x$ est la variable aléatoire qui donne le nombre de défauts d'un produit tiré au hasard.
+\begin{enumerate}
+\item Donner la loi de probabilité de $X$ \bareme{1}
+\reponse{
+
+\begin{tabular}{|c|c|c|c|c|}
+\hline
+$x_i$ & 0 & 1 & 2 & 3 \\
+\hline
+$P(X = x_i)$ & 0,85 & 0,1 & 0,04 & 0,01 \\
+\hline
+\end{tabular}
+
+En effet, $P(X = 0) = 1- P(X=1) - P(X=2) - P(X=3) = 1-0,1 - 0,04 - 0,01 = 0,85$
+}
+\item Calculer $P(X\geq 2)$, et $P(X<1)$.\bareme{0,5 chaque}
+\reponse{
+\[
+P(X \geq 2) = P(X=2) + P(X=3) = 0,04 + 0,01 = 0,05 
+\]
+\[
+P(X<1) = P(X=0) = 0,85
+\]
+}
+\item Déterminer l'espérance mathématique de $X$. \bareme{1}
+\reponse{
+\[
+\Esp(X) = 0,85 \times 0 + 0,1 \times 1 + 0,04 \times 2 + 0,01 \times 3 = 0,21 \text{ défaut}
+\]}
+\item L'entreprise qui vend ces produits décide de proposer une garantie sur les défauts de fabrication : elle prend en charge les réparations, ce qui lui coûte $50 \eur$ par défaut à corriger.
+\begin{enumerate}
+       \item Quel est le coût moyen, pour l'entreprise, de ces réparations ? \bareme{1}
+\reponse{Comme un produit a en moyenne $0,21$ défaut, le coût de la garantie est de $50 \times 0,21 = 10,50 \eur$ en moyenne.}
+       \item Quel doit être le prix de la garantie pour que l'entreprise réalise un bénéfice moyen de 30 \eur sur cette garantie ? \bareme{0,5}
+\reponse{Pour réaliser un bénéfice moyen de $30 \eur$ sur la garantie, il faut donc fixer le prix de la garantie à $10,50 + 30 = 40,50 \eur$.}
+\end{enumerate}
+\end{enumerate}
+
+\section{Probabilités : expériences répétées (4)}
+En 2015, environ $91~\%$ des élèves de terminale ES ont eu leur bac. On suppose que les pourcentages restent les mêmes l'année suivante. On choisit au hasard 3 élèves de terminale.
+\begin{enumerate}
+\item Dessiner un arbre pondéré représentant la situation. On pourra noter $B$ l'événement \og l'élève va avoir son bac \fg et $\bar{B}$ l'événement contraire. \bareme{1}
+\item Quelle est la probabilité que les 3 élèves ratent leur bac ? \bareme{0,5}
+\reponse{\[
+P(\bar{B}\bar{B}\bar{B}) = 0,09 \times 0,09 \times 0,09 = 7,29 \times 10^{-4}
+\]}
+\item Quelle est la probabilité qu'exactement un élève sur les trois rate son bac ? \bareme{0,5}
+\reponse{
+\begin{eqnarray*}
+P(\text{\og un élève sur 3 rate son bac \fg}) & = & P(\{B\bar{B}\bar{B}; \bar{B}B\bar{B}; \bar{B}\bar{B}B \}) \\
+& = & 0,09 \times 0,91^2 + 0,91 \times 0,09 \times 0,91 + 0,91^2 \times 0,09 \\
+& = & \simeq 0,223
+\end{eqnarray*}
+}
+\item Quelle est la probabilité qu'au moins un élève sur les trois rate son bac ? \bareme{1}
+\reponse{
+\[P(\text{\og Au moins un élève rate son bac \fg}) = 1 - P(\text{\og Tous les élèves réussissent\fg}) \]
+car l'événement contraire de \og au moins un élève rate \fg est \og tous les élèves réussissent \fg.
+\[P(\text{\og Au moins un élève rate son bac \fg}) = 1 - P(BBB) = 1-0,91^3 \simeq 0,246
+ \]
+
+Remarque : on peut vérifier la cohérence des résultats : la probabilité qu'au moins un élève rate est un peu plus élevée que la probabilité qu'\emph{exactement} un élève rate. C'est plutôt normal, puisque dans la première, l'événement comprend les cas \og exactement un élève rate \fg, \og exactement deux élèves ratent \fg et \og les trois élèves ratent \fg. On pouvait s'attendre à trouver un nombre légèrement plus élevé.
+}
+\item On reprend l'énoncé avec une classe de $26$ élèves. Quelle est la probabilité qu'au moins un élève rate son bac ? \bareme{1} \reponse{
+\begin{eqnarray*}
+P(\text{\og Au moins un élève rate son bac \fg}) &  = & 1 - P(\text{\og Tous les élèves réussissent\fg}) \\
+& = & 1-P(BBBB \ldots B) \\
+& = & 1-0,91^26 \\
+& \simeq & 0,914
+\end{eqnarray*}
+Il y a donc $91,4 \%$ de chances qu'un élève au moins rate son bac.}
+%\item On suppose cette fois qu'on prend $n$ élèves, avec $n \geq 1$. Exprimer la probabilité qu'au moins un élève sur les $n$ rate son bac. \bareme{1}
+%\item Déterminer, à l'aide de la calculatrice, à partir de quel $n$ cette probabilité dépasse $0,95$. \bareme{1}
+\end{enumerate}
+
+\section{Second degré (5,5)}
+
+\begin{enumerate}
+\item Voici quatre paraboles, représentant quatre fonctions $f$, $g$, $h$, $i$. En justifiant, indiquer quelle parabole représente quelle fonction. \bareme{2}
+
+\begin{minipage}{11cm}
+\includegraphics[width=11cm]{exoparabole.pdf}
+\end{minipage}
+\begin{minipage}{4cm}
+\[f(x) = -x^2 -x +2 \]
+\[g(x) = x^2 + 2x \]
+\[h(x) = \frac{1}{3}x^2 + 2 \]
+\[i(x) = \frac{1}{2}x^2 - \frac{3}{2}x \]
+\end{minipage}
+\reponse{\begin{itemize}
+\item $f$ correspond à la courbe en pointillés \og tirets-points \fg, car c'est la seule à être tournée vers le bas, et $f$ est la seule fonction à avoir un coefficient $a<0$.
+\item $h$ correspond à la courbe en trait plein, car on y lit $c=2$ et c'est la seule dans ce cas (hormis $f$ qui est déjà attribuée).
+\item $g$ correspond à la courbe en pointillés \og longs \fg, car on voit son sommet à abscisse $-1$, et pour $h$ on peut calculer facilement $\alpha = \frac{-b}{2a} = \frac{-2}{2} = 0$. Pour $i$ on a $\alpha = \frac{- (-3/2)}{2\times (1/2)} = \frac{3}{2}$, donc on est sûr que ce n'est pas $i$.
