From 9be024d3c970eec15d24021a8b7272ffab6abc27 Mon Sep 17 00:00:00 2001 From: Benjamin Bertrand Date: Tue, 2 Feb 2016 11:28:52 +0300 Subject: [PATCH] add explications on compilation and corr --- .../source/_downloads/{3_DM.tex => 01_DM.tex} | 94 ++++++++-------- .../source/_downloads/{1_DM.tex => 02_DM.tex} | 101 ++++++++--------- .../source/_downloads/{2_DM.tex => 03_DM.tex} | 102 +++++++++--------- documentation/source/_downloads/all_DM.pdf | Bin 125403 -> 126400 bytes documentation/source/_downloads/corr_DM.pdf | Bin 0 -> 165170 bytes documentation/source/tutorial.rst | 40 ++++++- 6 files changed, 187 insertions(+), 150 deletions(-) rename documentation/source/_downloads/{3_DM.tex => 01_DM.tex} (60%) rename documentation/source/_downloads/{1_DM.tex => 02_DM.tex} (59%) rename documentation/source/_downloads/{2_DM.tex => 03_DM.tex} (58%) create mode 100644 documentation/source/_downloads/corr_DM.pdf diff --git a/documentation/source/_downloads/3_DM.tex b/documentation/source/_downloads/01_DM.tex similarity index 60% rename from documentation/source/_downloads/3_DM.tex rename to documentation/source/_downloads/01_DM.tex index b1987e6..0758339 100644 --- a/documentation/source/_downloads/3_DM.tex +++ b/documentation/source/_downloads/01_DM.tex @@ -33,33 +33,33 @@ \maketitle -Sujet numéro 3 +Sujet numéro 01 \section{Exercice} - Dans un sac, il y a 6 bonbons à la menthe, 24 bonbons à la fraise et 5 au chocolat. On choisit un bonbon au hasard dans ce sac. + Dans un sac, il y a 20 bonbons à la menthe, 40 bonbons à la fraise et 2 au chocolat. On choisit un bonbon au hasard dans ce sac. \begin{enumerate} \item Calculer la probabilité de tirer un bonbon à la fraise. \begin{solution} - $T($ tirer un bonbon à la fraise $) = \dfrac{6}{35}$ + $T($ tirer un bonbon à la fraise $) = \dfrac{20}{62}$ \end{solution} \item Calculer la probabilité de tirer un bonbon qui n'est pas au chocolat. \begin{solution} - $T($ tirer un bonbon à la fraise ou à la menthe $) = \dfrac{30}{35}$ + $T($ tirer un bonbon à la fraise ou à la menthe $) = \dfrac{60}{62}$ \end{solution} \item Calculer la probabilité de tirer un bonbon au réglisse. \begin{solution} - $T($ tirer un bonbon au réglisse $) = \dfrac{0}{35} = 0$ + $T($ tirer un bonbon au réglisse $) = \dfrac{0}{62} = 0$ \end{solution} \item Dans un autre sac, on place 25 bonbons à la menthe et 34 bonbons à la fraise. Lise préfère les bonbons à la menthe. Dans quel sac doit-elle tirer un bonbon pour avoir le plus de chance d'avoir un bonbon qu'elle préfère? \begin{solution} Elle prefera tirer dans le deuxième sac car \begin{eqnarray*} - \frac{6}{35} & < & \frac{25}{34} + \frac{20}{62} & < & \frac{25}{34} \end{eqnarray*} @@ -74,82 +74,78 @@ Sujet numéro 3 \hspace{-1cm} \begin{center} % - $\dfrac{10}{3} = \dfrac{\ldots}{9}$ + $\dfrac{9}{6} = \dfrac{\ldots}{18}$ \hfill % - $\dfrac{9}{4} = \dfrac{\ldots}{20}$ + $\dfrac{7}{6} = \dfrac{\ldots}{48}$ \hfill % - $\dfrac{\cdots}{8} = \dfrac{8}{4}$ + $\dfrac{\cdots}{48} = \dfrac{5}{6}$ \hfill % - $\dfrac{10}{9} = \dfrac{20}{\cdots}$ + $\dfrac{4}{3} = \dfrac{32}{\cdots}$ \end{center} \item Faire les calculs suivants en détaillant les étapes (penser à simplifier les fractions quand c'est possible). \begin{enumerate} - \item $A = \frac{ 3 }{ 4 } + \frac{ 3 }{ 4 }$ + \item $A = \frac{ 10 }{ 2 } + \frac{ 8 }{ 2 }$ \begin{solution} \begin{eqnarray*} - A & = & \frac{ 3 }{ 4 } + \frac{ 3 }{ 4 } \\ -A & = & \frac{ 3 + 3 }{ 4 } \\ -A & = & \frac{ 6 }{ 4 } \\ -A & = & \frac{ 3 \times 2 }{ 2 \times 2 } \\ -A & = & \frac{ 3 }{ 2 } + A & = & \frac{ 10 }{ 2 } + \frac{ 8 }{ 2 } \\ +A & = & \frac{ 10 + 8 }{ 2 } \\ +A & = & 9 \end{eqnarray*} \end{solution} - \item $B = \frac{ 1 }{ 9 } + \frac{ -1 }{ 9 }$ + \item $B = \frac{ 6 }{ 7 } + \frac{ -5 }{ 7 }$ \begin{solution} \begin{eqnarray*} - B & = & \frac{ 1 }{ 9 } + \frac{ -1 }{ 9 } \\ -B & = & \frac{ 1 - 1 }{ 9 } \\ -B & = & 0 + B & = & \frac{ 6 }{ 7 } + \frac{ -5 }{ 7 } \\ +B & = & \frac{ 6 - 5 }{ 7 } \\ +B & = & \frac{ 1 }{ 7 } \end{eqnarray*} \end{solution} - \item $C = \frac{ 2 }{ 3 } + \frac{ 6 }{ 6 }$ + \item $C = \frac{ 1 }{ 7 } + \frac{ 8 }{ 63 }$ \begin{solution} \begin{eqnarray*} - C & = & \frac{ 2 }{ 3 } + \frac{ 6 }{ 6 } \\ -C & = & \frac{ 2 \times 2 }{ 3 \times 2 } + \frac{ 6 \times 1 }{ 6 \times 1 } \\ -C & = & \frac{ 4 }{ 6 } + \frac{ 6 }{ 6 } \\ -C & = & \frac{ 4 + 6 }{ 6 } \\ -C & = & \frac{ 10 }{ 6 } \\ -C & = & \frac{ 5 \times 2 }{ 3 \times 2 } \\ -C & = & \frac{ 5 }{ 3 } + C & = & \frac{ 1 }{ 7 } + \frac{ 8 }{ 63 } \\ +C & = & \frac{ 1 \times 9 }{ 7 \times 9 } + \frac{ 8 \times 1 }{ 63 \times 1 } \\ +C & = & \frac{ 9 }{ 63 } + \frac{ 8 }{ 63 } \\ +C & = & \frac{ 9 + 8 }{ 63 } \\ +C & = & \frac{ 17 }{ 63 } \end{eqnarray*} \end{solution} - \item $D = \frac{ -8 }{ 10 } + \frac{ -2 }{ 70 }$ + \item $D = \frac{ 3 }{ 2 } + \frac{ -3 }{ 16 }$ \begin{solution} \begin{eqnarray*} - D & = & \frac{ -8 }{ 10 } + \frac{ -2 }{ 70 } \\ -D & = & \frac{ -8 \times 7 }{ 10 \times 7 } + \frac{ -2 \times 1 }{ 70 \times 1 } \\ -D & = & \frac{ -56 }{ 70 } + \frac{ -2 }{ 70 } \\ -D & = & \frac{ -56 - 2 }{ 70 } \\ -D & = & \frac{ -58 }{ 70 } \\ -D & = & \frac{ -29 \times 2 }{ 35 \times 2 } \\ -D & = & \frac{ -29 }{ 35 } + D & = & \frac{ 3 }{ 2 } + \frac{ -3 }{ 16 } \\ +D & = & \frac{ 3 \times 8 }{ 2 \times 8 } + \frac{ -3 \times 1 }{ 16 \times 1 } \\ +D & = & \frac{ 24 }{ 16 } + \frac{ -3 }{ 16 } \\ +D & = & \frac{ 24 - 3 }{ 16 } \\ +D & = & \frac{ 21 }{ 16 } \end{eqnarray*} \end{solution} - \item $E = \frac{ 5 }{ 3 } \times 8$ + \item $E = \frac{ 4 }{ 5 } \times 6$ \begin{solution} \begin{eqnarray*} - E & = & \frac{ 5 }{ 3 } \times 8 \\ -E & = & \frac{ 5 \times 8 }{ 3 } \\ -E & = & \frac{ 40 }{ 3 } + E & = & \frac{ 4 }{ 5 } \times 6 \\ +E & = & \frac{ 4 \times 6 }{ 5 } \\ +E & = & \frac{ 24 }{ 5 } \end{eqnarray*} \end{solution} - \item $F = \frac{ 6 }{ 6 } \times \frac{ 9 }{ 4 }$ + \item $F = \frac{ 3 }{ 7 } \times \frac{ 9 }{ 8 }$ \begin{solution} \begin{eqnarray*} - F & = & \frac{ 6 }{ 6 } \times \frac{ 9 }{ 4 } \\ -F & = & \frac{ 9 }{ 4 } + F & = & \frac{ 3 }{ 7 } \times \frac{ 9 }{ 8 } \\ +F & = & \frac{ 9 }{ 8 } \times \frac{ 3 }{ 7 } \\ +F & = & \frac{ 9 \times 3 }{ 8 \times 7 } \\ +F & = & \frac{ 27 }{ 56 } \end{eqnarray*} \end{solution} \end{enumerate} @@ -160,11 +156,11 @@ F & = & \frac{ 9 }{ 4 } \section{Exercice} -Dans la figure suivante, $(AB)$ et $(CD)$ sont parallèles, $AO = 12$, $OD = 14$, $CD = 15$ et $OB = 14$. +Dans la figure suivante, $(AB)$ et $(CD)$ sont parallèles, $AO = 8$, $OD = 15$, $CD = 2$ et $OB = 18$. -\includegraphics[scale=0.4]{thales2} +\includegraphics[scale=0.4]{thales1} Calculer les longueurs $OC$ et $AB$. @@ -179,20 +175,20 @@ Calculer les longueurs $OC$ et $AB$. \begin{tabular}{|c|*{3}{c|}} \hline - Triangle $OAB$ & $AO = 12$ & $OB = 14$ & $AB $ \\ + Triangle $OAB$ & $AO = 8$ & $OB = 18$ & $AB $ \\ \hline - Triangle $OCD$ & $DO = 14$ & $OC $ & $CD = 15$ \\ + Triangle $OCD$ & $DO = 15$ & $OC $ & $CD = 2$ \\ \hline \end{tabular} est un tableau de proportionnalité. On en déduit que \begin{eqnarray*} - OC & = & \frac{DO \times OB}{AO} = \frac{14 \times 14}{12} = 16.333333333333336 + OC & = & \frac{DO \times OB}{AO} = \frac{15 \times 18}{8} = 33.75 \end{eqnarray*} Et que \begin{eqnarray*} - AB & = & \frac{CD \times AO}{DO} = \frac{15 \times 12}{14} = 12.857142857142856 + AB & = & \frac{CD \times AO}{DO} = \frac{2 \times 8}{15} = 1.0666666666666667 \end{eqnarray*} \end{solution} diff --git a/documentation/source/_downloads/1_DM.tex b/documentation/source/_downloads/02_DM.tex similarity index 59% rename from documentation/source/_downloads/1_DM.tex rename to documentation/source/_downloads/02_DM.tex index 339d4c0..fa46ea5 100644 --- a/documentation/source/_downloads/1_DM.tex +++ b/documentation/source/_downloads/02_DM.tex @@ -33,33 +33,33 @@ \maketitle -Sujet numéro 1 +Sujet numéro 02 \section{Exercice} - Dans un sac, il y a 18 bonbons à la menthe, 45 bonbons à la fraise et 8 au chocolat. On choisit un bonbon au hasard dans ce sac. + Dans un sac, il y a 10 bonbons à la menthe, 15 bonbons à la fraise et 6 au chocolat. On choisit un bonbon au hasard dans ce sac. \begin{enumerate} \item Calculer la probabilité de tirer un bonbon à la fraise. \begin{solution} - $T($ tirer un bonbon à la fraise $) = \dfrac{18}{71}$ + $T($ tirer un bonbon à la fraise $) = \dfrac{10}{31}$ \end{solution} \item Calculer la probabilité de tirer un bonbon qui n'est pas au chocolat. \begin{solution} - $T($ tirer un bonbon à la fraise ou à la menthe $) = \dfrac{63}{71}$ + $T($ tirer un bonbon à la fraise ou à la menthe $) = \dfrac{25}{31}$ \end{solution} \item Calculer la probabilité de tirer un bonbon au réglisse. \begin{solution} - $T($ tirer un bonbon au réglisse $) = \dfrac{0}{71} = 0$ + $T($ tirer un bonbon au réglisse $) = \dfrac{0}{31} = 0$ \end{solution} \item Dans un autre sac, on place 25 bonbons à la menthe et 34 bonbons à la fraise. Lise préfère les bonbons à la menthe. Dans quel sac doit-elle tirer un bonbon pour avoir le plus de chance d'avoir un bonbon qu'elle préfère? \begin{solution} Elle prefera tirer dans le deuxième sac car \begin{eqnarray*} - \frac{18}{71} & < & \frac{25}{34} + \frac{10}{31} & < & \frac{25}{34} \end{eqnarray*} @@ -74,83 +74,84 @@ Sujet numéro 1 \hspace{-1cm} \begin{center} % - $\dfrac{7}{3} = \dfrac{\ldots}{27}$ + $\dfrac{6}{2} = \dfrac{\ldots}{10}$ \hfill % - $\dfrac{10}{3} = \dfrac{\ldots}{30}$ + $\dfrac{5}{6} = \dfrac{\ldots}{60}$ \hfill % - $\dfrac{\cdots}{50} = \dfrac{3}{5}$ + $\dfrac{\cdots}{45} = \dfrac{3}{5}$ \hfill % - $\dfrac{9}{2} = \dfrac{18}{\cdots}$ + $\dfrac{3}{6} = \dfrac{18}{\cdots}$ \end{center} \item Faire les calculs suivants en détaillant les étapes (penser à simplifier les fractions quand c'est possible). \begin{enumerate} - \item $A = \frac{ 2 }{ 6 } + \frac{ 6 }{ 6 }$ + \item $A = \frac{ 2 }{ 3 } + \frac{ 7 }{ 3 }$ \begin{solution} \begin{eqnarray*} - A & = & \frac{ 2 }{ 6 } + \frac{ 6 }{ 6 } \\ -A & = & \frac{ 2 + 6 }{ 6 } \\ -A & = & \frac{ 8 }{ 6 } \\ -A & = & \frac{ 4 \times 2 }{ 3 \times 2 } \\ -A & = & \frac{ 4 }{ 3 } + A & = & \frac{ 2 }{ 3 } + \frac{ 7 }{ 3 } \\ +A & = & \frac{ 2 + 7 }{ 3 } \\ +A & = & 3 \end{eqnarray*} \end{solution} - \item $B = \frac{ 8 }{ 2 } + \frac{ 2 }{ 2 }$ + \item $B = \frac{ 3 }{ 10 } + \frac{ 10 }{ 10 }$ \begin{solution} \begin{eqnarray*} - B & = & \frac{ 8 }{ 2 } + \frac{ 2 }{ 2 } \\ -B & = & \frac{ 8 + 2 }{ 2 } \\ -B & = & 5 + B & = & \frac{ 3 }{ 10 } + \frac{ 10 }{ 10 } \\ +B & = & \frac{ 3 + 10 }{ 10 } \\ +B & = & \frac{ 13 }{ 10 } \end{eqnarray*} \end{solution} - \item $C = \frac{ 10 }{ 7 } + \frac{ 8 }{ 35 }$ + \item $C = \frac{ -10 }{ 6 } + \frac{ 4 }{ 12 }$ \begin{solution} \begin{eqnarray*} - C & = & \frac{ 10 }{ 7 } + \frac{ 8 }{ 35 } \\ -C & = & \frac{ 10 \times 5 }{ 7 \times 5 } + \frac{ 8 \times 1 }{ 35 \times 1 } \\ -C & = & \frac{ 50 }{ 35 } + \frac{ 8 }{ 35 } \\ -C & = & \frac{ 50 + 8 }{ 35 } \\ -C & = & \frac{ 58 }{ 35 } + C & = & \frac{ -10 }{ 6 } + \frac{ 4 }{ 12 } \\ +C & = & \frac{ -10 \times 2 }{ 6 \times 2 } + \frac{ 4 \times 1 }{ 12 \times 1 } \\ +C & = & \frac{ -20 }{ 12 } + \frac{ 4 }{ 12 } \\ +C & = & \frac{ -20 + 4 }{ 12 } \\ +C & = & \frac{ -16 }{ 12 } \\ +C & = & \frac{ -4 \times 4 }{ 3 \times 4 } \\ +C & = & \frac{ -4 }{ 3 } \end{eqnarray*} \end{solution} - \item $D = \frac{ -8 }{ 4 } + \frac{ -1 }{ 40 }$ + \item $D = \frac{ 10 }{ 6 } + \frac{ -8 }{ 42 }$ \begin{solution} \begin{eqnarray*} - D & = & \frac{ -8 }{ 4 } + \frac{ -1 }{ 40 } \\ -D & = & \frac{ -8 \times 10 }{ 4 \times 10 } + \frac{ -1 \times 1 }{ 40 \times 1 } \\ -D & = & \frac{ -80 }{ 40 } + \frac{ -1 }{ 40 } \\ -D & = & \frac{ -80 - 1 }{ 40 } \\ -D & = & \frac{ -81 }{ 40 } + D & = & \frac{ 10 }{ 6 } + \frac{ -8 }{ 42 } \\ +D & = & \frac{ 10 \times 7 }{ 6 \times 7 } + \frac{ -8 \times 1 }{ 42 \times 1 } \\ +D & = & \frac{ 70 }{ 42 } + \frac{ -8 }{ 42 } \\ +D & = & \frac{ 70 - 8 }{ 42 } \\ +D & = & \frac{ 62 }{ 42 } \\ +D & = & \frac{ 31 \times 2 }{ 21 \times 2 } \\ +D & = & \frac{ 31 }{ 21 } \end{eqnarray*} \end{solution} - \item $E = \frac{ 9 }{ 5 } \times 4$ + \item $E = \frac{ 6 }{ 9 } \times 4$ \begin{solution} \begin{eqnarray*} - E & = & \frac{ 9 }{ 5 } \times 4 \\ -E & = & \frac{ 9 \times 4 }{ 5 } \\ -E & = & \frac{ 36 }{ 5 } + E & = & \frac{ 6 }{ 9 } \times 4 \\ +E & = & \frac{ 6 \times 4 }{ 9 } \\ +E & = & \frac{ 24 }{ 9 } \\ +E & = & \frac{ 8 \times 3 }{ 3 \times 3 } \\ +E & = & \frac{ 8 }{ 3 } \end{eqnarray*} \end{solution} - \item $F = \frac{ 6 }{ 2 } \times \frac{ 7 }{ 9 }$ + \item $F = \frac{ 9 }{ 2 } \times \frac{ 9 }{ 5 }$ \begin{solution} \begin{eqnarray*} - F & = & \frac{ 6 }{ 2 } \times \frac{ 7 }{ 9 } \\ -F & = & \frac{ 7 }{ 9 } \times \frac{ 6 }{ 2 } \\ -F & = & \frac{ 7 \times 2 \times 3 }{ 3 \times 3 \times 2 } \\ -F & = & \frac{ 7 \times 6 }{ 9 \times 2 } \\ -F & = & \frac{ 42 }{ 18 } \\ -F & = & \frac{ 7 \times 6 }{ 3 \times 6 } \\ -F & = & \frac{ 7 }{ 3 } + F & = & \frac{ 9 }{ 2 } \times \frac{ 9 }{ 5 } \\ +F & = & \frac{ 9 }{ 5 } \times \frac{ 9 }{ 2 } \\ +F & = & \frac{ 9 \times 9 }{ 5 \times 2 } \\ +F & = & \frac{ 81 }{ 10 } \end{eqnarray*} \end{solution} \end{enumerate} @@ -161,11 +162,11 @@ F & = & \frac{ 7 }{ 3 } \section{Exercice} -Dans la figure suivante, $(AB)$ et $(CD)$ sont parallèles, $AO = 4$, $OD = 16$, $CD = 1$ et $OB = 7$. +Dans la figure suivante, $(AB)$ et $(CD)$ sont parallèles, $AO = 11$, $OD = 18$, $CD = 6$ et $OB = 14$. -\includegraphics[scale=0.4]{thales2} +\includegraphics[scale=0.4]{thales1} Calculer les longueurs $OC$ et $AB$. @@ -180,20 +181,20 @@ Calculer les longueurs $OC$ et $AB$. \begin{tabular}{|c|*{3}{c|}} \hline - Triangle $OAB$ & $AO = 4$ & $OB = 7$ & $AB $ \\ + Triangle $OAB$ & $AO = 11$ & $OB = 14$ & $AB $ \\ \hline - Triangle $OCD$ & $DO = 16$ & $OC $ & $CD = 1$ \\ + Triangle $OCD$ & $DO = 18$ & $OC $ & $CD = 6$ \\ \hline \end{tabular} est un tableau de proportionnalité. On en déduit que \begin{eqnarray*} - OC & = & \frac{DO \times OB}{AO} = \frac{16 \times 7}{4} = 28.0 + OC & = & \frac{DO \times OB}{AO} = \frac{18 \times 14}{11} = 22.90909090909091 \end{eqnarray*} Et