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100644 index 0000000..dbcde5a --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/01_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill ABOUHAFS Yasmine} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{9}{5} + \dfrac{8}{5}$ + \item $\dfrac{2}{9} + 3$ + + \item $\dfrac{4}{5} + \dfrac{10}{25}$ + \item $\dfrac{6}{3} + \dfrac{10}{7}$ + + \item $\dfrac{3}{8} \times 2$ + \item $\dfrac{1}{2} \times \dfrac{9}{2}$ + + \item $\dfrac{- 2}{7} \times \dfrac{- 8}{70}$ + \item $\dfrac{\dfrac{1}{4}}{\dfrac{9}{7}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{9}{5} + \dfrac{8}{5}=\dfrac{9 + 8}{5}=\dfrac{17}{5} = \dfrac{17}{5}$ + \item $\dfrac{2}{9} + 3=\dfrac{2}{9} + \dfrac{3}{1}=\dfrac{2}{9} + \dfrac{3 \times 9}{1 \times 9}=\dfrac{2}{9} + \dfrac{27}{9}=\dfrac{2 + 27}{9}=\dfrac{29}{9} = \dfrac{29}{9}$ + \item $\dfrac{4}{5} + \dfrac{10}{25}=\dfrac{4 \times 5}{5 \times 5} + \dfrac{10}{25}=\dfrac{20}{25} + \dfrac{10}{25}=\dfrac{20 + 10}{25}=\dfrac{30}{25} = \dfrac{6}{5}$ + \item $\dfrac{6}{3} + \dfrac{10}{7}=\dfrac{6 \times 7}{3 \times 7} + \dfrac{10 \times 3}{7 \times 3}=\dfrac{42}{21} + \dfrac{30}{21}=\dfrac{42 + 30}{21}=\dfrac{72}{21} = \dfrac{24}{7}$ + + \item $\dfrac{3}{8} \times 2=\dfrac{3 \times 2}{8}=\dfrac{6}{8} = \dfrac{3}{4}$ + \item $\dfrac{1}{2} \times \dfrac{9}{2}=\dfrac{1 \times 9}{2 \times 2}=\dfrac{9}{4} = \dfrac{9}{4}$ + \item $\dfrac{- 2}{7} \times \dfrac{- 8}{70}=\dfrac{- 2(- 8)}{7 \times 70}=\dfrac{16}{490} = \dfrac{8}{245}$ + \item $\dfrac{\dfrac{1}{4}}{\dfrac{9}{7}}=\dfrac{1}{4} \times \dfrac{7}{9}=\dfrac{1 \times 7}{4 \times 9}=\dfrac{7}{36} = \dfrac{7}{36}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 54 photos prises dont 25 ratées. + \item en juillet, il y a eu 39 photos réussies et 37 ratées. + \item en août, il y a eu 58 photos dont une proportion de 0.26 de photos ratées. + \item en septembre, il y a eu 9 photos ratées, ce qui correspondait à 15.52\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 29 & 39 & 43 & 49 & 160\\ + \hline + Ratées & 25 & 37 & 15 & 9 & 86\\ + \hline + Total & 54 & 76 & 58 & 58 & 246\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{160}{246} = 0.65 = 65\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{37 - 25}{25} = \frac{12}{25} = 0.48 = 48\% + \] + \item De juillet à août + \[ + \frac{15 - 37}{37} = \frac{-22}{37} = -0.59 = -59\% + \] + \item De août à septembre + \[ + \frac{9 - 15}{15} = \frac{-6}{15} = -0.4 = -40\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/02_DM1.tex b/2nd/Evaluations/DM_2021-09-27/02_DM1.tex new file mode 100644 index 0000000..c8d8c8a --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/02_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill AKEAZI Hafsa} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{2}{9} + \dfrac{2}{9}$ + \item $\dfrac{9}{6} + 9$ + + \item $\dfrac{9}{4} + \dfrac{8}{12}$ + \item $\dfrac{1}{7} + \dfrac{6}{8}$ + + \item $\dfrac{6}{10} \times 4$ + \item $\dfrac{3}{4} \times \dfrac{2}{4}$ + + \item $\dfrac{- 6}{10} \times \dfrac{6}{30}$ + \item $\dfrac{\dfrac{7}{3}}{\dfrac{4}{3}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{2}{9} + \dfrac{2}{9}=\dfrac{2 + 2}{9}=\dfrac{4}{9} = \dfrac{4}{9}$ + \item $\dfrac{9}{6} + 9=\dfrac{9}{6} + \dfrac{9}{1}=\dfrac{9}{6} + \dfrac{9 \times 6}{1 \times 6}=\dfrac{9}{6} + \dfrac{54}{6}=\dfrac{9 + 54}{6}=\dfrac{63}{6} = \dfrac{21}{2}$ + \item $\dfrac{9}{4} + \dfrac{8}{12}=\dfrac{9 \times 3}{4 \times 3} + \dfrac{8}{12}=\dfrac{27}{12} + \dfrac{8}{12}=\dfrac{27 + 8}{12}=\dfrac{35}{12} = \dfrac{35}{12}$ + \item $\dfrac{1}{7} + \dfrac{6}{8}=\dfrac{1 \times 8}{7 \times 8} + \dfrac{6 \times 7}{8 \times 7}=\dfrac{8}{56} + \dfrac{42}{56}=\dfrac{8 + 42}{56}=\dfrac{50}{56} = \dfrac{25}{28}$ + + \item $\dfrac{6}{10} \times 4=\dfrac{6 \times 4}{10}=\dfrac{24}{10} = \dfrac{12}{5}$ + \item $\dfrac{3}{4} \times \dfrac{2}{4}=\dfrac{3 \times 2}{4 \times 4}=\dfrac{6}{16} = \dfrac{3}{8}$ + \item $\dfrac{- 6}{10} \times \dfrac{6}{30}=\dfrac{- 6 \times 6}{10 \times 30}=\dfrac{- 36}{300} = \dfrac{- 3}{25}$ + \item $\dfrac{\dfrac{7}{3}}{\dfrac{4}{3}}=\dfrac{7}{3} \times \dfrac{3}{4}=\dfrac{7 \times 3}{3 \times 4}=\dfrac{21}{12} = \dfrac{7}{4}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 52 photos prises dont 25 ratées. + \item en juillet, il y a eu 49 photos réussies et 36 ratées. + \item en août, il y a eu 60 photos dont une proportion de 0.22 de photos ratées. + \item en septembre, il y a eu 5 photos ratées, ce qui correspondait à 9.62\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 27 & 49 & 47 & 47 & 170\\ + \hline + Ratées & 25 & 36 & 13 & 5 & 79\\ + \hline + Total & 52 & 85 & 60 & 52 & 249\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{170}{249} = 0.68 = 68\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{36 - 25}{25} = \frac{11}{25} = 0.44 = 44\% + \] + \item De juillet à août + \[ + \frac{13 - 36}{36} = \frac{-23}{36} = -0.64 = -63\% + \] + \item De août à septembre + \[ + \frac{5 - 13}{13} = \frac{-8}{13} = -0.62 = -61\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/03_DM1.tex b/2nd/Evaluations/DM_2021-09-27/03_DM1.tex new file mode 100644 index 0000000..3c58e0c --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/03_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill AZIZ Nihal} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{1}{10} + \dfrac{2}{10}$ + \item $\dfrac{4}{6} + 5$ + + \item $\dfrac{10}{3} + \dfrac{5}{27}$ + \item $\dfrac{1}{10} + \dfrac{2}{9}$ + + \item $\dfrac{5}{9} \times 9$ + \item $\dfrac{8}{7} \times \dfrac{9}{7}$ + + \item $\dfrac{- 6}{7} \times \dfrac{10}{28}$ + \item $\dfrac{\dfrac{1}{7}}{\dfrac{1}{9}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{1}{10} + \dfrac{2}{10}=\dfrac{1 + 2}{10}=\dfrac{3}{10} = \dfrac{3}{10}$ + \item $\dfrac{4}{6} + 5=\dfrac{4}{6} + \dfrac{5}{1}=\dfrac{4}{6} + \dfrac{5 \times 6}{1 \times 6}=\dfrac{4}{6} + \dfrac{30}{6}=\dfrac{4 + 30}{6}=\dfrac{34}{6} = \dfrac{17}{3}$ + \item $\dfrac{10}{3} + \dfrac{5}{27}=\dfrac{10 \times 9}{3 \times 9} + \dfrac{5}{27}=\dfrac{90}{27} + \dfrac{5}{27}=\dfrac{90 + 5}{27}=\dfrac{95}{27} = \dfrac{95}{27}$ + \item $\dfrac{1}{10} + \dfrac{2}{9}=\dfrac{1 \times 9}{10 \times 9} + \dfrac{2 \times 10}{9 \times 10}=\dfrac{9}{90} + \dfrac{20}{90}=\dfrac{9 + 20}{90}=\dfrac{29}{90} = \dfrac{29}{90}$ + + \item $\dfrac{5}{9} \times 9=\dfrac{5 \times 9}{9}=\dfrac{45}{9} = 5$ + \item $\dfrac{8}{7} \times \dfrac{9}{7}=\dfrac{8 \times 9}{7 \times 7}=\dfrac{72}{49} = \dfrac{72}{49}$ + \item $\dfrac{- 6}{7} \times \dfrac{10}{28}=\dfrac{- 6 \times 10}{7 \times 28}=\dfrac{- 60}{196} = \dfrac{- 15}{49}$ + \item $\dfrac{\dfrac{1}{7}}{\dfrac{1}{9}}=\dfrac{1}{7} \times \dfrac{9}{1}=\dfrac{1 \times 9}{7 \times 1}=\dfrac{9}{7} = \dfrac{9}{7}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 55 photos prises dont 27 ratées. + \item en juillet, il y a eu 35 photos réussies et 45 ratées. + \item en août, il y a eu 66 photos dont une proportion de 0.29 de photos ratées. + \item en septembre, il y a eu 10 photos ratées, ce qui correspondait à 19.61\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 28 & 35 & 47 & 41 & 151\\ + \hline + Ratées & 27 & 45 & 19 & 10 & 101\\ + \hline + Total & 55 & 80 & 66 & 51 & 252\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{151}{252} = 0.6 = 59\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{45 - 27}{27} = \frac{18}{27} = 0.67 = 66\% + \] + \item De juillet à août + \[ + \frac{19 - 45}{45} = \frac{-26}{45} = -0.58 = -57\% + \] + \item De août à septembre + \[ + \frac{10 - 19}{19} = \frac{-9}{19} = -0.47 = -47\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/04_DM1.tex b/2nd/Evaluations/DM_2021-09-27/04_DM1.tex new file mode 100644 index 0000000..2696e60 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/04_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill BARDOUSSE Yanis} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{10}{4} + \dfrac{10}{4}$ + \item $\dfrac{4}{5} + 7$ + + \item $\dfrac{8}{6} + \dfrac{2}{30}$ + \item $\dfrac{7}{2} + \dfrac{3}{2}$ + + \item $\dfrac{8}{2} \times 3$ + \item $\dfrac{1}{9} \times \dfrac{5}{9}$ + + \item $\dfrac{3}{9} \times \dfrac{1}{18}$ + \item $\dfrac{\dfrac{6}{7}}{\dfrac{4}{3}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{10}{4} + \dfrac{10}{4}=\dfrac{10 + 10}{4}=\dfrac{20}{4} = 5$ + \item $\dfrac{4}{5} + 7=\dfrac{4}{5} + \dfrac{7}{1}=\dfrac{4}{5} + \dfrac{7 \times 5}{1 \times 5}=\dfrac{4}{5} + \dfrac{35}{5}=\dfrac{4 + 35}{5}=\dfrac{39}{5} = \dfrac{39}{5}$ + \item $\dfrac{8}{6} + \dfrac{2}{30}=\dfrac{8 \times 5}{6 \times 5} + \dfrac{2}{30}=\dfrac{40}{30} + \dfrac{2}{30}=\dfrac{40 + 2}{30}=\dfrac{42}{30} = \dfrac{7}{5}$ + \item $\dfrac{7}{2} + \dfrac{3}{2}=\dfrac{7 + 3}{2}=\dfrac{10}{2} = 5$ + + \item $\dfrac{8}{2} \times 3=\dfrac{8 \times 3}{2}=\dfrac{24}{2} = 12$ + \item $\dfrac{1}{9} \times \dfrac{5}{9}=\dfrac{1 \times 5}{9 \times 9}=\dfrac{5}{81} = \dfrac{5}{81}$ + \item $\dfrac{3}{9} \times \dfrac{1}{18}=\dfrac{3 \times 1}{9 \times 18}=\dfrac{3}{162} = \dfrac{1}{54}$ + \item $\dfrac{\dfrac{6}{7}}{\dfrac{4}{3}}=\dfrac{6}{7} \times \dfrac{3}{4}=\dfrac{6 \times 3}{7 \times 4}=\dfrac{18}{28} = \dfrac{9}{14}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 42 photos prises dont 20 ratées. + \item en juillet, il y a eu 30 photos réussies et 36 ratées. + \item en août, il y a eu 57 photos dont une proportion de 0.21 de photos ratées. + \item en