+\item $i$ correspond à la courbe en pontillés \og fins \fg, car c'est la seule qui reste (et on peut confirmer la valeur de $\alpha$).
+
+\end{itemize}}
+\item Résoudre l'inéquation suivante : 
+\[ (-12x^2 +x +1)(x-1) \geq 0 \]
+Vous pourrez vous aider d'un tableau de signes et de la règle du signe du produit. \bareme{2, dont 1,5 pour le tableau de signe}
+\reponse{
+Racines de $-12x^2 + x + 1$~:
+\[
+\Delta = 1^2 - 4 \times 1 \times (-12) = 49 >0
+\]
+\[x_1 = \frac{-1 + 7}{-24} = -\frac{1}{4} \qquad x_2 = \frac{-1-7}{-24} = \frac{1}{3} \]
+
+On obtient le tableau de signe suivant :
+
+\variations
+x & \mI & & -1/4 & & 1/3 & & 1 & & \pI \\
+-12x^2 +x +1 & \ga- & \z & + & \z & - & \l & \dr- \\
+x-1 & \ga- & \l& - & \l & - & \z & \dr+ \\
+(-12x^2 +x +1)(x-1) & \ga+ & \z & - & \z & + & \z & \dr- \\
+\fin
+
+On a donc \cadrem{\Sol = ]-\infty, -1/4] \cup [1/3; 1]}
+
+}
+\item Si on augmente de $3$ cm la longueur du côté d'un carré, son aire augmente de 30 \%. Quelle est cette longueur ? \bareme{1,5}
+\reponse{
+On note $x$ le côté du carré. Son aire est donc $x^2$. Le carré augmenté a pour côté $x+3$ et son aire est $x \times 1,30$, ce qui donne~:
+\begin{eqnarray*}
+(x+3)^2 = 1,3x & \equi & x^2 + 6 x + 9 = 1,3x \\
+& \equi & -0,3x^2 + 6x + 9 = 0 
+\end{eqnarray*}
+\[
+\Delta = 6^2 - 4 \times 9 \times (-0,3) = 46,8 >0
+\]
+\[
+x_1 \simeq -1,4 \qquad x_2 \simeq 21,4
+\]
+Comme le côté ne peut pas être négatif, c'est que la longueur du côté cherché est de $21,4$~cm.
+}
+\end{enumerate}
+
+\section{Problème : des cubes (6)}
+Une entreprise fabrique des cubes en plastique : des cubes vides et des cubes pleins. Pour les cubes vides (formés de 6 faces), le coût de fabrication est de $1 \eur$ par cm$^2$ de surface nécessaire. Pour les cubes pleins, le coût de fabrication est de $1 \eur$ par cm$^3$.
+
+Les cubes ont pour côté $x$ cm. On appelle $v$ la fonction qui à $x$ associe le prix de revient du cube vide, et $p$ la fonction qui à $x$ associe le prix de revient du cube plein.
+
+\begin{enumerate}
+\item Exprimer $v(x)$ et $p(x)$ en fonction de $x$. \bareme{1}
+\reponse{On a $v(x) = 6x^2$ puisque l'aire de chaque face est de $x^2$ cm$^2$,  et $p(x) = x^3$ puisque le volume du cube est de $x^3$ cm$^3$.
+}
+\item Représenter, sur la calculatrice, les courbes $v$ et $p$ pour $x \in [0; 8]$. Répondre alors aux questions suivantes à l'aide de ce graphique.
+\reponse{On obtient, avec la bonne fenêtre :
+
+\includegraphics[width=5cm]{capturecourbe.png}}
+\begin{enumerate}      
+       \item Pour quelle longueur de côté le cube plein coûte-t-il $100 \eur$ à produire ? \bareme{0,5} Quel est alors le prix de revient du cube vide ? \bareme{0,5}
+\reponse{On trouve (avec l'outil trace), que c'est pour $x\simeq 4,6$ cm. Le cube vide coûte alors environ $130\eur$ à produire.}
+       \item Pour quelle longueur de côté le cube vide coûte-t-il $300 \eur$ à produire ? \bareme{0,5} Quel est alors le prix de revient du cube plein ? \bareme{0,5}
+\reponse{On trouve que c'est pour $x \simeq 7$ cm. Le cube plein coûte alors environ $352$\eur à produire.}
+       \item Pour quelle(s) longueur(s) le cube vide et le cube plein ont-ils le même prix de revient ? \bareme{0,5}
+\reponse{On le lit à l'intersection des courbes : à environ $6$ cm (ainsi qu'à $0$ cm).}
+\end{enumerate}
+\item Retrouver les résultats précédents de manière algébrique. \bareme{2,5}
+\reponse{
+\begin{enumerate}
+\item On cherche à résoudre $p(x) = 100 \equi x^3 = 100 \equi x = \sqrt[3]{100} \simeq 4,64 $ cm.
+
+On a alors $v(4,64) \simeq 129$ \eur.
+\item On cherche à résoudre $v(x) = 300 \equi 6x^2 = 300 \equi x^2 = 50 \equi x = \sqrt{50}$ puisque $x$ est un nombre positif. Donc $x \simeq 7,07$cm.
+
+On a alors $p(7,07) \simeq 353$ \eur.
+\item On cherche à résoudre \begin{eqnarray*}
+p(x) = v(x) & \equi & x^3 = 6x^2 \\
+& \equi & x^3 - 6x^2 = 0 \\
+& \equi & x^2(x-6) = 0 \\
+&\equi & x^2 = 0 \text{ ou } x-6 = 0 \\
+&\equi & x = 0 \text{ ou } x= 6
+\end{eqnarray*}
+C'est donc à exactement $6$cm et $0$cm que les deux prix sont égaux.
+\end{enumerate}
+}
+\end{enumerate}
+
+\section{Bonus}
+Picsou place une certaine somme d'argent en banque, avec un taux d'intérêt cumulatif de 5 \% par an. Au bout de combien de temps aura-t-il triplé son capital ?
+\reponse{
+Indication : au bout de l'année $n$, la somme de Picsou sera multipliée par $\left( 1 + \frac{5}{100} \right)^n$... Trouver alors quand ce coefficient multiplicateur dépasse $3$.