que \begin{eqnarray*} - AB & = & \frac{CD \times AO}{DO} = \frac{1 \times 4}{16} = 0.25 + AB & = & \frac{CD \times AO}{DO} = \frac{6 \times 11}{18} = 3.666666666666667 \end{eqnarray*} \end{solution} diff --git a/documentation/source/_downloads/2_DM.tex b/documentation/source/_downloads/03_DM.tex similarity index 58% rename from documentation/source/_downloads/2_DM.tex rename to documentation/source/_downloads/03_DM.tex index 8924cbf..f6f4ff4 100644 --- a/documentation/source/_downloads/2_DM.tex +++ b/documentation/source/_downloads/03_DM.tex @@ -33,33 +33,33 @@ \maketitle -Sujet numéro 2 +Sujet numéro 03 \section{Exercice} - Dans un sac, il y a 40 bonbons à la menthe, 80 bonbons à la fraise et 5 au chocolat. On choisit un bonbon au hasard dans ce sac. + Dans un sac, il y a 56 bonbons à la menthe, 70 bonbons à la fraise et 6 au chocolat. On choisit un bonbon au hasard dans ce sac. \begin{enumerate} \item Calculer la probabilité de tirer un bonbon à la fraise. \begin{solution} - $T($ tirer un bonbon à la fraise $) = \dfrac{40}{125}$ + $T($ tirer un bonbon à la fraise $) = \dfrac{56}{132}$ \end{solution} \item Calculer la probabilité de tirer un bonbon qui n'est pas au chocolat. \begin{solution} - $T($ tirer un bonbon à la fraise ou à la menthe $) = \dfrac{120}{125}$ + $T($ tirer un bonbon à la fraise ou à la menthe $) = \dfrac{126}{132}$ \end{solution} \item Calculer la probabilité de tirer un bonbon au réglisse. \begin{solution} - $T($ tirer un bonbon au réglisse $) = \dfrac{0}{125} = 0$ + $T($ tirer un bonbon au réglisse $) = \dfrac{0}{132} = 0$ \end{solution} \item Dans un autre sac, on place 25 bonbons à la menthe et 34 bonbons à la fraise. Lise préfère les bonbons à la menthe. Dans quel sac doit-elle tirer un bonbon pour avoir le plus de chance d'avoir un bonbon qu'elle préfère? \begin{solution} Elle prefera tirer dans le deuxième sac car \begin{eqnarray*} - \frac{40}{125} & < & \frac{25}{34} + \frac{56}{132} & < & \frac{25}{34} \end{eqnarray*} @@ -74,82 +74,88 @@ Sujet numéro 2 \hspace{-1cm} \begin{center} % - $\dfrac{3}{6} = \dfrac{\ldots}{42}$ + $\dfrac{8}{9} = \dfrac{\ldots}{72}$ \hfill % - $\dfrac{10}{7} = \dfrac{\ldots}{14}$ + $\dfrac{6}{3} = \dfrac{\ldots}{30}$ \hfill % - $\dfrac{\cdots}{32} = \dfrac{10}{8}$ + $\dfrac{\cdots}{6} = \dfrac{7}{2}$ \hfill % - $\dfrac{5}{10} = \dfrac{40}{\cdots}$ + $\dfrac{7}{8} = \dfrac{49}{\cdots}$ \end{center} \item Faire les calculs suivants en détaillant les étapes (penser à simplifier les fractions quand c'est possible). \begin{enumerate} - \item $A = \frac{ 5 }{ 5 } + \frac{ 8 }{ 5 }$ + \item $A = \frac{ 2 }{ 10 } + \frac{ 2 }{ 10 }$ \begin{solution} \begin{eqnarray*} - A & = & \frac{ 5 }{ 5 } + \frac{ 8 }{ 5 } \\ -A & = & \frac{ 5 + 8 }{ 5 } \\ -A & = & \frac{ 13 }{ 5 } + A & = & \frac{ 2 }{ 10 } + \frac{ 2 }{ 10 } \\ +A & = & \frac{ 2 + 2 }{ 10 } \\ +A & = & \frac{ 4 }{ 10 } \\ +A & = & \frac{ 2 \times 2 }{ 5 \times 2 } \\ +A & = & \frac{ 2 }{ 5 } \end{eqnarray*} \end{solution} - \item $B = \frac{ -6 }{ 5 } + \frac{ -2 }{ 5 }$ + \item $B = \frac{ -5 }{ 4 } + \frac{ -2 }{ 4 }$ \begin{solution} \begin{eqnarray*} - B & = & \frac{ -6 }{ 5 } + \frac{ -2 }{ 5 } \\ -B & = & \frac{ -6 - 2 }{ 5 } \\ -B & = & \frac{ -8 }{ 5 } + B & = & \frac{ -5 }{ 4 } + \frac{ -2 }{ 4 } \\ +B & = & \frac{ -5 - 2 }{ 4 } \\ +B & = & \frac{ -7 }{ 4 } \end{eqnarray*} \end{solution} - \item $C = \frac{ 9 }{ 8 } + \frac{ 5 }{ 80 }$ + \item $C = \frac{ -8 }{ 2 } + \frac{ 10 }{ 16 }$ \begin{solution} \begin{eqnarray*} - C & = & \frac{ 9 }{ 8 } + \frac{ 5 }{ 80 } \\ -C & = & \frac{ 9 \times 10 }{ 8 \times 10 } + \frac{ 5 \times 1 }{ 80 \times 1 } \\ -C & = & \frac{ 90 }{ 80 } + \frac{ 5 }{ 80 } \\ -C & = & \frac{ 90 + 5 }{ 80 } \\ -C & = & \frac{ 95 }{ 80 } \\ -C & = & \frac{ 19 \times 5 }{ 16 \times 5 } \\ -C & = & \frac{ 19 }{ 16 } + C & = & \frac{ -8 }{ 2 } + \frac{ 10 }{ 16 } \\ +C & = & \frac{ -8 \times 8 }{ 2 \times 8 } + \frac{ 10 \times 1 }{ 16 \times 1 } \\ +C & = & \frac{ -64 }{ 16 } + \frac{ 10 }{ 16 } \\ +C & = & \frac{ -64 + 10 }{ 16 } \\ +C & = & \frac{ -54 }{ 16 } \\ +C & = & \frac{ -27 \times 2 }{ 8 \times 2 } \\ +C & = & \frac{ -27 }{ 8 } \end{eqnarray*} \end{solution} - \item $D = \frac{ 6 }{ 6 } + \frac{ -10 }{ 30 }$ + \item $D = \frac{ -9 }{ 2 } + \frac{ -4 }{ 14 }$ \begin{solution} \begin{eqnarray*} - D & = & \frac{ 6 }{ 6 } + \frac{ -10 }{ 30 } \\ -D & = & \frac{ 6 \times 5 }{ 6 \times 5 } + \frac{ -10 \times 1 }{ 30 \times 1 } \\ -D & = & \frac{ 30 }{ 30 } + \frac{ -10 }{ 30 } \\ -D & = & \frac{ 30 - 10 }{ 30 } \\ -D & = & \frac{ 20 }{ 30 } \\ -D & = & \frac{ 2 \times 10 }{ 3 \times 10 } \\ -D & = & \frac{ 2 }{ 3 } + D & = & \frac{ -9 }{ 2 } + \frac{ -4 }{ 14 } \\ +D & = & \frac{ -9 \times 7 }{ 2 \times 7 } + \frac{ -4 \times 1 }{ 14 \times 1 } \\ +D & = & \frac{ -63 }{ 14 } + \frac{ -4 }{ 14 } \\ +D & = & \frac{ -63 - 4 }{ 14 } \\ +D & = & \frac{ -67 }{ 14 } \end{eqnarray*} \end{solution} - \item $E = \frac{ 6 }{ 6 } \times 5$ + \item $E = \frac{ 5 }{ 8 } \times 4$ \begin{solution} \begin{eqnarray*} - E & = & \frac{ 6 }{ 6 } \times 5 \\ -E & = & \frac{ 6 \times 5 }{ 6 } \\ -E & = & 5 + E & = & \frac{ 5 }{ 8 } \times 4 \\ +E & = & \frac{ 5 \times 1 \times 4 }{ 2 \times 4 } \\ +E & = & \frac{ 5 \times 4 }{ 8 } \\ +E & = & \frac{ 20 }{ 8 } \\ +E & = & \frac{ 5 \times 4 }{ 2 \times 4 } \\ +E & = & \frac{ 5 }{ 2 } \end{eqnarray*} \end{solution} - \item $F = \frac{ 5 }{ 8 } \times \frac{ 3 }{ 2 }$ + \item $F = \frac{ 6 }{ 7 } \times \frac{ 3 }{ 8 }$ \begin{solution} \begin{eqnarray*} - F & = & \frac{ 5 }{ 8 } \times \frac{ 3 }{ 2 } \\ -F & = & \frac{ 3 }{ 2 } \times \frac{ 5 }{ 8 } \\ -F & = & \frac{ 3 \times 5 }{ 2 \times 8 } \\ -F & = & \frac{ 15 }{ 16 } + F & = & \frac{ 6 }{ 7 } \times \frac{ 3 }{ 8 } \\ +F & = & \frac{ 3 }{ 8 } \times \frac{ 6 }{ 7 } \\ +F & = & \frac{ 3 \times 3 \times 2 }{ 4 \times 2 \times 7 } \\ +F & = & \frac{ 3 \times 6 }{ 8 \times 7 } \\ +F & = & \frac{ 18 }{ 56 } \\ +F & = & \frac{ 9 \times 2 }{ 28 \times 2 } \\ +F & = & \frac{ 9 }{ 28 } \end{eqnarray*} \end{solution} \end{enumerate} @@ -160,7 +166,7 @@ F & = & \frac{ 15 }{ 16 } \section{Exercice} -Dans la figure suivante, $(AB)$ et $(CD)$ sont parallèles, $AO = 2$, $OD = 6$, $CD = 20$ et $OB = 14$. +Dans la figure suivante, $(AB)$ et $(CD)$ sont parallèles, $AO = 3$, $OD = 7$, $CD = 5$ et $OB = 2$. @@ -179,20 +185,20 @@ Calculer les longueurs $OC$ et $AB$. \begin{tabular}{|c|*{3}{c|}} \hline - Triangle $OAB$ & $AO = 2$ & $OB = 14$ & $AB $ \\ + Triangle $OAB$ & $AO = 3$ & $OB = 2$ & $AB $ \\ \hline - Triangle $OCD$ & $DO = 6$ & $OC $ & $CD = 20$ \\ + Triangle $OCD$ & $DO = 7$ & $OC $ & $CD = 5$ \\ \hline \end{tabular} est un tableau de proportionnalité. On en déduit que \begin{eqnarray*} - OC & = & \frac{DO \times OB}{AO} = \frac{6 \times 14}{2} = 42.0 + OC & = & \frac{DO \times OB}{AO} = \frac{7 \times 2}{3} = 4.666666666666666 \end{eqnarray*} Et que \begin{eqnarray*} - AB & = & \frac{CD \times AO}{DO} = \frac{20 \times 2}{6} = 6.666666666666666 + AB & = & \frac{CD \times AO}{DO} = \frac{5 \times 3}{7} = 2.142857142857143 \end{eqnarray*} \end{solution} diff --git a/documentation/source/_downloads/all_DM.pdf b/documentation/source/_downloads/all_DM.pdf index 44f569b1aa5262f8cae56bba2fd54371b724df6f..931c649c045beda8451f81e934f2c71ce4e8c245 100644 GIT binary patch delta 44036 zcmeFYRZyL6x~+}72X}XOcXxM5aCd?;aSJ|iw?J@r4;I|r-Q6L;Px|YxclTQB-&K1b z@3UvldW)i7iZP!18uwV4f$m;`Mx{^|mtcLpFhRRW+Tl%4tGe}#!7xHzCqP zGtKPX?BT|;3ECvHSKchSv(uGvx1I_;r_F!_4y;^3B$Z&f z##i4p<*v?owlG?*<1&_ha%g3PZM8osYA0D4Cw+V^mB;~9l=}1zbpsf@Pxe~n$1SHt z)qfFDOVJVB`gV?=@brugC8Ad6qACm(c&)@m)r1SCNl!$d@w*c{3rvZa3LVUqmqe!f 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fichiers sources: + +- :download:`01_DM.tex <_downloads/01_DM.tex>` +- :download:`02_DM.tex <_downloads/02_DM.tex>` +- :download:`03_DM.tex <_downloads/03_DM.tex>` + +et les fichiers compilés ont été concaténés dans le fichier :download:`all_DM.pdf <_downloads/all_DM.pdf>`. + + +Pour obtenir la correction, on le demande poliement à Opytex + + .. code-block:: bash + + opytex -t tpl_DM.tex --only-corr + +Ce qui a pour effet de décommenter la ligne avec *\printanswers*, de recompiler les documents puis de les concatener dans :download:`corr_DM.pdf <_downloads/corr_DM.pdf>` sans regénérer de nouveaux sujets. + +Il est possible aussi de créer les sujets et les corrections en même temps avec + + .. code-block:: bash + + opytex -t tpl_DM.tex -c -N 60 +