septembre, il y a eu 7 photos ratées, ce qui correspondait à 14.58\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 22 & 30 & 45 & 41 & 138\\ + \hline + Ratées & 20 & 36 & 12 & 7 & 75\\ + \hline + Total & 42 & 66 & 57 & 48 & 213\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{138}{213} = 0.65 = 64\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{36 - 20}{20} = \frac{16}{20} = 0.8 = 80\% + \] + \item De juillet à août + \[ + \frac{12 - 36}{36} = \frac{-24}{36} = -0.67 = -66\% + \] + \item De août à septembre + \[ + \frac{7 - 12}{12} = \frac{-5}{12} = -0.42 = -41\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/05_DM1.tex b/2nd/Evaluations/DM_2021-09-27/05_DM1.tex new file mode 100644 index 0000000..ccdee5f --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/05_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill BILLET Simon} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{9}{7} + \dfrac{4}{7}$ + \item $\dfrac{1}{3} + 7$ + + \item $\dfrac{9}{2} + \dfrac{4}{10}$ + \item $\dfrac{1}{6} + \dfrac{9}{10}$ + + \item $\dfrac{1}{7} \times 10$ + \item $\dfrac{10}{2} \times \dfrac{8}{2}$ + + \item $\dfrac{- 10}{2} \times \dfrac{- 4}{18}$ + \item $\dfrac{\dfrac{6}{3}}{\dfrac{4}{10}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{9}{7} + \dfrac{4}{7}=\dfrac{9 + 4}{7}=\dfrac{13}{7} = \dfrac{13}{7}$ + \item $\dfrac{1}{3} + 7=\dfrac{1}{3} + \dfrac{7}{1}=\dfrac{1}{3} + \dfrac{7 \times 3}{1 \times 3}=\dfrac{1}{3} + \dfrac{21}{3}=\dfrac{1 + 21}{3}=\dfrac{22}{3} = \dfrac{22}{3}$ + \item $\dfrac{9}{2} + \dfrac{4}{10}=\dfrac{9 \times 5}{2 \times 5} + \dfrac{4}{10}=\dfrac{45}{10} + \dfrac{4}{10}=\dfrac{45 + 4}{10}=\dfrac{49}{10} = \dfrac{49}{10}$ + \item $\dfrac{1}{6} + \dfrac{9}{10}=\dfrac{1 \times 5}{6 \times 5} + \dfrac{9 \times 3}{10 \times 3}=\dfrac{5}{30} + \dfrac{27}{30}=\dfrac{5 + 27}{30}=\dfrac{32}{30} = \dfrac{16}{15}$ + + \item $\dfrac{1}{7} \times 10=\dfrac{1 \times 10}{7}=\dfrac{10}{7} = \dfrac{10}{7}$ + \item $\dfrac{10}{2} \times \dfrac{8}{2}=\dfrac{10 \times 8}{2 \times 2}=\dfrac{80}{4} = 20$ + \item $\dfrac{- 10}{2} \times \dfrac{- 4}{18}=\dfrac{- 10(- 4)}{2 \times 18}=\dfrac{40}{36} = \dfrac{10}{9}$ + \item $\dfrac{\dfrac{6}{3}}{\dfrac{4}{10}}=\dfrac{6}{3} \times \dfrac{10}{4}=\dfrac{6 \times 10}{3 \times 4}=\dfrac{60}{12} = 5$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 42 photos prises dont 22 ratées. + \item en juillet, il y a eu 44 photos réussies et 32 ratées. + \item en août, il y a eu 54 photos dont une proportion de 0.26 de photos ratées. + \item en septembre, il y a eu 10 photos ratées, ce qui correspondait à 18.87\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 20 & 44 & 40 & 43 & 147\\ + \hline + Ratées & 22 & 32 & 14 & 10 & 78\\ + \hline + Total & 42 & 76 & 54 & 53 & 225\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{147}{225} = 0.65 = 65\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{32 - 22}{22} = \frac{10}{22} = 0.45 = 45\% + \] + \item De juillet à août + \[ + \frac{14 - 32}{32} = \frac{-18}{32} = -0.56 = -56\% + \] + \item De août à septembre + \[ + \frac{10 - 14}{14} = \frac{-4}{14} = -0.29 = -28\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/06_DM1.tex b/2nd/Evaluations/DM_2021-09-27/06_DM1.tex new file mode 100644 index 0000000..64e7d39 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/06_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill BOUAFIA Lina} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{1}{3} + \dfrac{9}{3}$ + \item $\dfrac{5}{2} + 2$ + + \item $\dfrac{10}{2} + \dfrac{6}{2}$ + \item $\dfrac{5}{6} + \dfrac{4}{9}$ + + \item $\dfrac{6}{8} \times 5$ + \item $\dfrac{5}{2} \times \dfrac{5}{2}$ + + \item $\dfrac{6}{2} \times \dfrac{- 4}{10}$ + \item $\dfrac{\dfrac{7}{9}}{\dfrac{7}{2}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{1}{3} + \dfrac{9}{3}=\dfrac{1 + 9}{3}=\dfrac{10}{3} = \dfrac{10}{3}$ + \item $\dfrac{5}{2} + 2=\dfrac{5}{2} + \dfrac{2}{1}=\dfrac{5}{2} + \dfrac{2 \times 2}{1 \times 2}=\dfrac{5}{2} + \dfrac{4}{2}=\dfrac{5 + 4}{2}=\dfrac{9}{2} = \dfrac{9}{2}$ + \item $\dfrac{10}{2} + \dfrac{6}{2}=\dfrac{10 + 6}{2}=\dfrac{16}{2} = 8$ + \item $\dfrac{5}{6} + \dfrac{4}{9}=\dfrac{5 \times 3}{6 \times 3} + \dfrac{4 \times 2}{9 \times 2}=\dfrac{15}{18} + \dfrac{8}{18}=\dfrac{15 + 8}{18}=\dfrac{23}{18} = \dfrac{23}{18}$ + + \item $\dfrac{6}{8} \times 5=\dfrac{6 \times 5}{8}=\dfrac{30}{8} = \dfrac{15}{4}$ + \item $\dfrac{5}{2} \times \dfrac{5}{2}=\dfrac{5 \times 5}{2 \times 2}=\dfrac{25}{4} = \dfrac{25}{4}$ + \item $\dfrac{6}{2} \times \dfrac{- 4}{10}=\dfrac{6(- 4)}{2 \times 10}=\dfrac{- 24}{20} = \dfrac{- 6}{5}$ + \item $\dfrac{\dfrac{7}{9}}{\dfrac{7}{2}}=\dfrac{7}{9} \times \dfrac{2}{7}=\dfrac{7 \times 2}{9 \times 7}=\dfrac{14}{63} = \dfrac{2}{9}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 51 photos prises dont 25 ratées. + \item en juillet, il y a eu 37 photos réussies et 32 ratées. + \item en août, il y a eu 65 photos dont une proportion de 0.26 de photos ratées. + \item en septembre, il y a eu 8 photos ratées, ce qui correspondait à 14.55\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 26 & 37 & 48 & 47 & 158\\ + \hline + Ratées & 25 & 32 & 17 & 8 & 82\\ + \hline + Total & 51 & 69 & 65 & 55 & 240\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{158}{240} = 0.66 = 65\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{32 - 25}{25} = \frac{7}{25} = 0.28 = 28\% + \] + \item De juillet à août + \[ + \frac{17 - 32}{32} = \frac{-15}{32} = -0.47 = -46\% + \] + \item De août à septembre + \[ + \frac{8 - 17}{17} = \frac{-9}{17} = -0.53 = -52\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/07_DM1.tex b/2nd/Evaluations/DM_2021-09-27/07_DM1.tex new file mode 100644 index 0000000..72dcadc --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/07_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill DESGLENE Anthony} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{4}{6} + \dfrac{1}{6}$ + \item $\dfrac{6}{7} + 6$ + + \item $\dfrac{5}{4} + \dfrac{6}{24}$ + \item $\dfrac{3}{6} + \dfrac{6}{8}$ + + \item $\dfrac{3}{7} \times 7$ + \item $\dfrac{8}{4} \times \dfrac{5}{4}$ + + \item $\dfrac{4}{10} \times \dfrac{- 5}{50}$ + \item $\dfrac{\dfrac{10}{9}}{\dfrac{5}{7}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{4}{6} + \dfrac{1}{6}=\dfrac{4 + 1}{6}=\dfrac{5}{6} = \dfrac{5}{6}$ + \item $\dfrac{6}{7} + 6=\dfrac{6}{7} + \dfrac{6}{1}=\dfrac{6}{7} + \dfrac{6 \times 7}{1 \times 7}=\dfrac{6}{7} + \dfrac{42}{7}=\dfrac{6 + 42}{7}=\dfrac{48}{7} = \dfrac{48}{7}$ + \item $\dfrac{5}{4} + \dfrac{6}{24}=\dfrac{5 \times 6}{4 \times 6} + \dfrac{6}{24}=\dfrac{30}{24} + \dfrac{6}{24}=\dfrac{30 + 6}{24}=\dfrac{36}{24} = \dfrac{3}{2}$ + \item $\dfrac{3}{6} + \dfrac{6}{8}=\dfrac{3 \times 4}{6 \times 4} + \dfrac{6 \times 3}{8 \times 3}=\dfrac{12}{24} + \dfrac{18}{24}=\dfrac{12 + 18}{24}=\dfrac{30}{24} = \dfrac{5}{4}$ + + \item $\dfrac{3}{7} \times 7=\dfrac{3 \times 7}{7}=\dfrac{21}{7} = 3$ + \item $\dfrac{8}{4} \times \dfrac{5}{4}=\dfrac{8 \times 5}{4 \times 4}=\dfrac{40}{16} = \dfrac{5}{2}$ + \item $\dfrac{4}{10} \times \dfrac{- 5}{50}=\dfrac{4(- 5)}{10 \times 50}=\dfrac{- 20}{500} = \dfrac{- 1}{25}$ + \item $\dfrac{\dfrac{10}{9}}{\dfrac{5}{7}}=\dfrac{10}{9} \times \dfrac{7}{5}=\dfrac{10 \times 7}{9 \times 5}=\dfrac{70}{45} = \dfrac{14}{9}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 50 photos prises dont 20 ratées. + \item en juillet, il y a eu 47 photos réussies et 44 ratées. + \item en août, il y a eu 53 photos dont une proportion de 0.25 de photos ratées. + \item en septembre, il y a eu 9 photos ratées, ce qui correspondait à 16.98\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 30 & 47 & 40 & 44 & 161\\ + \hline + Ratées & 20 & 44 & 13 & 9 & 86\\ + \hline + Total & 50 & 91 & 53 & 53 & 247\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{161}{247} = 0.65 = 65\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{44 - 20}{20} = \frac{24}{20} = 1.2 = 120\% + \] + \item De juillet à août + \[ + \frac{13 - 44}{44} = \frac{-31}{44} = -0.7 = -70\% + \] + \item De août à septembre + \[ + \frac{9 - 13}{13} = \frac{-4}{13} = -0.31 = -30\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/08_DM1.tex b/2nd/Evaluations/DM_2021-09-27/08_DM1.tex new file mode 100644 index 0000000..1f0ba0d --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/08_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill DROUOT Marine} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{3}{7} + \dfrac{3}{7}$ + \item $\dfrac{8}{3} + 9$ + + \item $\dfrac{1}{4} + \dfrac{3}{28}$ + \item $\dfrac{4}{7} + \dfrac{6}{2}$ + + \item $\dfrac{9}{4} \times 8$ + \item $\dfrac{5}{7} \times \dfrac{3}{7}$ + + \item $\dfrac{- 10}{8} \times \dfrac{- 2}{40}$ + \item $\dfrac{\dfrac{4}{9}}{\dfrac{6}{9}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{3}{7} + \dfrac{3}{7}=\dfrac{3 + 3}{7}=\dfrac{6}{7} = \dfrac{6}{7}$ + \item $\dfrac{8}{3} + 9=\dfrac{8}{3} + \dfrac{9}{1}=\dfrac{8}{3} + \dfrac{9 \times 3}{1 \times 3}=\dfrac{8}{3} + \dfrac{27}{3}=\dfrac{8 + 27}{3}=\dfrac{35}{3} = \dfrac{35}{3}$ + \item $\dfrac{1}{4} + \dfrac{3}{28}=\dfrac{1 \times 7}{4 \times 7} + \dfrac{3}{28}=\dfrac{7}{28} + \dfrac{3}{28}=\dfrac{7 + 3}{28}=\dfrac{10}{28} = \dfrac{5}{14}$ + \item $\dfrac{4}{7} + \dfrac{6}{2}=\dfrac{4 \times 2}{7 \times 2} + \dfrac{6 \times 7}{2 \times 7}=\dfrac{8}{14} + \dfrac{42}{14}=\dfrac{8 + 42}{14}=\dfrac{50}{14} = \dfrac{25}{7}$ + + \item $\dfrac{9}{4} \times 8=\dfrac{9 \times 8}{4}=\dfrac{72}{4} = 18$ + \item $\dfrac{5}{7} \times \dfrac{3}{7}=\dfrac{5 \times 3}{7 \times 7}=\dfrac{15}{49} = \dfrac{15}{49}$ + \item $\dfrac{- 10}{8} \times \dfrac{- 2}{40}=\dfrac{- 10(- 2)}{8 \times 40}=\dfrac{20}{320} = \dfrac{1}{16}$ + \item $\dfrac{\dfrac{4}{9}}{\dfrac{6}{9}}=\dfrac{4}{9} \times \dfrac{9}{6}=\dfrac{4 \times 9}{9 \times 6}=\dfrac{36}{54} = \dfrac{2}{3}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 45 photos prises dont 21 ratées. + \item en juillet, il y a eu 39 photos réussies et 30 ratées. + \item en août, il y a eu 54 photos dont une proportion de 0.19 de photos ratées. + \item en septembre, il y a eu 7 photos ratées, ce qui correspondait à 14.0\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 24 & 39 & 44 & 43 & 150\\ + \hline + Ratées & 21 & 30 & 10 & 7 & 68\\ + \hline + Total & 45 & 69 & 54 & 50 & 218\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{150}{218} = 0.69 = 68\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{30 - 21}{21} = \frac{9}{21} = 0.43 = 42\% + \] + \item De juillet à août + \[ + \frac{10 - 30}{30} = \frac{-20}{30} = -0.67 = -66\% + \] + \item De août à septembre + \[ + \frac{7 - 10}{10} = \frac{-3}{10} = -0.3 = -30\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/09_DM1.tex b/2nd/Evaluations/DM_2021-09-27/09_DM1.tex new file mode 100644 index 0000000..7740962 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/09_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill FLACHERON Maylie} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{5}{4} + \dfrac{7}{4}$ + \item $\dfrac{2}{4} + 5$ + + \item $\dfrac{2}{5} + \dfrac{9}{30}$ + \item $\dfrac{1}{7} + \dfrac{4}{6}$ + + \item $\dfrac{8}{9} \times 3$ + \item $\dfrac{2}{5} \times \dfrac{7}{5}$ + + \item $\dfrac{4}{7} \times \dfrac{- 2}{70}$ + \item $\dfrac{\dfrac{5}{4}}{\dfrac{1}{3}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{5}{4} + \dfrac{7}{4}=\dfrac{5 + 7}{4}=\dfrac{12}{4} = 3$ + \item $\dfrac{2}{4} + 5=\dfrac{2}{4} + \dfrac{5}{1}=\dfrac{2}{4} + \dfrac{5 \times 4}{1 \times 4}=\dfrac{2}{4} + \dfrac{20}{4}=\dfrac{2 + 20}{4}=\dfrac{22}{4} = \dfrac{11}{2}$ + \item $\dfrac{2}{5} + \dfrac{9}{30}=\dfrac{2 \times 6}{5 \times 6} + \dfrac{9}{30}=\dfrac{12}{30} + \dfrac{9}{30}=\dfrac{12 + 9}{30}=\dfrac{21}{30} = \dfrac{7}{10}$ + \item $\dfrac{1}{7} + \dfrac{4}{6}=\dfrac{1 \times 6}{7 \times 6} + \dfrac{4 \times 7}{6 \times 7}=\dfrac{6}{42} + \dfrac{28}{42}=\dfrac{6 + 28}{42}=\dfrac{34}{42} = \dfrac{17}{21}$ + + \item $\dfrac{8}{9} \times 3=\dfrac{8 \times 3}{9}=\dfrac{24}{9} = \dfrac{8}{3}$ + \item $\dfrac{2}{5} \times \dfrac{7}{5}=\dfrac{2 \times 7}{5 \times 5}=\dfrac{14}{25} = \dfrac{14}{25}$ + \item $\dfrac{4}{7} \times \dfrac{- 2}{70}=\dfrac{4(- 2)}{7 \times 70}=\dfrac{- 8}{490} = \dfrac{- 4}{245}$ + \item $\dfrac{\dfrac{5}{4}}{\dfrac{1}{3}}=\dfrac{5}{4} \times \dfrac{3}{1}=\dfrac{5 \times 3}{4 \times 1}=\dfrac{15}{4} = \dfrac{15}{4}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 51 photos prises dont 24 ratées. + \item en juillet, il y a eu 42 photos réussies et 39 ratées. + \item en août, il y a eu 55 photos dont une proportion de 0.25 de photos ratées. + \item en septembre, il y a eu 14 photos ratées, ce qui correspondait à 25.0\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 27 & 42 & 41 & 42 & 152\\ + \hline + Ratées & 24 & 39 & 14 & 14 & 91\\ + \hline + Total & 51 & 81 & 55 & 56 & 243\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{152}{243} = 0.63 = 62\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{39 - 24}{24} = \frac{15}{24} = 0.62 = 62\% + \] + \item De juillet à août + \[ + \frac{14 - 39}{39} = \frac{-25}{39} = -0.64 = -64\% + \] + \item De août à septembre + \[ + \frac{14 - 14}{14} = \frac{0}{14} = 0.0 = 0\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/10_DM1.tex b/2nd/Evaluations/DM_2021-09-27/10_DM1.tex new file mode 100644 index 0000000..4d9be84 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/10_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill GARCIA MORENO Alberto} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{7}{2} + \dfrac{8}{2}$ + \item $\dfrac{8}{6} + 5$ + + \item $\dfrac{10}{6} + \dfrac{9}{48}$ + \item $\dfrac{9}{7} + \dfrac{6}{2}$ + + \item $\dfrac{2}{6} \times 6$ + \item $\dfrac{1}{7} \times \dfrac{3}{7}$ + + \item $\dfrac{- 7}{7} \times \dfrac{2}{35}$ + \item $\dfrac{\dfrac{10}{8}}{\dfrac{6}{2}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{7}{2} + \dfrac{8}{2}=\dfrac{7 + 8}{2}=\dfrac{15}{2} = \dfrac{15}{2}$ + \item $\dfrac{8}{6} + 5=\dfrac{8}{6} + \dfrac{5}{1}=\dfrac{8}{6} + \dfrac{5 \times 6}{1 \times 6}=\dfrac{8}{6} + \dfrac{30}{6}=\dfrac{8 + 30}{6}=\dfrac{38}{6} = \dfrac{19}{3}$ + \item $\dfrac{10}{6} + \dfrac{9}{48}=\dfrac{10 \times 8}{6 \times 8} + \dfrac{9}{48}=\dfrac{80}{48} + \dfrac{9}{48}=\dfrac{80 + 9}{48}=\dfrac{89}{48} = \dfrac{89}{48}$ + \item $\dfrac{9}{7} + \dfrac{6}{2}=\dfrac{9 \times 2}{7 \times 2} + \dfrac{6 \times 7}{2 \times 7}=\dfrac{18}{14} + \dfrac{42}{14}=\dfrac{18 + 42}{14}=\dfrac{60}{14} = \dfrac{30}{7}$ + + \item $\dfrac{2}{6} \times 6=\dfrac{2 \times 6}{6}=\dfrac{12}{6} = 2$ + \item $\dfrac{1}{7} \times \dfrac{3}{7}=\dfrac{1 \times 3}{7 \times 7}=\dfrac{3}{49} = \dfrac{3}{49}$ + \item $\dfrac{- 7}{7} \times \dfrac{2}{35}=\dfrac{- 7 \times 2}{7 \times 35}=\dfrac{- 14}{245} = \dfrac{- 2}{35}$ + \item $\dfrac{\dfrac{10}{8}}{\dfrac{6}{2}}=\dfrac{10}{8} \times \dfrac{2}{6}=\dfrac{10 \times 2}{8 \times 6}=\dfrac{20}{48} = \dfrac{5}{12}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 50 photos prises dont 26 ratées. + \item en juillet, il y a eu 43 photos réussies et 32 ratées. + \item en août, il y a eu 61 photos dont une proportion de 0.2 de photos ratées. + \item en septembre, il y a eu 5 photos ratées, ce qui correspondait à 9.26\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 24 & 43 & 49 & 49 & 165\\ + \hline + Ratées & 26 & 32 & 12 & 5 & 75\\ + \hline + Total & 50 & 75 & 61 & 54 & 240\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{165}{240} = 0.69 = 68\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{32 - 26}{26} = \frac{6}{26} = 0.23 = 23\% + \] + \item De juillet à août + \[ + \frac{12 - 32}{32} = \frac{-20}{32} = -0.62 = -62\% + \] + \item De août à septembre + \[ + \frac{5 - 12}{12} = \frac{-7}{12} = -0.58 = -58\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/11_DM1.tex b/2nd/Evaluations/DM_2021-09-27/11_DM1.tex new file mode 100644 index 0000000..9fa1fe4 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/11_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill GNUI Kadia} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{10}{5} + \dfrac{2}{5}$ + \item $\dfrac{8}{9} + 6$ + + \item $\dfrac{3}{4} + \dfrac{1}{24}$ + \item $\dfrac{2}{4} + \dfrac{1}{2}$ + + \item $\dfrac{2}{4} \times 1$ + \item $\dfrac{1}{5} \times \dfrac{1}{5}$ + + \item $\dfrac{- 2}{10} \times \dfrac{- 5}{20}$ + \item $\dfrac{\dfrac{4}{7}}{\dfrac{7}{4}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{10}{5} + \dfrac{2}{5}=\dfrac{10 + 2}{5}=\dfrac{12}{5} = \dfrac{12}{5}$ + \item $\dfrac{8}{9} + 6=\dfrac{8}{9} + \dfrac{6}{1}=\dfrac{8}{9} + \dfrac{6 \times 9}{1 \times 9}=\dfrac{8}{9} + \dfrac{54}{9}=\dfrac{8 + 54}{9}=\dfrac{62}{9} = \dfrac{62}{9}$ + \item $\dfrac{3}{4} + \dfrac{1}{24}=\dfrac{3 \times 6}{4 \times 6} + \dfrac{1}{24}=\dfrac{18}{24} + \dfrac{1}{24}=\dfrac{18 + 1}{24}=\dfrac{19}{24} = \dfrac{19}{24}$ + \item $\dfrac{2}{4} + \dfrac{1}{2}=\dfrac{2}{4} + \dfrac{1 \times 2}{2 \times 2}=\dfrac{2}{4} + \dfrac{2}{4}=\dfrac{2 + 2}{4}=\dfrac{4}{4} = 1$ + + \item $\dfrac{2}{4} \times 1=\dfrac{2}{4} = \dfrac{1}{2}$ + \item $\dfrac{1}{5} \times \dfrac{1}{5}=\dfrac{1 \times 1}{5 \times 5}=\dfrac{1}{25} = \dfrac{1}{25}$ + \item $\dfrac{- 2}{10} \times \dfrac{- 5}{20}=\dfrac{- 2(- 5)}{10 \times 20}=\dfrac{10}{200} = \dfrac{1}{20}$ + \item $\dfrac{\dfrac{4}{7}}{\dfrac{7}{4}}=\dfrac{4}{7} \times \dfrac{4}{7}=\dfrac{4 \times 4}{7 \times 7}=\dfrac{16}{49} = \dfrac{16}{49}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 52 photos prises dont 28 ratées. + \item en juillet, il y a eu 39 photos réussies et 36 ratées. + \item en août, il y a eu 51 photos dont une proportion de 0.2 de photos ratées. + \item en septembre, il y a eu 5 photos ratées, ce qui correspondait à 10.42\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 24 & 39 & 41 & 43 & 147\\ + \hline + Ratées & 28 & 36 & 10 & 5 & 79\\ + \hline + Total & 52 & 75 & 51 & 48 & 226\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{147}{226} = 0.65 = 65\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{36 - 28}{28} = \frac{8}{28} = 0.29 = 28\% + \] + \item De juillet à août + \[ + \frac{10 - 36}{36} = \frac{-26}{36} = -0.72 = -72\% + \] + \item De août à septembre + \[ + \frac{5 - 10}{10} = \frac{-5}{10} = -0.5 = -50\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/12_DM1.tex b/2nd/Evaluations/DM_2021-09-27/12_DM1.tex new file mode 100644 index 0000000..bc0226a --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/12_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill GOSSET Jules} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{6}{8} + \dfrac{7}{8}$ + \item $\dfrac{9}{5} + 8$ + + \item $\dfrac{2}{5} + \dfrac{10}{35}$ + \item $\dfrac{6}{3} + \dfrac{8}{6}$ + + \item $\dfrac{7}{4} \times 8$ + \item $\dfrac{4}{8} \times \dfrac{5}{8}$ + + \item $\dfrac{- 6}{2} \times \dfrac{- 2}{10}$ + \item $\dfrac{\dfrac{3}{10}}{\dfrac{8}{10}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{6}{8} + \dfrac{7}{8}=\dfrac{6 + 7}{8}=\dfrac{13}{8} = \dfrac{13}{8}$ + \item $\dfrac{9}{5} + 8=\dfrac{9}{5} + \dfrac{8}{1}=\dfrac{9}{5} + \dfrac{8 \times 5}{1 \times 5}=\dfrac{9}{5} + \dfrac{40}{5}=\dfrac{9 + 40}{5}=\dfrac{49}{5} = \dfrac{49}{5}$ + \item $\dfrac{2}{5} + \dfrac{10}{35}=\dfrac{2 \times 7}{5 \times 7} + \dfrac{10}{35}=\dfrac{14}{35} + \dfrac{10}{35}=\dfrac{14 + 10}{35}=\dfrac{24}{35} = \dfrac{24}{35}$ + \item $\dfrac{6}{3} + \dfrac{8}{6}=\dfrac{6 \times 2}{3 \times 2} + \dfrac{8}{6}=\dfrac{12}{6} + \dfrac{8}{6}=\dfrac{12 + 8}{6}=\dfrac{20}{6} = \dfrac{10}{3}$ + + \item $\dfrac{7}{4} \times 8=\dfrac{7 \times 8}{4}=\dfrac{56}{4} = 14$ + \item $\dfrac{4}{8} \times \dfrac{5}{8}=\dfrac{4 \times 5}{8 \times 8}=\dfrac{20}{64} = \dfrac{5}{16}$ + \item $\dfrac{- 6}{2} \times \dfrac{- 2}{10}=\dfrac{- 6(- 2)}{2 \times 10}=\dfrac{12}{20} = \dfrac{3}{5}$ + \item $\dfrac{\dfrac{3}{10}}{\dfrac{8}{10}}=\dfrac{3}{10} \times \dfrac{10}{8}=\dfrac{3 \times 10}{10 \times 8}=\dfrac{30}{80} = \dfrac{3}{8}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 45 photos prises dont 20 ratées. + \item en juillet, il y a eu 39 photos réussies et 50 ratées. + \item en août, il y a eu 60 photos dont une proportion de 0.23 de photos ratées. + \item en septembre, il y a eu 15 photos ratées, ce qui correspondait à 26.32\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 25 & 39 & 46 & 42 & 152\\ + \hline + Ratées & 20 & 50 & 14 & 15 & 99\\ + \hline + Total & 45 & 89 & 60 & 57 & 251\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{152}{251} = 0.61 = 60\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{50 - 20}{20} = \frac{30}{20} = 1.5 = 150\% + \] + \item De juillet à août + \[ + \frac{14 - 50}{50} = \frac{-36}{50} = -0.72 = -72\% + \] + \item De août à septembre + \[ + \frac{15 - 14}{14} = \frac{1}{14} = 0.07 = 7\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/13_DM1.tex b/2nd/Evaluations/DM_2021-09-27/13_DM1.tex new file mode 100644 index 0000000..2e39712 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/13_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill GOUGEAUD William} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{1}{2} + \dfrac{8}{2}$ + \item $\dfrac{3}{8} + 5$ + + \item $\dfrac{9}{7} + \dfrac{8}{63}$ + \item $\dfrac{2}{10} + \dfrac{7}{10}$ + + \item $\dfrac{8}{2} \times 10$ + \item $\dfrac{9}{2} \times \dfrac{8}{2}$ + + \item $\dfrac{- 9}{7} \times \dfrac{8}{14}$ + \item $\dfrac{\dfrac{1}{7}}{\dfrac{9}{4}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{1}{2} + \dfrac{8}{2}=\dfrac{1 + 8}{2}=\dfrac{9}{2} = \dfrac{9}{2}$ + \item $\dfrac{3}{8} + 5=\dfrac{3}{8} + \dfrac{5}{1}=\dfrac{3}{8} + \dfrac{5 \times 8}{1 \times 8}=\dfrac{3}{8} + \dfrac{40}{8}=\dfrac{3 + 40}{8}=\dfrac{43}{8} = \dfrac{43}{8}$ + \item $\dfrac{9}{7} + \dfrac{8}{63}=\dfrac{9 \times 9}{7 \times 9} + \dfrac{8}{63}=\dfrac{81}{63} + \dfrac{8}{63}=\dfrac{81 + 8}{63}=\dfrac{89}{63} = \dfrac{89}{63}$ + \item $\dfrac{2}{10} + \dfrac{7}{10}=\dfrac{2 + 7}{10}=\dfrac{9}{10} = \dfrac{9}{10}$ + + \item $\dfrac{8}{2} \times 10=\dfrac{8 \times 10}{2}=\dfrac{80}{2} = 40$ + \item $\dfrac{9}{2} \times \dfrac{8}{2}=\dfrac{9 \times 8}{2 \times 2}=\dfrac{72}{4} = 18$ + \item $\dfrac{- 9}{7} \times \dfrac{8}{14}=\dfrac{- 9 \times 8}{7 \times 14}=\dfrac{- 72}{98} = \dfrac{- 36}{49}$ + \item $\dfrac{\dfrac{1}{7}}{\dfrac{9}{4}}=\dfrac{1}{7} \times \dfrac{4}{9}=\dfrac{1 \times 4}{7 \times 9}=\dfrac{4}{63} = \dfrac{4}{63}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 46 photos prises dont 25 ratées. + \item en juillet, il y a eu 45 photos réussies et 33 ratées. + \item en août, il y a eu 66 photos dont une proportion de 0.24 de photos ratées. + \item en septembre, il y a eu 13 photos ratées, ce qui correspondait à 23.21\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 21 & 45 & 50 & 43 & 159\\ + \hline + Ratées & 25 & 33 & 16 & 13 & 87\\ + \hline + Total & 46 & 78 & 66 & 56 & 246\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{159}{246} = 0.65 = 64\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{33 - 25}{25} = \frac{8}{25} = 0.32 = 32\% + \] + \item De juillet à août + \[ + \frac{16 - 33}{33} = \frac{-17}{33} = -0.52 = -51\% + \] + \item De août à septembre + \[ + \frac{13 - 16}{16} = \frac{-3}{16} = -0.19 = -18\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/14_DM1.tex b/2nd/Evaluations/DM_2021-09-27/14_DM1.tex new file mode 100644 index 0000000..42f3595 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/14_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill GRISON Jade} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{3}{6} + \dfrac{7}{6}$ + \item $\dfrac{2}{7} + 3$ + + \item $\dfrac{6}{2} + \dfrac{4}{14}$ + \item $\dfrac{4}{8} + \dfrac{2}{3}$ + + \item $\dfrac{4}{8} \times 8$ + \item $\dfrac{4}{2} \times \dfrac{7}{2}$ + + \item $\dfrac{10}{8} \times \dfrac{- 2}{64}$ + \item $\dfrac{\dfrac{4}{6}}{\dfrac{7}{9}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{3}{6} + \dfrac{7}{6}=\dfrac{3 + 7}{6}=\dfrac{10}{6} = \dfrac{5}{3}$ + \item $\dfrac{2}{7} + 3=\dfrac{2}{7} + \dfrac{3}{1}=\dfrac{2}{7} + \dfrac{3 \times 7}{1 \times 7}=\dfrac{2}{7} + \dfrac{21}{7}=\dfrac{2 + 21}{7}=\dfrac{23}{7} = \dfrac{23}{7}$ + \item $\dfrac{6}{2} + \dfrac{4}{14}=\dfrac{6 \times 7}{2 \times 7} + \dfrac{4}{14}=\dfrac{42}{14} + \dfrac{4}{14}=\dfrac{42 + 4}{14}=\dfrac{46}{14} = \dfrac{23}{7}$ + \item $\dfrac{4}{8} + \dfrac{2}{3}=\dfrac{4 \times 3}{8 \times 3} + \dfrac{2 \times 8}{3 \times 8}=\dfrac{12}{24} + \dfrac{16}{24}=\dfrac{12 + 16}{24}=\dfrac{28}{24} = \dfrac{7}{6}$ + + \item $\dfrac{4}{8} \times 8=\dfrac{4 \times 8}{8}=\dfrac{32}{8} = 4$ + \item $\dfrac{4}{2} \times \dfrac{7}{2}=\dfrac{4 \times 7}{2 \times 2}=\dfrac{28}{4} = 7$ + \item $\dfrac{10}{8} \times \dfrac{- 2}{64}=\dfrac{10(- 2)}{8 \times 64}=\dfrac{- 20}{512} = \dfrac{- 5}{128}$ + \item $\dfrac{\dfrac{4}{6}}{\dfrac{7}{9}}=\dfrac{4}{6} \times \dfrac{9}{7}=\dfrac{4 \times 9}{6 \times 7}=\dfrac{36}{42} = \dfrac{6}{7}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 58 photos prises dont 30 ratées. + \item en juillet, il y a eu 34 photos réussies et 33 ratées. + \item en août, il y a eu 57 photos dont une proportion de 0.19 de photos ratées. + \item en septembre, il y a eu 10 photos ratées, ce qui correspondait à 18.52\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 28 & 34 & 46 & 44 & 152\\ + \hline + Ratées & 30 & 33 & 11 & 10 & 84\\ + \hline + Total & 58 & 67 & 57 & 54 & 236\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{152}{236} = 0.64 = 64\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{33 - 30}{30} = \frac{3}{30} = 0.1 = 10\% + \] + \item De juillet à août + \[ + \frac{11 - 33}{33} = \frac{-22}{33} = -0.67 = -66\% + \] + \item De août à septembre + \[ + \frac{10 - 11}{11} = \frac{-1}{11} = -0.09 = -9\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/15_DM1.tex b/2nd/Evaluations/DM_2021-09-27/15_DM1.tex new file mode 100644 index 0000000..6cfaf28 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/15_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill HAMIOT Anaïs} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{7}{8} + \dfrac{5}{8}$ + \item $\dfrac{1}{5} + 6$ + + \item $\dfrac{3}{7} + \dfrac{4}{35}$ + \item $\dfrac{1}{3} + \dfrac{8}{10}$ + + \item $\dfrac{2}{9} \times 6$ + \item $\dfrac{7}{5} \times \dfrac{7}{5}$ + + \item $\dfrac{- 7}{4} \times \dfrac{- 4}{12}$ + \item $\dfrac{\dfrac{8}{7}}{\dfrac{3}{7}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{7}{8} + \dfrac{5}{8}=\dfrac{7 + 5}{8}=\dfrac{12}{8} = \dfrac{3}{2}$ + \item $\dfrac{1}{5} + 6=\dfrac{1}{5} + \dfrac{6}{1}=\dfrac{1}{5} + \dfrac{6 \times 5}{1 \times 5}=\dfrac{1}{5} + \dfrac{30}{5}=\dfrac{1 + 30}{5}=\dfrac{31}{5} = \dfrac{31}{5}$ + \item $\dfrac{3}{7} + \dfrac{4}{35}=\dfrac{3 \times 5}{7 \times 5} + \dfrac{4}{35}=\dfrac{15}{35} + \dfrac{4}{35}=\dfrac{15 + 4}{35}=\dfrac{19}{35} = \dfrac{19}{35}$ + \item $\dfrac{1}{3} + \dfrac{8}{10}=\dfrac{1 \times 10}{3 \times 10} + \dfrac{8 \times 3}{10 \times 3}=\dfrac{10}{30} + \dfrac{24}{30}=\dfrac{10 + 24}{30}=\dfrac{34}{30} = \dfrac{17}{15}$ + + \item $\dfrac{2}{9} \times 6=\dfrac{2 \times 6}{9}=\dfrac{12}{9} = \dfrac{4}{3}$ + \item $\dfrac{7}{5} \times \dfrac{7}{5}=\dfrac{7 \times 7}{5 \times 5}=\dfrac{49}{25} = \dfrac{49}{25}$ + \item $\dfrac{- 7}{4} \times \dfrac{- 4}{12}=\dfrac{- 7(- 4)}{4 \times 12}=\dfrac{28}{48} = \dfrac{7}{12}$ + \item $\dfrac{\dfrac{8}{7}}{\dfrac{3}{7}}=\dfrac{8}{7} \times \dfrac{7}{3}=\dfrac{8 \times 7}{7 \times 3}=\dfrac{56}{21} = \dfrac{8}{3}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 46 photos prises dont 21 ratées. + \item en juillet, il y a eu 48 photos réussies et 45 ratées. + \item en août, il y a eu 60 photos dont une proportion de 0.23 de photos ratées. + \item en septembre, il y a eu 10 photos ratées, ce qui correspondait à 16.67\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 25 & 48 & 46 & 50 & 169\\ + \hline + Ratées & 21 & 45 & 14 & 10 & 90\\ + \hline + Total & 46 & 93 & 60 & 60 & 259\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{169}{259} = 0.65 = 65\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{45 - 21}{21} = \frac{24}{21} = 1.14 = 114\% + \] + \item De juillet à août + \[ + \frac{14 - 45}{45} = \frac{-31}{45} = -0.69 = -68\% + \] + \item De août à septembre + \[ + \frac{10 - 14}{14} = \frac{-4}{14} = -0.29 = -28\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/16_DM1.tex