+}
+\end{document}
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diff --git a/1ere/calcul_mental/tableausigne.pdf b/1ere/calcul_mental/tableausigne.pdf
new file mode 100644 (file)
index 0000000..cb9582c
Binary files /dev/null and b/1ere/calcul_mental/tableausigne.pdf differ
diff --git a/1ere/calcul_mental/tableausigne.tex b/1ere/calcul_mental/tableausigne.tex
new file mode 100644 (file)
index 0000000..24ef5d3
--- /dev/null
@@ -0,0 +1,46 @@
+\input{../../header_beamer.tex}
+
+\begin{document}
+\slide{Déterminer le tableau de signe des expressions suivantes}
+
+\slide{1)
+\[ A(x) = -2x+7\]
+}
+
+\slide{2)
+\[ B(x) = (-2x+7)(x-1) \]
+
+}
+
+\slide{3)
+\[
+C(x) = x^2 - 6x +8 
+\]
+\[ \Delta = 4 \qquad x_1 = 4 \qquad x_2 = 2\]
+}
+
+\slide{4)
+\[D(x) = \frac{-2x+7}{x-1} \]
+
+}
+
+\slide{5)
+\[
+E(x) = (x^2 -6x + 8)(x-1)
+\]
+\[ \Delta = 4 \qquad x_1 = 4 \qquad x_2 = 2\]
+}
+
+\slide{\begin{enumerate}
+\item $A(x) = -2x+7$
+\item $B(x) = (-2x+7)(x-1)$
+\item $C(x) = x^2 - 6x +8 $
+\[ \Delta = 4 \qquad x_1 = 4 \qquad x_2 = 2\]
+\item $D(x) = \frac{-2x+7}{x-1}$
+\item $E(x) = (x^2 -6x + 8)(x-1)$
+\end{enumerate}
+
+
+}
+
+\end{document}
index 08cc48028e92c53c89e5ccebe9221673b263b48e..c9e55c3fc537c474f8170da10f32511bcd1206ed 100644 (file)
Binary files a/1ere/chapitre5_probas/chap5.pdf and b/1ere/chapitre5_probas/chap5.pdf differ
index a47a459f0b3b11e2aa1fb15d386c5eb232c8e08f..6924ffae4838bdbf7bc67f08f2a1e66eec16010b 100644 (file)
@@ -167,4 +167,54 @@ Il est dit \souligne{favorable au joueur} si l'espérance mathématique du gain
 Il est dit \souligne{défavorable au joueur} si l'espérance mathématique du gain du joueur est strictement négative.
 \end{defn}
 
+\newpage
+
+\section{Répétition d'expériences identiques et indépendantes}
+\subsection{Une expérience}
+On peut représenter une expérience aléatoire à peu d'issues à l'aide d'un arbre pondéré : les différentes issues sont alors représentées aux extrémités des branches, et la probabilité de chaque issue est inscrite sur la branche.
+
+Exemple : On pioche une boule dans une urne qui contient 20 boules noires, 5 boules bleues et 10 boules rouges. On notera $N$, $B$ et $R$ les différents événements associés.
+\vspace{4cm}
+
+\subsection{Plusieurs expériences}
+\begin{defn}
+Deux expériences sont dites \souligne{indépendantes}  si le résultat de l'une n'a aucune influence sur le résultat de l'autre.
+\end{defn}
+
+\smallskip
+
+Exemples : On pioche, deux fois, une boule dans l'urne après avoir remis la boule et mélangé l'urne : \lignepoint
+
+On pioche, deux fois, une boule dans l'urne, sans remettre la boule dans l'urne : \dotfill
+\lignepoint
+
+\bigskip
+
+On peut représenter plusieurs expériences aléatoires identiques et indépendantes par un arbre pondéré.
+
+Exemple : On pioche deux fois d'affilée, une boule dans l'urne (après avoir remis la boule et mélangé) :
+
+\vspace{6cm}
+
+
+\begin{prop}
+Dans un arbre pondéré représentant la répétition d'expériences identiques et \souligne{indépendantes}, la probabilité d'une liste de résultats est le \souligne{produit} des probabilités de chaque résultat.
+\end{prop}
+
+Exemple : Déterminer la probabilité de l'événement $RN$.
+
+\lignepoint
+
+Déterminer la probabilité de tirer une boule rouge et une boule noire.
+
+\lignepoint
+\lignepoint
+
+
+Déterminer la probabilité de n'avoir aucune boule bleue.
+
+\lignepoint
+\lignepoint
+
+
 \end{document}
diff --git a/1ere/chapitre5_probas/chap5_page3.pdf b/1ere/chapitre5_probas/chap5_page3.pdf
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index 0000000..3190a6f
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diff --git a/1ere/chapitre5_probas/exo59p204.pdf b/1ere/chapitre5_probas/exo59p204.pdf
new file mode 100644 (file)
index 0000000..22b0bc4
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diff --git a/1ere/chapitre5_probas/exo59p204.tex b/1ere/chapitre5_probas/exo59p204.tex
new file mode 100644 (file)
index 0000000..00b1c6a
--- /dev/null
@@ -0,0 +1,17 @@
+\input{../../header_a5.tex}
+
+\begin{document}
+\exo{59 p 204}
+
+Sur un jet de dés, la probabilité d'avoir un nombre pair est de $1/2$, et autant pour un nombre impair.
+
+Pour quatre jets de dés : $E = \{ PPPP, PPPI, PPIP, \ldots \}$ où "$P$" signifie "pair" et "$I$" impair.
+
+L'arbre à construire a donc une profondeur de $4$, et il y a des $1/2$ sur toutes les branches.
+
+\begin{eqnarray*}
+P(\text{\og Que des nombres pairs \fg}) & = & P(PPPP) \\
+& = & \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right)\times \left(\frac{1}{2}\right) \\
+& = & \frac{1}{16}
+\end{eqnarray*}
+\end{document}
diff --git a/1ere/chapitre6_derivee/activite_derivee.pdf b/1ere/chapitre6_derivee/activite_derivee.pdf
new file mode 100644 (file)
index 0000000..88526d2
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diff --git a/1ere/chapitre6_derivee/activite_derivee.tex b/1ere/chapitre6_derivee/activite_derivee.tex
new file mode 100644 (file)
index 0000000..126397a
--- /dev/null
@@ -0,0 +1,13 @@
+\input{../../header_a5.tex}
+
+\begin{document}
+\subsection*{Une courbe à la loupe, suite}
+\begin{enumerate}
+\item Tracer à la calculatrice la courbe représentative de la fonction $ x\mapsto  \frac{1}{x}$. Zoomer autour du point d'abscisse $2$ (de coordonnées $( \hspace{1cm}; \hspace{1cm})$, jusqu'à obtenir un tracé quasiment rectiligne.
+\item Calculer le coefficient directeur de cette \og pseudo droite \fg.
+\emph{Indication : ne pas hésiter à zoomer, puis prendre beaucoup de décimales car les nombres seront proches...}
+\item En déduire l'équation de cette droite. \emph{Utiliser comme point le point d'abscisse $2$)}
+\item Tracer la droite obtenue à la calculatrice, et vérifier l'aspect obtenu.
+\item Réitérer les opérations 1 et 2 en les points d'abscisse $1$, $3$, $0,5$, $0,25$, et noter les coefficients directeurs obtenus (éventuellement dans un tableau). Peut-on remarquer quelque chose ?
+\end{enumerate}
+\end{document}
diff --git a/1ere/chapitre6_derivee/chap6.pdf b/1ere/chapitre6_derivee/chap6.pdf
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index 0000000..6af097a
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diff --git a/1ere/chapitre6_derivee/chap6.tex b/1ere/chapitre6_derivee/chap6.tex
new file mode 100644 (file)
index 0000000..e2515ee
--- /dev/null
@@ -0,0 +1,71 @@
+\input{../../header.tex}
+
+\title{\vspace{-1cm}Chapitre 6 -- Dérivation \vspace{-1.5cm}}
+\date{}
+
+\begin{document}
+\maketitle
+
+\section{Nombre dérivé et tangente}
+$f$ est une fonction définie sur un intervalle $I$, $\C$ est sa représentation graphique dans un repère du plan, et $A$ est le point de $\C$ d'abscisse $a \in I$ : $A( \hspace{1cm}; \hspace{1cm} )$.
+
+\subsection{Nombre dérivé de $f$ en $a$}
+
+\begin{minipage}{5cm}
+\includegraphics[width=5cm]{courbe1.pdf}
+\end{minipage}
+\begin{minipage}{12cm}
+\begin{defn}
+Soit $h$ tel que $a+h \in I$. $M$ est le point de la courbe d'abscisse $a+h$ : $M( \hspace{1.5cm}; \hspace{2cm} )$.
+Le \souligne{taux d'accroissement} de $f$ entre $a$ et $a+h$ est le coefficient directeur de la droite $(AM)$, c'est-à-dire :
+
+\bigskip
+
+\[ r(h) = \hspace{8cm} \]
+
+\bigskip
+
+\end{defn}
+\end{minipage}
+
+Remarque : $r(0)$ n'est pas défini, mais on s'intéresse à ce rapport lorsque $h$ s'approche de $0$.
+
+\begin{defn}
+Si $r(h)$ tend vers un nombre réel quand $h$ tend vers $0$, on dit que $f$ est \souligne{dérivable en $a$}, et ce nombre est appelé le \souligne{nombre dérivé} de $f$ en $a$, noté $f'(a)$.
+On écrit :
+
+\vspace{2cm}
+\end{defn}
+
+Exemple : $f(x) = 5x^2 + 1$, on veut savoir si $f$ est dérivable en $2$.
+
+On écrit le taux d'accroissement :\\
+$r(h) = \dotfill$
+
+\smallskip
+
+\lignepoint
+
+\lignepoint
+
+\lignepoint
+
+\lignepoint
+
+\subsection{Tangente à une courbe}
+\begin{defn}
+Si $f$ est dérivable en $a$, on appelle tangente en $A$ à la courbe $\C$ la droite qui passe par $A$ et qui a pour coefficient directeur $f'(a)$.
+\end{defn}
+\begin{minipage}{5cm}
+\includegraphics[width=5cm]{courbe1.pdf}
+\end{minipage}
+\begin{minipage}{12cm}\begin{prop}
+Si $f$ est dérivable en $a$, une équation de la tangente en $A$ est donnée par :
+
+\vspace{2cm}
+\end{prop}
+\end{minipage}
+
+
+
+\end{document}
diff --git a/1ere/chapitre6_derivee/courbe1.pdf b/1ere/chapitre6_derivee/courbe1.pdf
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diff --git a/1ere/mathematiques_ES_L_term.pdf b/1ere/mathematiques_ES_L_term.pdf
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diff --git a/2nde/AP/liste_eleves_AP.ods b/2nde/AP/liste_eleves_AP.ods
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index 4c9ded3729df5113c0dd4e15a9c0fc2b6a65e975..fcf3c5a72fb2c70ce3891ed2eae8d021bf3c7dc1 100644 (file)
@@ -57,3 +57,17 @@ Marin G
 François D
 Cheima EF
 Mehdi B
+
+---
+Fonctions affines 19/02
+Christophe R
+Nael A
+Mahamé D
+Inès S
+Sibiry K
+Inès M
+Vincent J
+Alexandre H
+Illan Z
+
++ Maxime B et Julien P
diff --git a/2nde/DST_6/dst6.tex b/2nde/DST_6/dst6.tex
new file mode 100644 (file)
index 0000000..8442751
--- /dev/null
@@ -0,0 +1,241 @@
+\input{../../header.tex}
+
+\title{\vspace{-1.5cm}DST numéro 6 (petit) -- classe de 2nde 6  -- Version \version{A}{B} \vspace{-1.5cm}
+}
+\date{\dateoucorr{12/02/2015}}
+
+
+\begin{document}
+
+\maketitle
+
+
+\nomprenom
+%\bigskip
+
+\chapoDST{
+}
+
+\section{Généralités (13)}
+\begin{enumerate}
+\item Les fonctions ci-dessous sont-elles affines ? Justifier (dans le cas où la fonction est affine, donner les valeurs des coefficients $a$ et $b$).\bareme{1 chaque}
+\begin{enumerate}
+       \item $f(x) = \version{\frac{x}{2}}{\frac{2}{x}} $ 
+\corrige
+  \corrigeab{affine, avec $a = \frac{1}{2}$ et $b=0$.}{non affine, car il y a un $x$ au dénominateur.}
+\else
+\dotfill
+
+\smallskip
+
+\lignepoint
+
+\fi
+       \item $g(x) = \version{\frac{2}{x} + 1}{-4x+2}$ 
+\corrige
+\corrigeab{non affine, car il y a un $x$ au dénominateur.}{affine avec $a= -4$ et $b=2$.}
+\else\dotfill
+
+\smallskip
+
+
+\lignepoint
+\fi
+       \item $h(x) = \version{2+5x}{\frac{-4}{x}}$ \corrige
+\corrigeab{affine, avec $a=5$ et $b=2$.}{non-affine, car il y a un $x$ au dénominateur}
+\else
+\dotfill
+
+\smallskip
+
+
+\lignepoint