b/2nd/Evaluations/DM_2021-09-27/16_DM1.tex new file mode 100644 index 0000000..890763e --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/16_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill HAMMOUDI Lyna} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{5}{4} + \dfrac{6}{4}$ + \item $\dfrac{7}{4} + 6$ + + \item $\dfrac{8}{4} + \dfrac{9}{20}$ + \item $\dfrac{3}{10} + \dfrac{3}{7}$ + + \item $\dfrac{1}{4} \times 2$ + \item $\dfrac{3}{9} \times \dfrac{10}{9}$ + + \item $\dfrac{6}{2} \times \dfrac{4}{10}$ + \item $\dfrac{\dfrac{8}{9}}{\dfrac{9}{5}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{5}{4} + \dfrac{6}{4}=\dfrac{5 + 6}{4}=\dfrac{11}{4} = \dfrac{11}{4}$ + \item $\dfrac{7}{4} + 6=\dfrac{7}{4} + \dfrac{6}{1}=\dfrac{7}{4} + \dfrac{6 \times 4}{1 \times 4}=\dfrac{7}{4} + \dfrac{24}{4}=\dfrac{7 + 24}{4}=\dfrac{31}{4} = \dfrac{31}{4}$ + \item $\dfrac{8}{4} + \dfrac{9}{20}=\dfrac{8 \times 5}{4 \times 5} + \dfrac{9}{20}=\dfrac{40}{20} + \dfrac{9}{20}=\dfrac{40 + 9}{20}=\dfrac{49}{20} = \dfrac{49}{20}$ + \item $\dfrac{3}{10} + \dfrac{3}{7}=\dfrac{3 \times 7}{10 \times 7} + \dfrac{3 \times 10}{7 \times 10}=\dfrac{21}{70} + \dfrac{30}{70}=\dfrac{21 + 30}{70}=\dfrac{51}{70} = \dfrac{51}{70}$ + + \item $\dfrac{1}{4} \times 2=\dfrac{1 \times 2}{4}=\dfrac{2}{4} = \dfrac{1}{2}$ + \item $\dfrac{3}{9} \times \dfrac{10}{9}=\dfrac{3 \times 10}{9 \times 9}=\dfrac{30}{81} = \dfrac{10}{27}$ + \item $\dfrac{6}{2} \times \dfrac{4}{10}=\dfrac{6 \times 4}{2 \times 10}=\dfrac{24}{20} = \dfrac{6}{5}$ + \item $\dfrac{\dfrac{8}{9}}{\dfrac{9}{5}}=\dfrac{8}{9} \times \dfrac{5}{9}=\dfrac{8 \times 5}{9 \times 9}=\dfrac{40}{81} = \dfrac{40}{81}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 55 photos prises dont 27 ratées. + \item en juillet, il y a eu 31 photos réussies et 42 ratées. + \item en août, il y a eu 59 photos dont une proportion de 0.2 de photos ratées. + \item en septembre, il y a eu 11 photos ratées, ce qui correspondait à 21.57\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 28 & 31 & 47 & 40 & 146\\ + \hline + Ratées & 27 & 42 & 12 & 11 & 92\\ + \hline + Total & 55 & 73 & 59 & 51 & 238\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{146}{238} = 0.61 = 61\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{42 - 27}{27} = \frac{15}{27} = 0.56 = 55\% + \] + \item De juillet à août + \[ + \frac{12 - 42}{42} = \frac{-30}{42} = -0.71 = -71\% + \] + \item De août à septembre + \[ + \frac{11 - 12}{12} = \frac{-1}{12} = -0.08 = -8\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/17_DM1.tex b/2nd/Evaluations/DM_2021-09-27/17_DM1.tex new file mode 100644 index 0000000..80d25f9 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/17_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill JOUNEAU Cassandra} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{4}{8} + \dfrac{7}{8}$ + \item $\dfrac{4}{2} + 6$ + + \item $\dfrac{8}{7} + \dfrac{5}{49}$ + \item $\dfrac{4}{9} + \dfrac{7}{9}$ + + \item $\dfrac{6}{2} \times 3$ + \item $\dfrac{2}{10} \times \dfrac{9}{10}$ + + \item $\dfrac{- 4}{4} \times \dfrac{- 9}{36}$ + \item $\dfrac{\dfrac{6}{7}}{\dfrac{10}{6}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{4}{8} + \dfrac{7}{8}=\dfrac{4 + 7}{8}=\dfrac{11}{8} = \dfrac{11}{8}$ + \item $\dfrac{4}{2} + 6=\dfrac{4}{2} + \dfrac{6}{1}=\dfrac{4}{2} + \dfrac{6 \times 2}{1 \times 2}=\dfrac{4}{2} + \dfrac{12}{2}=\dfrac{4 + 12}{2}=\dfrac{16}{2} = 8$ + \item $\dfrac{8}{7} + \dfrac{5}{49}=\dfrac{8 \times 7}{7 \times 7} + \dfrac{5}{49}=\dfrac{56}{49} + \dfrac{5}{49}=\dfrac{56 + 5}{49}=\dfrac{61}{49} = \dfrac{61}{49}$ + \item $\dfrac{4}{9} + \dfrac{7}{9}=\dfrac{4 + 7}{9}=\dfrac{11}{9} = \dfrac{11}{9}$ + + \item $\dfrac{6}{2} \times 3=\dfrac{6 \times 3}{2}=\dfrac{18}{2} = 9$ + \item $\dfrac{2}{10} \times \dfrac{9}{10}=\dfrac{2 \times 9}{10 \times 10}=\dfrac{18}{100} = \dfrac{9}{50}$ + \item $\dfrac{- 4}{4} \times \dfrac{- 9}{36}=\dfrac{- 4(- 9)}{4 \times 36}=\dfrac{36}{144} = \dfrac{1}{4}$ + \item $\dfrac{\dfrac{6}{7}}{\dfrac{10}{6}}=\dfrac{6}{7} \times \dfrac{6}{10}=\dfrac{6 \times 6}{7 \times 10}=\dfrac{36}{70} = \dfrac{18}{35}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 48 photos prises dont 27 ratées. + \item en juillet, il y a eu 39 photos réussies et 45 ratées. + \item en août, il y a eu 59 photos dont une proportion de 0.27 de photos ratées. + \item en septembre, il y a eu 5 photos ratées, ce qui correspondait à 10.87\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 21 & 39 & 43 & 41 & 144\\ + \hline + Ratées & 27 & 45 & 16 & 5 & 93\\ + \hline + Total & 48 & 84 & 59 & 46 & 237\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{144}{237} = 0.61 = 60\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{45 - 27}{27} = \frac{18}{27} = 0.67 = 66\% + \] + \item De juillet à août + \[ + \frac{16 - 45}{45} = \frac{-29}{45} = -0.64 = -64\% + \] + \item De août à septembre + \[ + \frac{5 - 16}{16} = \frac{-11}{16} = -0.69 = -68\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/18_DM1.tex b/2nd/Evaluations/DM_2021-09-27/18_DM1.tex new file mode 100644 index 0000000..edea290 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/18_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill LAFUMAS Flora} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{10}{8} + \dfrac{2}{8}$ + \item $\dfrac{5}{10} + 3$ + + \item $\dfrac{1}{9} + \dfrac{1}{90}$ + \item $\dfrac{7}{9} + \dfrac{9}{4}$ + + \item $\dfrac{7}{6} \times 9$ + \item $\dfrac{1}{9} \times \dfrac{4}{9}$ + + \item $\dfrac{7}{3} \times \dfrac{- 2}{21}$ + \item $\dfrac{\dfrac{4}{7}}{\dfrac{5}{9}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{10}{8} + \dfrac{2}{8}=\dfrac{10 + 2}{8}=\dfrac{12}{8} = \dfrac{3}{2}$ + \item $\dfrac{5}{10} + 3=\dfrac{5}{10} + \dfrac{3}{1}=\dfrac{5}{10} + \dfrac{3 \times 10}{1 \times 10}=\dfrac{5}{10} + \dfrac{30}{10}=\dfrac{5 + 30}{10}=\dfrac{35}{10} = \dfrac{7}{2}$ + \item $\dfrac{1}{9} + \dfrac{1}{90}=\dfrac{1 \times 10}{9 \times 10} + \dfrac{1}{90}=\dfrac{10}{90} + \dfrac{1}{90}=\dfrac{10 + 1}{90}=\dfrac{11}{90} = \dfrac{11}{90}$ + \item $\dfrac{7}{9} + \dfrac{9}{4}=\dfrac{7 \times 4}{9 \times 4} + \dfrac{9 \times 9}{4 \times 9}=\dfrac{28}{36} + \dfrac{81}{36}=\dfrac{28 + 81}{36}=\dfrac{109}{36} = \dfrac{109}{36}$ + + \item $\dfrac{7}{6} \times 9=\dfrac{7 \times 9}{6}=\dfrac{63}{6} = \dfrac{21}{2}$ + \item $\dfrac{1}{9} \times \dfrac{4}{9}=\dfrac{1 \times 4}{9 \times 9}=\dfrac{4}{81} = \dfrac{4}{81}$ + \item $\dfrac{7}{3} \times \dfrac{- 2}{21}=\dfrac{7(- 2)}{3 \times 21}=\dfrac{- 14}{63} = \dfrac{- 2}{9}$ + \item $\dfrac{\dfrac{4}{7}}{\dfrac{5}{9}}=\dfrac{4}{7} \times \dfrac{9}{5}=\dfrac{4 \times 9}{7 \times 5}=\dfrac{36}{35} = \dfrac{36}{35}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 51 photos prises dont 24 ratées. + \item en juillet, il y a eu 40 photos réussies et 49 ratées. + \item en août, il y a eu 61 photos dont une proportion de 0.28 de photos ratées. + \item en septembre, il y a eu 10 photos ratées, ce qui correspondait à 18.18\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 27 & 40 & 44 & 45 & 156\\ + \hline + Ratées & 24 & 49 & 17 & 10 & 100\\ + \hline + Total & 51 & 89 & 61 & 55 & 256\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{156}{256} = 0.61 = 60\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{49 - 24}{24} = \frac{25}{24} = 1.04 = 104\% + \] + \item De juillet à août + \[ + \frac{17 - 49}{49} = \frac{-32}{49} = -0.65 = -65\% + \] + \item De août à septembre + \[ + \frac{10 - 17}{17} = \frac{-7}{17} = -0.41 = -41\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/19_DM1.tex b/2nd/Evaluations/DM_2021-09-27/19_DM1.tex new file mode 100644 index 0000000..be7895f --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/19_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill MONET--BRIFFOD Antonin} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{6}{2} + \dfrac{7}{2}$ + \item $\dfrac{4}{7} + 2$ + + \item $\dfrac{7}{2} + \dfrac{1}{16}$ + \item $\dfrac{8}{7} + \dfrac{4}{7}$ + + \item $\dfrac{5}{4} \times 10$ + \item $\dfrac{7}{8} \times \dfrac{4}{8}$ + + \item $\dfrac{3}{4} \times \dfrac{- 2}{12}$ + \item $\dfrac{\dfrac{4}{10}}{\dfrac{10}{4}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{6}{2} + \dfrac{7}{2}=\dfrac{6 + 7}{2}=\dfrac{13}{2} = \dfrac{13}{2}$ + \item $\dfrac{4}{7} + 2=\dfrac{4}{7} + \dfrac{2}{1}=\dfrac{4}{7} + \dfrac{2 \times 7}{1 \times 7}=\dfrac{4}{7} + \dfrac{14}{7}=\dfrac{4 + 14}{7}=\dfrac{18}{7} = \dfrac{18}{7}$ + \item $\dfrac{7}{2} + \dfrac{1}{16}=\dfrac{7 \times 8}{2 \times 8} + \dfrac{1}{16}=\dfrac{56}{16} + \dfrac{1}{16}=\dfrac{56 + 1}{16}=\dfrac{57}{16} = \dfrac{57}{16}$ + \item $\dfrac{8}{7} + \dfrac{4}{7}=\dfrac{8 + 4}{7}=\dfrac{12}{7} = \dfrac{12}{7}$ + + \item $\dfrac{5}{4} \times 10=\dfrac{5 \times 10}{4}=\dfrac{50}{4} = \dfrac{25}{2}$ + \item $\dfrac{7}{8} \times \dfrac{4}{8}=\dfrac{7 \times 4}{8 \times 8}=\dfrac{28}{64} = \dfrac{7}{16}$ + \item $\dfrac{3}{4} \times \dfrac{- 2}{12}=\dfrac{3(- 2)}{4 \times 12}=\dfrac{- 6}{48} = \dfrac{- 1}{8}$ + \item $\dfrac{\dfrac{4}{10}}{\dfrac{10}{4}}=\dfrac{4}{10} \times \dfrac{4}{10}=\dfrac{4 \times 4}{10 \times 10}=\dfrac{16}{100} = \dfrac{4}{25}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 47 photos prises dont 26 ratées. + \item en juillet, il y a eu 31 photos réussies et 37 ratées. + \item en août, il y a eu 60 photos dont une proportion de 0.32 de photos ratées. + \item en septembre, il y a eu 7 