+\fi
+
+       \item $i(x) = \version{2x^2 -1}{3x^3 + 2} $ \corrige
+\corrigeab{pas affine, car il y a un terme en $x^2$.}{pas affine, car il y a un terme en $x^3$.}
+\else
+\dotfill
+
+\smallskip
+
+\lignepoint
+
+\fi
+\end{enumerate}
+\item Voici trois fonctions affines :
+\[ \version{
+f(x) = 2x-2 \qquad g(x) = -3 \qquad h(x) =  -\frac{1}{3}x}{ f(x) = \frac{1}{2}x \qquad g(x) = -3x + 4 \qquad h(x) = 2}
+\]
+\begin{enumerate}
+\item Quel est le sens de variations de chacune d'elle ? Justifier brièvement. \bareme{1,5}
+
+\hspace{-2cm}\begin{tabular}{p{0.3\textwidth}|p{0.35\textwidth}|p{0.3\textwidth}}
+
+\corrige
+$f$ & $g$ & $h$ \\
+\corrigeab{croissante car $a=2>0$}{croissante car $a=\frac{1}{2}>0$} 
+& \corrigeab{constante car $a=0$}{décroissante car $a=-3<0$}
+& \corrigeab{décroissante car $a=-\frac{1}{3}<0$}{constante car $a=0$} \\
+\else
+\[f\] & \[g\] & \[h\] \\
+\vspace{1.5cm} ~ & & \\
+\fi
+\end{tabular}
+\item Donner le signe de chacune d'elle (de préférence sous forme d'un tableau). \bareme{4,5}
+
+\hspace{-2cm}\begin{tabular}{p{0.3\textwidth}|p{0.35\textwidth}|p{0.3\textwidth}}
+\corrige 
+$f$ & $g$ & $h$ \\
+\corrigeab{
+$-\frac{b}{a} = -\frac{-2}{2} = 1$
+
+\variations
+x & \mI & & 1 & & \pI\\
+f(x) & \ga- & \z & \dr+ \\
+\fin}{
+$-\frac{b}{a} = -\frac{0}{1/2} = 0$
+
+\variations
+x & \mI & & -2 & & \pI\\
+f(x) & \ga- & \z & \dr+ \\
+\fin
+}
+& \corrigeab{
+\variations
+x & \mI & & \pI \\
+g(x) & & - & \\
+\fin
+}{$-\frac{b}{a} = -\frac{4}{-3} = \frac{4}{3}$ 
+
+\variations
+x & \mI & & 4/3 & & \pI\\
+g(x) & \ga+ & \z & \dr- \\
+\fin
+}
+&
+\corrigeab{
+$-\frac{b}{a} = -\frac{0}{-1/3} = 0$ 
+
+\variations
+x & \mI & & 0 & & \pI\\
+g(x) & \ga+ & \z & \dr- \\
+\fin
+}{
+
+\variations
+x & \mI & & \pI \\
+h(x) & & + & \\
+\fin
+
+} \\
+\else
+\[f\] & \[g\] & \[h\] \\
+\vspace{4cm} ~ & & \\
+\fi
+\end{tabular}
+\corrige
+%\end{enumerate}
+\begin{minipage}{8cm}
+\item Représenter dans le repère ci-dessous les trois fonctions affines suivantes (les détails du tracé ne sont pas exigés mais peuvent être valorisés si la représentation graphique n'est pas correcte...) \bareme{3} \end{minipage}
+\begin{minipage}{8cm}
+\version{\includegraphics[width=8cm]{reperea.pdf}}{\includegraphics[width=8cm]{repereb.pdf}}
+\end{minipage}
+\else
+\item Représenter dans le repère ci-dessous les trois fonctions affines suivantes (les détails du tracé ne sont pas exigés mais peuvent être valorisés si la représentation graphique n'est pas correcte...) \bareme{3}
+\includegraphics[width=16cm]{repere.pdf}
+\fi
+
+\end{enumerate}
+
+\end{enumerate}
+
+\section{Retrouver une fonction affine (5)}
+\begin{enumerate}
+\item $f$ est une fonction affine de coefficient directeur \version{$2$}{$-2$} et telle que $f(3) = 0$. Déterminer l'expression de $f$. \bareme{1} \corrigeab{
+$f$ est de la forme $f(x) = 2x+b$.
+\begin{eqnarray*}
+f(3)  =  0 & \equi & 2\times 3 + b = 0 \\
+& \equi & b = -6
+\end{eqnarray*}
+Donc \cadrem{ f(x) = 2x-6}
+}{
+$f$ est de la forme $f(x) = -2x+b$.
+\begin{eqnarray*}
+f(3)  =  0 & \equi & -2\times 3 + b = 0 \\
+& \equi & b = 6
+\end{eqnarray*}
+Donc \cadrem{f(x) = -2x+6}}
+\item $g$ est une fonction affine telle que $g(-2) = 8$ et \version{$g(3) = 3$}{$g(4) = 11$}. Déterminer l'expression de $g$. \bareme{2} \corrigeab{
+\[ a = \frac{g(-2) - g(3)}{-2 - 3} = \frac{8-3}{-5} = -1 \]
+On a donc $g(x) = -x + b$
+\begin{eqnarray*}
+g(3) = 3 & \equi & -3 + b = 3 \\
+& \equi & b = 6
+\end{eqnarray*}
+Donc \cadrem{g(x) = -x+6}}{
+\[ a = \frac{g(-2) - g(4)}{-2 - 4} = \frac{8-11}{-6} = \frac{1}{2} \]
+On a donc $g(x) = \frac{1}{2}x + b$
+\begin{eqnarray*}
+g(4) = 11 & \equi & \frac{1}{2}\times 4 + b = 11 \\
+& \equi & b = 11 - 2 = 9
+\end{eqnarray*}
+Donc \cadrem{g(x) = \frac{x}{2}+9} }
+\item $h$ est une fonction linéaire, dont la représentation graphique passe par le point d'intersection des représentations graphique de $f$ et $g$. Déterminer l'expression de $h$. \bareme{2}
+\reponse{
+On commence par trouver le point d'intersection :
+\begin{eqnarray*}
+f(x) = g(x) & \equi & \version{2x - 6 = -x + 6}{-2x+6 = \frac{x}{2} + 9} \\
+& \equi & \version{3x = 12}{-\frac{5}{2}x = 3} \\
+& \equi & \version{x = 4}{x = - \frac{6}{5}}
+\end{eqnarray*}
+On a \version{$f(4) = 2\times 4 -6 = 2$}{$f\left(-\frac{6}{5}\right) = -2 \times -\frac{6}{5} + 6 = \frac{42}{5}$}
+
+On cherche $h$ linéaire qui vérifie \version{$h(4) = 2$}{$h\left(-\frac{6}{5}\right) =\frac{42}{5}$}. On a $h(0) = 0$ puisqu'elle est linéaire.