photos ratées, ce qui correspondait à 14.89\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 21 & 31 & 41 & 40 & 133\\ + \hline + Ratées & 26 & 37 & 19 & 7 & 89\\ + \hline + Total & 47 & 68 & 60 & 47 & 222\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{133}{222} = 0.6 = 59\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{37 - 26}{26} = \frac{11}{26} = 0.42 = 42\% + \] + \item De juillet à août + \[ + \frac{19 - 37}{37} = \frac{-18}{37} = -0.49 = -48\% + \] + \item De août à septembre + \[ + \frac{7 - 19}{19} = \frac{-12}{19} = -0.63 = -63\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/20_DM1.tex b/2nd/Evaluations/DM_2021-09-27/20_DM1.tex new file mode 100644 index 0000000..4379cba --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/20_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill MONOD Mélissa} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{1}{4} + \dfrac{3}{4}$ + \item $\dfrac{6}{7} + 3$ + + \item $\dfrac{8}{10} + \dfrac{8}{70}$ + \item $\dfrac{7}{8} + \dfrac{7}{9}$ + + \item $\dfrac{9}{5} \times 2$ + \item $\dfrac{6}{2} \times \dfrac{10}{2}$ + + \item $\dfrac{- 8}{4} \times \dfrac{7}{16}$ + \item $\dfrac{\dfrac{9}{7}}{\dfrac{4}{3}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{1}{4} + \dfrac{3}{4}=\dfrac{1 + 3}{4}=\dfrac{4}{4} = 1$ + \item $\dfrac{6}{7} + 3=\dfrac{6}{7} + \dfrac{3}{1}=\dfrac{6}{7} + \dfrac{3 \times 7}{1 \times 7}=\dfrac{6}{7} + \dfrac{21}{7}=\dfrac{6 + 21}{7}=\dfrac{27}{7} = \dfrac{27}{7}$ + \item $\dfrac{8}{10} + \dfrac{8}{70}=\dfrac{8 \times 7}{10 \times 7} + \dfrac{8}{70}=\dfrac{56}{70} + \dfrac{8}{70}=\dfrac{56 + 8}{70}=\dfrac{64}{70} = \dfrac{32}{35}$ + \item $\dfrac{7}{8} + \dfrac{7}{9}=\dfrac{7 \times 9}{8 \times 9} + \dfrac{7 \times 8}{9 \times 8}=\dfrac{63}{72} + \dfrac{56}{72}=\dfrac{63 + 56}{72}=\dfrac{119}{72} = \dfrac{119}{72}$ + + \item $\dfrac{9}{5} \times 2=\dfrac{9 \times 2}{5}=\dfrac{18}{5} = \dfrac{18}{5}$ + \item $\dfrac{6}{2} \times \dfrac{10}{2}=\dfrac{6 \times 10}{2 \times 2}=\dfrac{60}{4} = 15$ + \item $\dfrac{- 8}{4} \times \dfrac{7}{16}=\dfrac{- 8 \times 7}{4 \times 16}=\dfrac{- 56}{64} = \dfrac{- 7}{8}$ + \item $\dfrac{\dfrac{9}{7}}{\dfrac{4}{3}}=\dfrac{9}{7} \times \dfrac{3}{4}=\dfrac{9 \times 3}{7 \times 4}=\dfrac{27}{28} = \dfrac{27}{28}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 48 photos prises dont 27 ratées. + \item en juillet, il y a eu 31 photos réussies et 32 ratées. + \item en août, il y a eu 61 photos dont une proportion de 0.3 de photos ratées. + \item en septembre, il y a eu 9 photos ratées, ce qui correspondait à 18.37\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 21 & 31 & 43 & 40 & 135\\ + \hline + Ratées & 27 & 32 & 18 & 9 & 86\\ + \hline + Total & 48 & 63 & 61 & 49 & 221\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{135}{221} = 0.61 = 61\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{32 - 27}{27} = \frac{5}{27} = 0.19 = 18\% + \] + \item De juillet à août + \[ + \frac{18 - 32}{32} = \frac{-14}{32} = -0.44 = -43\% + \] + \item De août à septembre + \[ + \frac{9 - 18}{18} = \frac{-9}{18} = -0.5 = -50\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/21_DM1.tex b/2nd/Evaluations/DM_2021-09-27/21_DM1.tex new file mode 100644 index 0000000..86fcae1 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/21_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill MULTIN Théo} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{2}{6} + \dfrac{8}{6}$ + \item $\dfrac{6}{3} + 5$ + + \item $\dfrac{1}{9} + \dfrac{6}{36}$ + \item $\dfrac{6}{10} + \dfrac{8}{6}$ + + \item $\dfrac{1}{4} \times 4$ + \item $\dfrac{3}{10} \times \dfrac{3}{10}$ + + \item $\dfrac{- 8}{6} \times \dfrac{2}{24}$ + \item $\dfrac{\dfrac{4}{10}}{\dfrac{2}{10}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{2}{6} + \dfrac{8}{6}=\dfrac{2 + 8}{6}=\dfrac{10}{6} = \dfrac{5}{3}$ + \item $\dfrac{6}{3} + 5=\dfrac{6}{3} + \dfrac{5}{1}=\dfrac{6}{3} + \dfrac{5 \times 3}{1 \times 3}=\dfrac{6}{3} + \dfrac{15}{3}=\dfrac{6 + 15}{3}=\dfrac{21}{3} = 7$ + \item $\dfrac{1}{9} + \dfrac{6}{36}=\dfrac{1 \times 4}{9 \times 4} + \dfrac{6}{36}=\dfrac{4}{36} + \dfrac{6}{36}=\dfrac{4 + 6}{36}=\dfrac{10}{36} = \dfrac{5}{18}$ + \item $\dfrac{6}{10} + \dfrac{8}{6}=\dfrac{6 \times 3}{10 \times 3} + \dfrac{8 \times 5}{6 \times 5}=\dfrac{18}{30} + \dfrac{40}{30}=\dfrac{18 + 40}{30}=\dfrac{58}{30} = \dfrac{29}{15}$ + + \item $\dfrac{1}{4} \times 4=\dfrac{1 \times 4}{4}=\dfrac{4}{4} = 1$ + \item $\dfrac{3}{10} \times \dfrac{3}{10}=\dfrac{3 \times 3}{10 \times 10}=\dfrac{9}{100} = \dfrac{9}{100}$ + \item $\dfrac{- 8}{6} \times \dfrac{2}{24}=\dfrac{- 8 \times 2}{6 \times 24}=\dfrac{- 16}{144} = \dfrac{- 1}{9}$ + \item $\dfrac{\dfrac{4}{10}}{\dfrac{2}{10}}=\dfrac{4}{10} \times \dfrac{10}{2}=\dfrac{4 \times 10}{10 \times 2}=\dfrac{40}{20} = 2$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 46 photos prises dont 22 ratées. + \item en juillet, il y a eu 49 photos réussies et 39 ratées. + \item en août, il y a eu 54 photos dont une proportion de 0.24 de photos ratées. + \item en septembre, il y a eu 8 photos ratées, ce qui correspondait à 14.81\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 24 & 49 & 41 & 46 & 160\\ + \hline + Ratées & 22 & 39 & 13 & 8 & 82\\ + \hline + Total & 46 & 88 & 54 & 54 & 242\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{160}{242} = 0.66 = 66\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{39 - 22}{22} = \frac{17}{22} = 0.77 = 77\% + \] + \item De juillet à août + \[ + \frac{13 - 39}{39} = \frac{-26}{39} = -0.67 = -66\% + \] + \item De août à septembre + \[ + \frac{8 - 13}{13} = \frac{-5}{13} = -0.38 = -38\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/22_DM1.tex b/2nd/Evaluations/DM_2021-09-27/22_DM1.tex new file mode 100644 index 0000000..3f919d4 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/22_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill NEIVA Diego} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{6}{3} + \dfrac{1}{3}$ + \item $\dfrac{1}{8} + 10$ + + \item $\dfrac{1}{9} + \dfrac{3}{18}$ + \item $\dfrac{9}{7} + \dfrac{7}{3}$ + + \item $\dfrac{7}{4} \times 2$ + \item $\dfrac{7}{3} \times \dfrac{10}{3}$ + + \item $\dfrac{- 10}{2} \times \dfrac{- 9}{4}$ + \item $\dfrac{\dfrac{3}{6}}{\dfrac{6}{8}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{6}{3} + \dfrac{1}{3}=\dfrac{6 + 1}{3}=\dfrac{7}{3} = \dfrac{7}{3}$ + \item $\dfrac{1}{8} + 10=\dfrac{1}{8} + \dfrac{10}{1}=\dfrac{1}{8} + \dfrac{10 \times 8}{1 \times 8}=\dfrac{1}{8} + \dfrac{80}{8}=\dfrac{1 + 80}{8}=\dfrac{81}{8} = \dfrac{81}{8}$ + \item $\dfrac{1}{9} + \dfrac{3}{18}=\dfrac{1 \times 2}{9 \times 2} + \dfrac{3}{18}=\dfrac{2}{18} + \dfrac{3}{18}=\dfrac{2 + 3}{18}=\dfrac{5}{18} = \dfrac{5}{18}$ + \item $\dfrac{9}{7} + \dfrac{7}{3}=\dfrac{9 \times 3}{7 \times 3} + \dfrac{7 \times 7}{3 \times 7}=\dfrac{27}{21} + \dfrac{49}{21}=\dfrac{27 + 49}{21}=\dfrac{76}{21} = \dfrac{76}{21}$ + + \item $\dfrac{7}{4} \times 2=\dfrac{7 \times 2}{4}=\dfrac{14}{4} = \dfrac{7}{2}$ + \item $\dfrac{7}{3} \times \dfrac{10}{3}=\dfrac{7 \times 10}{3 \times 3}=\dfrac{70}{9} = \dfrac{70}{9}$ + \item $\dfrac{- 10}{2} \times \dfrac{- 9}{4}=\dfrac{- 10(- 9)}{2 \times 4}=\dfrac{90}{8} = \dfrac{45}{4}$ + \item $\dfrac{\dfrac{3}{6}}{\dfrac{6}{8}}=\dfrac{3}{6} \times \dfrac{8}{6}=\dfrac{3 \times 8}{6 \times 6}=\dfrac{24}{36} = \dfrac{2}{3}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 52 photos prises dont 26 ratées. + \item en juillet, il y a eu 42 photos réussies et 41 ratées. + \item en août, il y a eu 65 photos dont une proportion de 0.25 de photos ratées. + \item en septembre, il y a eu 12 photos ratées, ce qui correspondait à 19.35\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 26 & 42 & 49 & 50 & 167\\ + \hline + Ratées & 26 & 41 & 16 & 12 & 95\\ + \hline + Total & 52 & 83 & 65 & 62 & 262\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{167}{262} = 0.64 = 63\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{41 - 26}{26} = \frac{15}{26} = 0.58 = 57\% + \] + \item De juillet à août + \[ + \frac{16 - 41}{41} = \frac{-25}{41} = -0.61 = -60\% + \] + \item De août à septembre + \[ + \frac{12 - 16}{16} = \frac{-4}{16} = -0.25 = -25\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/23_DM1.tex b/2nd/Evaluations/DM_2021-09-27/23_DM1.tex new file mode 100644 index 0000000..ba86029 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/23_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill PERROTIN Léonie} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{5}{6} + \dfrac{9}{6}$ + \item $\dfrac{2}{8} + 8$ + + \item $\dfrac{2}{10} + \dfrac{2}{80}$ + \item $\dfrac{2}{7} + \dfrac{8}{5}$ + + \item $\dfrac{3}{4} \times 1$ + \item $\dfrac{7}{3} \times \dfrac{2}{3}$ + + \item $\dfrac{- 2}{5} \times \dfrac{- 7}{20}$ + \item $\dfrac{\dfrac{3}{6}}{\dfrac{5}{8}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{5}{6} + \dfrac{9}{6}=\dfrac{5 + 9}{6}=\dfrac{14}{6} = \dfrac{7}{3}$ + \item $\dfrac{2}{8} + 8=\dfrac{2}{8} + \dfrac{8}{1}=\dfrac{2}{8} + \dfrac{8 \times 8}{1 \times 8}=\dfrac{2}{8} + \dfrac{64}{8}=\dfrac{2 + 64}{8}=\dfrac{66}{8} = \dfrac{33}{4}$ + \item $\dfrac{2}{10} + \dfrac{2}{80}=\dfrac{2 \times 8}{10 \times 8} + \dfrac{2}{80}=\dfrac{16}{80} + \dfrac{2}{80}=\dfrac{16 + 2}{80}=\dfrac{18}{80} = \dfrac{9}{40}$ + \item $\dfrac{2}{7} + \dfrac{8}{5}=\dfrac{2 \times 5}{7 \times 5} + \dfrac{8 \times 7}{5 \times 7}=\dfrac{10}{35} + \dfrac{56}{35}=\dfrac{10 + 