+
+\[a = \version{ \frac{h(4) - h(0)}{4 - 0} = \frac{2 - 0}{4} = \frac{1}{2}
+}{ \frac{h\left(-\frac{6}{5} \right) - h(0)}{-\frac{6}{5} - 0} = \frac{\frac{42}{5}}{-\frac{6}{5}} = -7
+} \]
+
+Donc, comme $b=0$, on a \cadrem{h(x) = \version{\frac{1}{2}x}{-7x}}
+
+}
+\end{enumerate}
+
+\section{Problème (4)}
+
+Albert habite au 17e étage d'un immeuble (sans ascenseur), et son ami Gontran vient le visiter. Celui-ci monte les marches à la vitesse de 3 marches par seconde. Albert, pressé de le voir, descend les marches à sa rencontre, à la vitesse de 4 marches par secondes.
+Sachant qu'il y a \version{21}{14} marches par étage et que les deux amis ont commencé à courir en même temps, au bout de combien de temps et sur quelle marche vont-ils se retrouver ?
+
+\corrige
+\else
+\emph{N'hésitez pas à laisser les traces de vos recherches, même si elles n'aboutissent pas.}
+\fi
+
+\reponse{Tout d'abord, il y a $17 \times \version{21}{14} = \version{357}{238}$ marches jusqu'à l'appartement d'Albert.
+
+On appelle $f$ la fonction qui donne, en fonction du temps, la marche sur laquelle se trouve Albert. On a
+$f(t) = \version{357}{238} - 4t $ puisqu'il part du 17e étage et qu'il descend à la vitesse de 4 marches par seconde.
+
+$g$ est la fonction qui donne, en fonction du temps, la marche sur laquelle se trouve Gontran. On a $
+g(t) = 3t$
+puisqu'il monte à 3 marches/seconde.
+
+On cherche alors quand ils se rencontrent :
+\begin{eqnarray*}
+f(t) = g(t) & \equi & \version{357}{238} - 4t = 3t \\
+& \equi & \version{357}{238} = 7t \\
+& \equi & t = \frac{\version{357}{238}}{7} = \version{51}{34}~s
+\end{eqnarray*}
+$g(\version{51}{34}) = 3 \times \version{51}{34} = \version{153}{102}$
+
+Ils se rencontrent sur la \version{153}{102}\ieme marche, au bout de \version{51}{34} secondes.
+
+}
+
+%\corrigeab{
+%153e marche et 51 sec}{102e marche et 34 secondes}
+
+
+
+\end{document}
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diff --git a/2nde/calcul_mental/boiteamoustaches.png b/2nde/calcul_mental/boiteamoustaches.png
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diff --git a/2nde/calcul_mental/boitemoustache.pdf b/2nde/calcul_mental/boitemoustache.pdf
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diff --git a/2nde/calcul_mental/boitemoustache.tex b/2nde/calcul_mental/boitemoustache.tex
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index 0000000..3a1e4e2
--- /dev/null
@@ -0,0 +1,50 @@
+\input{../../header_beamer.tex}
+
+\begin{document}
+\slide{Statistiques~: lire un graphique}
+
+\newcommand\diagramme{\includegraphics[width=8cm]{boiteamoustaches.png}}
+
+\slide{On considère le diagramme en boîte~:
+
+\diagramme
+
+1) Déterminer la médiane de cette série.
+}
+
+\slide{ \diagramme
+
+2) Déterminer l'étendue de cette série.
+}
+
+\slide{ \diagramme
+
+3) Quel est, environ, le pourcentage des valeurs inférieures ou égales à $14$~?
+
+}
+
+\slide{ \diagramme
+
+4) Déterminer l'écart interquartile de cette série
+
+}
+
+\slide{ \diagramme
+
+5) Quel est, environ, le pourcentage des valeurs situées dans l'intervalle interquartile~?
+
+}
+
+\slide {\diagramme
+
+\begin{enumerate}
+\item Déterminer la médiane de cette série.
+\item Déterminer l'étendue de cette série.
+\item Quel est, environ, le pourcentage des valeurs inférieures ou égales à $14$~?
+\item Déterminer l'écart interquartile de cette série
+\item Quel est, environ, le pourcentage des valeurs situées dans l'intervalle interquartile~?
+\end{enumerate}
+
+}
+
+\end{document}
diff --git a/2nde/calcul_mental/coeffdir.pdf b/2nde/calcul_mental/coeffdir.pdf
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diff --git a/2nde/calcul_mental/coeffdir.tex b/2nde/calcul_mental/coeffdir.tex
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index 0000000..2568342
--- /dev/null
@@ -0,0 +1,35 @@
+\input{../../header_beamer.tex}
+
+\begin{document}
+
+\slide{Coefficients directeurs}
+
+\slide{1)
+$f$ est telle que $f(2) = 3$ et $f(3) = 7$}
+
+\slide{2)
+$g$ est telle que $g(-2) = 8$ et $g(1) = -1$
+}
+
+\slide{3)
+$h$ est une fonction linéaire telle que $h(-5) = -2$
+}
+
+\slide{4)
+$i$ est une fonction dont la représentation graphique passe par les points $A(-1; 0)$ et $B(4; 1)$
+}
+
+\slide{5)
+$j$ est une fonction constante
+}
+
+
+\slide{\begin{enumerate}
+\item $f$ est telle que $f(2) = 3$ et $f(3) = 7$
+\item $g$ est telle que $g(-2) = 8$ et $g(1) = -1$
+\item $h$ est une fonction linéaire telle que $h(-5) = -2$
+\item $i$ est une fonction dont la représentation graphique passe par les points $A(-1; 0)$ et $B(4; 1)$
+\item $j$ est une fonction constante
+\end{enumerate}
+}
+\end{document}
diff --git a/2nde/calcul_mental/signe1deg.pdf b/2nde/calcul_mental/signe1deg.pdf
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diff --git a/2nde/calcul_mental/signe1deg.tex b/2nde/calcul_mental/signe1deg.tex
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index 0000000..28cf2c9
--- /dev/null
@@ -0,0 +1,45 @@
+\input{../../header_beamer.tex}
+
+\begin{document}
+\slide{Signe d'une fonction affine
+}
+
+\slide{1)
+\[
+f(x) = x+3
+\]
+
+}
+\slide{2)
+\[
+g(x) = -2x +4 
+\]
+}
+
+\slide{3)
+\[ 
+h(x) = -\frac{1}{2}
+\]
+}
+
+\slide{4)
+\[
+i(x) = x
+\]
+}
+
+\slide{5)
+\[
+j(x) = \frac{1}{2}x + \frac{1}{3}
+\]
+}
+
+\slide{\begin{enumerate}
+\item $f(x) = x+3$
+\item $g(x) = -2x +4 $
+\item $h(x) = -\frac{1}{2}$
+\item $i(x) = x$
+\item $j(x) = \frac{1}{2}x + \frac{1}{3}$
+\end{enumerate}
+}
+\end{document}
diff --git a/2nde/chapitre6_fct_affines/enigme.pdf b/2nde/chapitre6_fct_affines/enigme.pdf
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+\input{../../header_a5.tex}
+
+\begin{document}
+\newcommand\bla{\exon{Réductions}
+Laquelle de ces deux promotions est la plus intéressante ?
+\begin{itemize}
+       \item \og Super promo, 15 \% de réduction sur le prix ! \fg
+       \item \og Super affaire, +15 \% de produit en plus ! \fg
+\end{itemize}
+
+}
+
+\bla
+
+\vspace{1cm}
+
+\bla
+
+\vspace{1cm}
+\bla
+
+\vspace{1cm}
+\bla
+
+\vspace{1cm}
+\bla
+
+\vspace{1cm}
+
+
+\end{document}
diff --git a/2nde/chapitre6_fct_affines/enigme_2pages.pdf b/2nde/chapitre6_fct_affines/enigme_2pages.pdf
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diff --git a/2nde/chapitre7_echantillonnage/TP_donnees.pdf b/2nde/chapitre7_echantillonnage/TP_donnees.pdf
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diff --git a/2nde/chapitre7_echantillonnage/TP_echantillon.pdf b/2nde/chapitre7_echantillonnage/TP_echantillon.pdf
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--- /dev/null
@@ -0,0 +1,28 @@
+\input{../../header_a5.tex}
+
+\begin{document}
+\section*{TP : Lancer des dés avec une calculatrice}
+Nous allons simuler l'expérience de l'activité 1p268 :  réaliser plusieurs échantillons de 30 lancers de dés, et comptabiliser le nombre de 1 dans chaque échantillon.
+
+\begin{enumerate}
+\item Effectuer les étapes 1 et 2 du TD1 p274 du livre, avec non pas 10, mais 30 lancers. Pour vous aider :
+\begin{itemize}
+\item NbrAléat est dans le menu \bouton{math}, puis menu PROB.
+\item suite est dans le menu \bouton{2nde} \bouton{Listes}, menu "OP"
+\item Pour obtenir ce qui est dans le livre pour l'expression "suite", désactiver l'\og assistant stats\fg. Pour cela, \bouton{mode}, sélectionner "assistant stats" et choisir "NAFF". %Sinon il proposeun menu qui n'est pas forcément plus simple.
+%\item Le symbole "=" se trouve dans le menu \bouton{2nde} \bouton{tests}
+\end{itemize}
+\item Compter et mettre de côté le nombre de \og 1 \fg obtenus (dans la liste L1), et refaire cette expérience jusqu'à 10 fois.
+\emph{Astuce aller vite : vous pouvez utiliser la commande suivante : "som(L1=1)" 
+qui comptabilise tous les \og 1 \fg de la liste 1.
+}
+\item Mise en commun (feuille qui circule) : noter le nombre de 1 pour chaque expérience, et continuer le TP pendant ce temps.
+\item Quel est l'intervalle de fluctuation au seuil de 0,95 pour cette expérience ? (vous pouvez supposer que tous les élèves ont réalisé 10 échantillons)
+\item Dans votre propre série d'expérience, combien de fréquences d'apparition du nombre \og 1 \fg sont en dehors de l'intervalle de fluctuation ? 
+\item Mise en commun : combien y en a-t-il dans le groupe ? À quelle proportion cela correspond-il ?
+\end{enumerate}
+
+\section*{Pour aller plus loin}
+Chercher, en utilisant toujours l'instruction NrAléat, une façon de simuler un pile ou face biaisé, où pile apparaît avec une probabilité $p$, c'est-à-dire qu'on doit obtenir 1 avec probabilité $p$ et 0 avec probabilité $1-p$. Comment cela peut-il s'intégrer dans un programme ?
+
+\end{document}
diff --git a/2nde/chapitre7_echantillonnage/TP_echantillon_2pages.pdf b/2nde/chapitre7_echantillonnage/TP_echantillon_2pages.pdf
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diff --git a/2nde/chapitre7_echantillonnage/chap7.pdf b/2nde/chapitre7_echantillonnage/chap7.pdf
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--- /dev/null
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+\input{../../header.tex}
+
+\title{\vspace{-1cm}Chapitre 7 -- Échantillonnage \vspace{-1.5cm}}
+\date{}
+
+\begin{document}
+\maketitle
+
+\section{Échantillon}
+
+Lorsqu'on étudie un caractère dans une population, on peut rarement observer la population entière. On se contente d'un \souligne{échantillon} de la population. Pour que l'échantillon soit valable, il est indispensable qu'il soit tiré au hasard.
+
+\begin{defn}
+Une expérience aléatoire est une expérience renouvelable dont on ne peut pas déterminer de façon sûre quelle sera l'issue.
+\end{defn}
+\begin{defn}
+Un \souligne{échantillon} de taille $n$ est la liste des $n$ résultats obtenus par $n$ répétitions indépendantes de la même expérience.
+\end{defn}
+
+Exemples : \lignepoint
+\lignepoint
+\lignepoint
+
+\begin{defn}
+Deux échantillons de même taille issus de la même expérience aléatoire ne sont généralement pas identiques : on parle de 
+\vspace{1cm}
+\end{defn}
+
+Exemples : Si on effectue 1000 lancers à pile ou face d'une pièce équilibrée, \dotfill
+
+\lignepoint \lignepoint
+
+
+\section{Intervalle de fluctuation ($p$ est connu)}
+
+Dans une population, la proportion d'un caractère est de $p$. On produit un échantillon de taille $n$, et on détermine la fréquence $f$ de ce caractère dans l'échantillon.
+
+\begin{prop}
+
+\lignepoint
+
+\smallskip
+
+\lignepoint
+
+\smallskip
+
+\vspace{1cm}
+%Si $p$ est compris entre $0,2$ et $0,8$ et que $n\geq 25$, alors $f$ appartient à l'intervalle 
+%\[ \left[p - \frac{1}{\sqrt n} ; p+ \frac{1}{\sqrt n}\right]\]
+%dans $95 \%$ des cas.
+
+On appelle cet intervalle \lignepoint
+%l'\souligne{intervalle de fluctuation} au seuil de $0,95$.
+\end{prop}
+
+\smallskip
+
+Exemple : Dans la réserve indienne d’Aamjiwnaag, située au
+Canada, à proximité d'industries chimiques, il est
+né entre 1999 et 2003, 132 enfants dont 46 garçons.
+Est ce normal ?
+
+On supposera que normalement, la probabilité qu'un enfant qui naisse soit un garçon est de $0,5$.
+
+Solution : 
+\lignepoint
+\lignepoint
+\lignepoint
+\lignepoint
+\lignepoint
+
+
+\newpage
+
+\section{Intervalle de confiance ($p$ est inconnu)}
+
+Dans une population, on étudie un caractère dont on cherche la proportion. On a déterminé la fréquence $f$ de ce caractère dans l'échantillon.
+
+\begin{prop}
+\lignepoint
+
+\smallskip
+
+\lignepoint
+
+\smallskip
+
+\vspace{1cm}
+%Si $p$ est compris entre $0,2$ et $0,8$ et que $n\geq 25$, alors $f$ appartient à l'intervalle 
+%\[ \left[p - \frac{1}{\sqrt n} ; p+ \frac{1}{\sqrt n}\right]\]
+%dans $95 \%$ des cas.
+
+On appelle cet intervalle \lignepoint
+\end{prop}
+
+\smallskip
+
+Exemple : Avant une élection, un sondage est fait auprès de 1000 électeurs. On obtient les promesses de vote suivantes :
+\begin{itemize}
+\item 55 \% des voix pour le candidat A,
+\item 45 \% des voix pour le candidat B.
+\end{itemize}
+
+Le candidat A est-il sûr d'être élu ?
+
+Solution :
+\lignepoint
+\lignepoint
+\lignepoint
+\lignepoint
+\lignepoint
+
+
+\end{document}
diff --git a/2nde/chapitre7_echantillonnage/donnees_recolter.pdf b/2nde/chapitre7_echantillonnage/donnees_recolter.pdf
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+\input{../../header_a5.tex}
+
+\begin{document}
+\exo{}
+Aux congrès des héros, on trouve des Jedis (J), des chevaliers de la Table Ronde (T) et des elfes des Terres du milieu (E).  
+
+
+    \begin{tabular}{|c|c|c|c|}\hline
+     Héros & J & T & E \\\hline
+     Effectifs  à Londres& 37&77&23\\\hline
+     Effectifs à Baltimore & 53 & 48 & 40 \\\hline
+    \end{tabular}
+\begin{enumerate}
+ \item Dans quelle ville de congrès,  les Jedis sont-ils les plus présents? 
+ \item Même question pour les chevaliers.
+ \item Pour ces deux relevés, calculer les fréquences de présence de chaque type de héros  à $0,01$ près.
+\end{enumerate}
+
+\exo{}
+ Un jeu consiste à miser sur le doigt des deux mains que va faire apparaître un animateur (qui ne connaît pas les paris). 
+ \begin{enumerate}
+  \item Quelle est la probabilité de gagner? 
+  
+  Répondre sans justifier.
+  \item Si je joue 10~fois, suis-je sûr de gagner?
+  \item Si je joue 100~fois, suis-je sûr de gagner 10~fois?
+  \item 10~personnes jouent. Elles ne connaissent pas le vote des autres.  Est-on sûr qu'au moins l'une d'entre elles va gagner?
+  \item 10~personnes jouent. Chacune a un vote différent des autres. Est-on sûr qu'au moins l'une d'entre elles va gagner?
+ \end{enumerate}
+
+\end{document}
diff --git a/2nde/chapitre7_echantillonnage/exorevision_2pages.pdf b/2nde/chapitre7_echantillonnage/exorevision_2pages.pdf
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index 0000000..1ba7c04
--- /dev/null
@@ -0,0 +1,20 @@
+\input{../../header_a5.tex}
+
+\newcommand\bla{\includegraphics[width=\textwidth]{resultTP.png}}
+
+\begin{document}
+
+\bla
+
+\vspace{1cm}
+
+\bla
+\newpage
+
+\bla
+
+\vspace{1cm}
+
+\bla
+
+\end{document}
diff --git a/2nde/chapitre7_echantillonnage/resultTP.png b/2nde/chapitre7_echantillonnage/resultTP.png
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index 0000000..769af22
--- /dev/null
@@ -0,0 +1,51 @@
+\input{../header.tex}
+
+\begin{document}
+Fiche de préparation de séance -- classe de 2nde 6, le 12/02/2016 à 13h.
+
+Note : la séance dure en réalité deux heures, sur la demi deuxième heure un petit contrôle est prévu sur le chapitre précédent.
+
+\bigskip
+\begin{itemize}
+\item But de la séance~: découvrir les fluctuations lors d'un échantillonnage
+\item Avant~: fin du chapitre précédent (fonctions affines), un petit exercice sur les fréquences et probabilités à faire à la maison.
+\item Après~: intervalle de fluctuation, et simulation de ces fluctuations à la calculatrice
+\end{itemize}
+
+\begin{tabular}{|p{1cm}|p{15cm}|}
+\hline
+Tps & Déroulé \\
+\hline
+1-3' & Installation des élèves, prise des HF. Rappels sur les téléphones portables, salle de samedi : 111 puis 217 en demi-groupe.\\
+\hline
+5' max & Activité mentale [vidéoproj + TNI]~: lecture d'un graphique \og boîte à moustaches \fg. \emph{C'est l'objet d'un chapitre précédent, mais cela ne fait pas de mal de revoir cela.}\\
+\hline
+5'-10' & Correction rapide de la feuille d'exercices, à l'oral. \\
+\hline
+20' & Activité 1 p268. Explication : samedi en demi-groupe, nous génèrerons nous-mêmes ces séries de données à la calculatrice. Au besoin, voir le 3p327 du livre, qui explique comment représenter un nuage de points. 
+
+\emph{Rentrer 50 valeurs peut être long pour ceux qui sont lents.} Au bout de 10 minutes, dire de s'arrêter où ils en sont des entrées de données, et faire le graphe puis passer à la suite, pour revenir ensuite au graphique éventuellement.
+
+\emph{Si le graphique ne ressemble à rien, dire de choisir une fenêtre adaptée : $x$ de $0$ à $50$, et $y$ de $0$ à $3/6$ par exemple.} \\
+\hline
+10' & Correction : [Vidéoproj] Montrer les écrans calculette pour le graphe et les listes. \emph{Il y a un émulateur TI installé sur les machines, mais rentrer les valeurs devant les élèves va être trop long ici, d'où les captures d'écran.} Interroger plusieurs élèves pour le nombre de fois qu'on obtient $1/6$. \\
+\hline
+ & Bilan cours (poly à trous à distribuer) : fluctuation d'échantillonnage, exemples d'échantillons (sondages, etc). \\
+\hline
+\hline
+12' & Petits exercices échantillons : 1, 4 et 6p276. \\
+7 & Correction \\
+\hline
+30' & Petit contrôle sur le chapitre précédent. \\
+\hline
+\end{tabular}
+
+\bigskip
+
+En parallèle : pour les rapides, faire l'exercice énigme de la veille (justification) !
+
+Pour samedi : 7p276 et ne pas oublier sa calculatrice (chargée) !
+
+
+
+\end{document}
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