56}{35}=\dfrac{66}{35} = \dfrac{66}{35}$ + + \item $\dfrac{3}{4} \times 1=\dfrac{3}{4} = \dfrac{3}{4}$ + \item $\dfrac{7}{3} \times \dfrac{2}{3}=\dfrac{7 \times 2}{3 \times 3}=\dfrac{14}{9} = \dfrac{14}{9}$ + \item $\dfrac{- 2}{5} \times \dfrac{- 7}{20}=\dfrac{- 2(- 7)}{5 \times 20}=\dfrac{14}{100} = \dfrac{7}{50}$ + \item $\dfrac{\dfrac{3}{6}}{\dfrac{5}{8}}=\dfrac{3}{6} \times \dfrac{8}{5}=\dfrac{3 \times 8}{6 \times 5}=\dfrac{24}{30} = \dfrac{4}{5}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 43 photos prises dont 23 ratées. + \item en juillet, il y a eu 35 photos réussies et 37 ratées. + \item en août, il y a eu 64 photos dont une proportion de 0.31 de photos ratées. + \item en septembre, il y a eu 12 photos ratées, ce qui correspondait à 21.82\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 20 & 35 & 44 & 43 & 142\\ + \hline + Ratées & 23 & 37 & 20 & 12 & 92\\ + \hline + Total & 43 & 72 & 64 & 55 & 234\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{142}{234} = 0.61 = 60\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{37 - 23}{23} = \frac{14}{23} = 0.61 = 60\% + \] + \item De juillet à août + \[ + \frac{20 - 37}{37} = \frac{-17}{37} = -0.46 = -45\% + \] + \item De août à septembre + \[ + \frac{12 - 20}{20} = \frac{-8}{20} = -0.4 = -40\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/24_DM1.tex b/2nd/Evaluations/DM_2021-09-27/24_DM1.tex new file mode 100644 index 0000000..2e23b03 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/24_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill PETIT Aidan} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{3}{10} + \dfrac{5}{10}$ + \item $\dfrac{1}{10} + 1$ + + \item $\dfrac{2}{7} + \dfrac{9}{49}$ + \item $\dfrac{10}{3} + \dfrac{5}{8}$ + + \item $\dfrac{2}{4} \times 5$ + \item $\dfrac{3}{7} \times \dfrac{4}{7}$ + + \item $\dfrac{10}{4} \times \dfrac{- 10}{28}$ + \item $\dfrac{\dfrac{6}{4}}{\dfrac{9}{3}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{3}{10} + \dfrac{5}{10}=\dfrac{3 + 5}{10}=\dfrac{8}{10} = \dfrac{4}{5}$ + \item $\dfrac{1}{10} + 1=\dfrac{1}{10} + \dfrac{1}{1}=\dfrac{1}{10} + \dfrac{1 \times 10}{1 \times 10}=\dfrac{1}{10} + \dfrac{10}{10}=\dfrac{1 + 10}{10}=\dfrac{11}{10} = \dfrac{11}{10}$ + \item $\dfrac{2}{7} + \dfrac{9}{49}=\dfrac{2 \times 7}{7 \times 7} + \dfrac{9}{49}=\dfrac{14}{49} + \dfrac{9}{49}=\dfrac{14 + 9}{49}=\dfrac{23}{49} = \dfrac{23}{49}$ + \item $\dfrac{10}{3} + \dfrac{5}{8}=\dfrac{10 \times 8}{3 \times 8} + \dfrac{5 \times 3}{8 \times 3}=\dfrac{80}{24} + \dfrac{15}{24}=\dfrac{80 + 15}{24}=\dfrac{95}{24} = \dfrac{95}{24}$ + + \item $\dfrac{2}{4} \times 5=\dfrac{2 \times 5}{4}=\dfrac{10}{4} = \dfrac{5}{2}$ + \item $\dfrac{3}{7} \times \dfrac{4}{7}=\dfrac{3 \times 4}{7 \times 7}=\dfrac{12}{49} = \dfrac{12}{49}$ + \item $\dfrac{10}{4} \times \dfrac{- 10}{28}=\dfrac{10(- 10)}{4 \times 28}=\dfrac{- 100}{112} = \dfrac{- 25}{28}$ + \item $\dfrac{\dfrac{6}{4}}{\dfrac{9}{3}}=\dfrac{6}{4} \times \dfrac{3}{9}=\dfrac{6 \times 3}{4 \times 9}=\dfrac{18}{36} = \dfrac{1}{2}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 54 photos prises dont 26 ratées. + \item en juillet, il y a eu 44 photos réussies et 32 ratées. + \item en août, il y a eu 61 photos dont une proportion de 0.26 de photos ratées. + \item en septembre, il y a eu 7 photos ratées, ce qui correspondait à 14.0\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 28 & 44 & 45 & 43 & 160\\ + \hline + Ratées & 26 & 32 & 16 & 7 & 81\\ + \hline + Total & 54 & 76 & 61 & 50 & 241\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{160}{241} = 0.66 = 66\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{32 - 26}{26} = \frac{6}{26} = 0.23 = 23\% + \] + \item De juillet à août + \[ + \frac{16 - 32}{32} = \frac{-16}{32} = -0.5 = -50\% + \] + \item De août à septembre + \[ + \frac{7 - 16}{16} = \frac{-9}{16} = -0.56 = -56\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/25_DM1.tex b/2nd/Evaluations/DM_2021-09-27/25_DM1.tex new file mode 100644 index 0000000..9fad912 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/25_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill PRAT Lilou} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{9}{8} + \dfrac{7}{8}$ + \item $\dfrac{9}{4} + 9$ + + \item $\dfrac{3}{7} + \dfrac{8}{14}$ + \item $\dfrac{5}{10} + \dfrac{2}{10}$ + + \item $\dfrac{5}{8} \times 1$ + \item $\dfrac{1}{4} \times \dfrac{5}{4}$ + + \item $\dfrac{1}{8} \times \dfrac{- 9}{80}$ + \item $\dfrac{\dfrac{8}{10}}{\dfrac{7}{2}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{9}{8} + \dfrac{7}{8}=\dfrac{9 + 7}{8}=\dfrac{16}{8} = 2$ + \item $\dfrac{9}{4} + 9=\dfrac{9}{4} + \dfrac{9}{1}=\dfrac{9}{4} + \dfrac{9 \times 4}{1 \times 4}=\dfrac{9}{4} + \dfrac{36}{4}=\dfrac{9 + 36}{4}=\dfrac{45}{4} = \dfrac{45}{4}$ + \item $\dfrac{3}{7} + \dfrac{8}{14}=\dfrac{3 \times 2}{7 \times 2} + \dfrac{8}{14}=\dfrac{6}{14} + \dfrac{8}{14}=\dfrac{6 + 8}{14}=\dfrac{14}{14} = 1$ + \item $\dfrac{5}{10} + \dfrac{2}{10}=\dfrac{5 + 2}{10}=\dfrac{7}{10} = \dfrac{7}{10}$ + + \item $\dfrac{5}{8} \times 1=\dfrac{5}{8} = \dfrac{5}{8}$ + \item $\dfrac{1}{4} \times \dfrac{5}{4}=\dfrac{1 \times 5}{4 \times 4}=\dfrac{5}{16} = \dfrac{5}{16}$ + \item $\dfrac{1}{8} \times \dfrac{- 9}{80}=\dfrac{1(- 9)}{8 \times 80}=\dfrac{- 9}{640} = \dfrac{- 9}{640}$ + \item $\dfrac{\dfrac{8}{10}}{\dfrac{7}{2}}=\dfrac{8}{10} \times \dfrac{2}{7}=\dfrac{8 \times 2}{10 \times 7}=\dfrac{16}{70} = \dfrac{8}{35}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 56 photos prises dont 29 ratées. + \item en juillet, il y a eu 50 photos réussies et 37 ratées. + \item en août, il y a eu 60 photos dont une proportion de 0.17 de photos ratées. + \item en septembre, il y a eu 11 photos ratées, ce qui correspondait à 21.15\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 27 & 50 & 50 & 41 & 168\\ + \hline + Ratées & 29 & 37 & 10 & 11 & 87\\ + \hline + Total & 56 & 87 & 60 & 52 & 255\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{168}{255} = 0.66 = 65\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{37 - 29}{29} = \frac{8}{29} = 0.28 = 27\% + \] + \item De juillet à août + \[ + \frac{10 - 37}{37} = \frac{-27}{37} = -0.73 = -72\% + \] + \item De août à septembre + \[ + \frac{11 - 10}{10} = \frac{1}{10} = 0.1 = 10\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/26_DM1.tex b/2nd/Evaluations/DM_2021-09-27/26_DM1.tex new file mode 100644 index 0000000..e62af9c --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/26_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill RINALDI Gianni} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{9}{7} + \dfrac{3}{7}$ + \item $\dfrac{5}{7} + 6$ + + \item $\dfrac{1}{7} + \dfrac{10}{14}$ + \item $\dfrac{6}{8} + \dfrac{1}{7}$ + + \item $\dfrac{1}{5} \times 1$ + \item $\dfrac{5}{8} \times \dfrac{7}{8}$ + + \item $\dfrac{- 7}{2} \times \dfrac{- 1}{14}$ + \item $\dfrac{\dfrac{7}{6}}{\dfrac{10}{9}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{9}{7} + \dfrac{3}{7}=\dfrac{9 + 3}{7}=\dfrac{12}{7} = \dfrac{12}{7}$ + \item $\dfrac{5}{7} + 6=\dfrac{5}{7} + \dfrac{6}{1}=\dfrac{5}{7} + \dfrac{6 \times 7}{1 \times 7}=\dfrac{5}{7} + \dfrac{42}{7}=\dfrac{5 + 42}{7}=\dfrac{47}{7} = \dfrac{47}{7}$ + \item $\dfrac{1}{7} + \dfrac{10}{14}=\dfrac{1 \times 2}{7 \times 2} + \dfrac{10}{14}=\dfrac{2}{14} + \dfrac{10}{14}=\dfrac{2 + 10}{14}=\dfrac{12}{14} = \dfrac{6}{7}$ + \item $\dfrac{6}{8} + \dfrac{1}{7}=\dfrac{6 \times 7}{8 \times 7} + \dfrac{1 \times 8}{7 \times 8}=\dfrac{42}{56} + \dfrac{8}{56}=\dfrac{42 + 8}{56}=\dfrac{50}{56} = \dfrac{25}{28}$ + + \item $\dfrac{1}{5} \times 1=\dfrac{1}{5} = \dfrac{1}{5}$ + \item $\dfrac{5}{8} \times \dfrac{7}{8}=\dfrac{5 \times 7}{8 \times 8}=\dfrac{35}{64} = \dfrac{35}{64}$ + \item $\dfrac{- 7}{2} \times \dfrac{- 1}{14}=\dfrac{- 7(- 1)}{2 \times 14}=\dfrac{7}{28} = \dfrac{1}{4}$ + \item $\dfrac{\dfrac{7}{6}}{\dfrac{10}{9}}=\dfrac{7}{6} \times \dfrac{9}{10}=\dfrac{7 \times 9}{6 \times 10}=\dfrac{63}{60} = \dfrac{21}{20}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 55 photos prises dont 26 ratées. + \item en juillet, il y a eu 39 photos réussies et 33 ratées. + \item en août, il y a eu 66 photos dont une proportion de 0.3 de photos ratées. + \item en septembre, il y a eu 11 photos ratées, ce qui correspondait à 19.64\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 29 & 39 & 46 & 45 & 159\\ + \hline + Ratées & 26 & 33 & 20 & 11 & 90\\ + \hline + Total & 55 & 72 & 66 & 56 & 249\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{159}{249} = 0.64 = 63\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{33 - 26}{26} = \frac{7}{26} = 0.27 = 26\% + \] + \item De juillet à août + \[ + \frac{20 - 33}{33} = \frac{-13}{33} = -0.39 = -39\% + \] + \item De août à septembre + \[ + \frac{11 - 20}{20} = \frac{-9}{20} = -0.45 = -45\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/27_DM1.tex b/2nd/Evaluations/DM_2021-09-27/27_DM1.tex new file mode 100644 index 0000000..be95c5d --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/27_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill RIVERA--DRENEUC Kerly} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{2}{9} + \dfrac{7}{9}$ + \item $\dfrac{2}{8} + 5$ + + \item $\dfrac{2}{5} + \dfrac{1}{30}$ + \item $\dfrac{3}{8} + \dfrac{5}{3}$ + + \item $\dfrac{7}{5} \times 2$ + \item $\dfrac{10}{9} \times \dfrac{3}{9}$ + + \item $\dfrac{9}{7} \times \dfrac{3}{49}$ + \item $\dfrac{\dfrac{3}{7}}{\dfrac{2}{9}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{2}{9} + \dfrac{7}{9}=\dfrac{2 + 7}{9}=\dfrac{9}{9} = 1$ + \item $\dfrac{2}{8} + 5=\dfrac{2}{8} + \dfrac{5}{1}=\dfrac{2}{8} + \dfrac{5 \times 8}{1 \times 8}=\dfrac{2}{8} + \dfrac{40}{8}=\dfrac{2 + 40}{8}=\dfrac{42}{8} = \dfrac{21}{4}$ + \item $\dfrac{2}{5} + \dfrac{1}{30}=\dfrac{2 \times 6}{5 \times 6} + \dfrac{1}{30}=\dfrac{12}{30} + \dfrac{1}{30}=\dfrac{12 + 1}{30}=\dfrac{13}{30} = \dfrac{13}{30}$ + \item $\dfrac{3}{8} + \dfrac{5}{3}=\dfrac{3 \times 3}{8 \times 3} + \dfrac{5 \times 8}{3 \times 8}=\dfrac{9}{24} + \dfrac{40}{24}=\dfrac{9 + 40}{24}=\dfrac{49}{24} = \dfrac{49}{24}$ + + \item $\dfrac{7}{5} \times 2=\dfrac{7 \times 2}{5}=\dfrac{14}{5} = \dfrac{14}{5}$ + \item $\dfrac{10}{9} \times \dfrac{3}{9}=\dfrac{10 \times 3}{9 \times 9}=\dfrac{30}{81} = \dfrac{10}{27}$ + \item $\dfrac{9}{7} \times \dfrac{3}{49}=\dfrac{9 \times 3}{7 \times 49}=\dfrac{27}{343} = \dfrac{27}{343}$ + \item $\dfrac{\dfrac{3}{7}}{\dfrac{2}{9}}=\dfrac{3}{7} \times \dfrac{9}{2}=\dfrac{3 \times 9}{7 \times 2}=\dfrac{27}{14} = \dfrac{27}{14}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 45 photos prises dont 21 ratées. + \item en juillet, il y a eu 36 photos réussies et 41 ratées. + \item en août, il y a eu 54 photos dont une proportion de 0.26 de photos ratées. + \item en septembre, il y a eu 5 photos ratées, ce qui correspondait à 9.43\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 24 & 36 & 40 & 48 & 148\\ + \hline + Ratées & 21 & 41 & 14 & 5 & 81\\ + \hline + Total & 45 & 77 & 54 & 53 & 229\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{148}{229} = 0.65 = 64\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{41 - 21}{21} = \frac{20}{21} = 0.95 = 95\% + \] + \item De juillet à août + \[ + \frac{14 - 41}{41} = \frac{-27}{41} = -0.66 = -65\% + \] + \item De août à septembre + \[ + \frac{5 - 14}{14} = \frac{-9}{14} = -0.64 = -64\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/28_DM1.tex b/2nd/Evaluations/DM_2021-09-27/28_DM1.tex new file mode 100644 index 0000000..68433e8 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/28_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill ROSA DOS SANTOS Andréa} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{8}{3} + \dfrac{4}{3}$ + \item $\dfrac{8}{7} + 7$ + + \item $\dfrac{7}{8} + \dfrac{6}{72}$ + \item $\dfrac{8}{3} + \dfrac{10}{7}$ + + \item $\dfrac{2}{7} \times 9$ + \item $\dfrac{4}{9} \times \dfrac{7}{9}$ + + \item $\dfrac{- 7}{8} \times \dfrac{7}{56}$ + \item $\dfrac{\dfrac{8}{10}}{\dfrac{1}{8}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{8}{3} + \dfrac{4}{3}=\dfrac{8 + 4}{3}=\dfrac{12}{3} = 4$ + \item $\dfrac{8}{7} + 7=\dfrac{8}{7} + \dfrac{7}{1}=\dfrac{8}{7} + \dfrac{7 \times 7}{1 \times 7}=\dfrac{8}{7} + \dfrac{49}{7}=\dfrac{8 + 49}{7}=\dfrac{57}{7} = \dfrac{57}{7}$ + \item $\dfrac{7}{8} + \dfrac{6}{72}=\dfrac{7 \times 9}{8 \times 9} + \dfrac{6}{72}=\dfrac{63}{72} + \dfrac{6}{72}=\dfrac{63 + 6}{72}=\dfrac{69}{72} = \dfrac{23}{24}$ + \item $\dfrac{8}{3} + \dfrac{10}{7}=\dfrac{8 \times 7}{3 \times 7} + \dfrac{10 \times 3}{7 \times 3}=\dfrac{56}{21} + \dfrac{30}{21}=\dfrac{56 + 30}{21}=\dfrac{86}{21} = \dfrac{86}{21}$ + + \item $\dfrac{2}{7} \times 9=\dfrac{2 \times 9}{7}=\dfrac{18}{7} = \dfrac{18}{7}$ + \item $\dfrac{4}{9} \times \dfrac{7}{9}=\dfrac{4 \times 7}{9 \times 9}=\dfrac{28}{81} = \dfrac{28}{81}$ + \item $\dfrac{- 7}{8} \times \dfrac{7}{56}=\dfrac{- 7 \times 7}{8 \times 56}=\dfrac{- 49}{448} = \dfrac{- 7}{64}$ + \item $\dfrac{\dfrac{8}{10}}{\dfrac{1}{8}}=\dfrac{8}{10} \times \dfrac{8}{1}=\dfrac{8 \times 8}{10 \times 1}=\dfrac{64}{10} = \dfrac{32}{5}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 50 photos prises dont 23 ratées. + \item en juillet, il y a eu 31 photos réussies et 48 ratées. + \item en août, il y a eu 60 photos dont une proportion de 0.32 de photos ratées. + \item en septembre, il y a eu 11 photos ratées, ce qui correspondait à 20.75\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 27 & 31 & 41 & 42 & 141\\ + \hline + Ratées & 23 & 48 & 19 & 11 & 101\\ + \hline + Total & 50 & 79 & 60 & 53 & 242\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{141}{242} = 0.58 = 58\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{48 - 23}{23} = \frac{25}{23} = 1.09 = 108\% + \] + \item De juillet à août + \[ + \frac{19 - 48}{48} = \frac{-29}{48} = -0.6 = -60\% + \] + \item De août à septembre + \[ + \frac{11 - 19}{19} = \frac{-8}{19} = -0.42 = -42\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/29_DM1.tex b/2nd/Evaluations/DM_2021-09-27/29_DM1.tex new file mode 100644 index 0000000..d5fd6ed --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/29_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill SALAHDINE Abdel-Mounim} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{6}{7} + \dfrac{8}{7}$ + \item $\dfrac{6}{8} + 10$ + + \item $\dfrac{1}{2} + \dfrac{3}{8}$ + \item $\dfrac{6}{2} + \dfrac{5}{10}$ + + \item $\dfrac{6}{10} \times 1$ + \item $\dfrac{3}{5} \times \dfrac{3}{5}$ + + \item $\dfrac{- 1}{9} \times \dfrac{3}{63}$ + \item $\dfrac{\dfrac{7}{3}}{\dfrac{4}{3}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{6}{7} + \dfrac{8}{7}=\dfrac{6 + 8}{7}=\dfrac{14}{7} = 2$ + \item $\dfrac{6}{8} + 10=\dfrac{6}{8} + \dfrac{10}{1}=\dfrac{6}{8} + \dfrac{10 \times 8}{1 \times 8}=\dfrac{6}{8} + \dfrac{80}{8}=\dfrac{6 + 80}{8}=\dfrac{86}{8} = \dfrac{43}{4}$ + \item $\dfrac{1}{2} + \dfrac{3}{8}=\dfrac{1 \times 4}{2 \times 4} + \dfrac{3}{8}=\dfrac{4}{8} + \dfrac{3}{8}=\dfrac{4 + 3}{8}=\dfrac{7}{8} = \dfrac{7}{8}$ + \item $\dfrac{6}{2} + \dfrac{5}{10}=\dfrac{6 \times 5}{2 \times 5} + \dfrac{5}{10}=\dfrac{30}{10} + \dfrac{5}{10}=\dfrac{30 + 5}{10}=\dfrac{35}{10} = \dfrac{7}{2}$ + + \item $\dfrac{6}{10} \times 1=\dfrac{6}{10} = \dfrac{3}{5}$ + \item $\dfrac{3}{5} \times \dfrac{3}{5}=\dfrac{3 \times 3}{5 \times 5}=\dfrac{9}{25} = \dfrac{9}{25}$ + \item $\dfrac{- 1}{9} \times \dfrac{3}{63}=\dfrac{- 1 \times 3}{9 \times 63}=\dfrac{- 3}{567} = \dfrac{- 1}{189}$ + \item $\dfrac{\dfrac{7}{3}}{\dfrac{4}{3}}=\dfrac{7}{3} \times \dfrac{3}{4}=\dfrac{7 \times 3}{3 \times 4}=\dfrac{21}{12} = \dfrac{7}{4}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 52 photos prises dont 26 ratées. + \item en juillet, il y a eu 48 photos réussies et 35 ratées. + \item en août, il y a eu 69 photos dont une proportion de 0.28 de photos ratées. + \item en septembre, il y a eu 11 photos ratées, ce qui correspondait à 19.3\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 26 & 48 & 50 & 46 & 170\\ + \hline + Ratées & 26 & 35 & 19 & 11 & 91\\ + \hline + Total & 52 & 83 & 69 & 57 & 261\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{170}{261} = 0.65 = 65\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{35 - 26}{26} = \frac{9}{26} = 0.35 = 34\% + \] + \item De juillet à août + \[ + \frac{19 - 35}{35} = \frac{-16}{35} = -0.46 = -45\% + \] + \item De août à septembre + \[ + \frac{11 - 19}{19} = \frac{-8}{19} = -0.42 = -42\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/30_DM1.tex b/2nd/Evaluations/DM_2021-09-27/30_DM1.tex new file mode 100644 index 0000000..0fb43a6 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/30_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill TAIBI Shaima} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{7}{9} + \dfrac{1}{9}$ + \item $\dfrac{9}{3} + 1$ + + \item $\dfrac{1}{2} + \dfrac{9}{6}$ + \item $\dfrac{6}{9} + \dfrac{3}{2}$ + + \item $\dfrac{4}{8} \times 3$ + \item $\dfrac{5}{4} \times \dfrac{1}{4}$ + + \item $\dfrac{- 2}{3} \times \dfrac{- 2}{30}$ + \item $\dfrac{\dfrac{5}{8}}{\dfrac{7}{3}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{7}{9} + \dfrac{1}{9}=\dfrac{7 + 1}{9}=\dfrac{8}{9} = \dfrac{8}{9}$ + \item $\dfrac{9}{3} + 1=\dfrac{9}{3} + \dfrac{1}{1}=\dfrac{9}{3} + \dfrac{1 \times 3}{1 \times 3}=\dfrac{9}{3} + \dfrac{3}{3}=\dfrac{9 + 3}{3}=\dfrac{12}{3} = 4$ + \item $\dfrac{1}{2} + \dfrac{9}{6}=\dfrac{1 \times 3}{2 \times 3} + \dfrac{9}{6}=\dfrac{3}{6} + \dfrac{9}{6}=\dfrac{3 + 9}{6}=\dfrac{12}{6} = 2$ + \item $\dfrac{6}{9} + \dfrac{3}{2}=\dfrac{6 \times 2}{9 \times 2} + \dfrac{3 \times 9}{2 \times 9}=\dfrac{12}{18} + \dfrac{27}{18}=\dfrac{12 + 27}{18}=\dfrac{39}{18} = \dfrac{13}{6}$ + + \item $\dfrac{4}{8} \times 3=\dfrac{4 \times 3}{8}=\dfrac{12}{8} = \dfrac{3}{2}$ + \item $\dfrac{5}{4} \times \dfrac{1}{4}=\dfrac{5 \times 1}{4 \times 4}=\dfrac{5}{16} = \dfrac{5}{16}$ + \item $\dfrac{- 2}{3} \times \dfrac{- 2}{30}=\dfrac{- 2(- 2)}{3 \times 30}=\dfrac{4}{90} = \dfrac{2}{45}$ + \item $\dfrac{\dfrac{5}{8}}{\dfrac{7}{3}}=\dfrac{5}{8} \times \dfrac{3}{7}=\dfrac{5 \times 3}{8 \times 7}=\dfrac{15}{56} = \dfrac{15}{56}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 49 photos prises dont 22 ratées. + \item en juillet, il y a eu 44 photos réussies et 43 ratées. + \item en août, il y a eu 65 photos dont une proportion de 0.28 de photos ratées. + \item en septembre, il y a eu 14 photos ratées, ce qui correspondait à 25.45\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 27 & 44 & 47 & 41 & 159\\ + \hline + Ratées & 22 & 43 & 18 & 14 & 97\\ + \hline + Total & 49 & 87 & 65 & 55 & 256\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{159}{256} = 0.62 = 62\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{43 - 22}{22} = \frac{21}{22} = 0.95 = 95\% + \] + \item De juillet à août + \[ + \frac{18 - 43}{43} = \frac{-25}{43} = -0.58 = -58\% + \] + \item De août à septembre + \[ + \frac{14 - 18}{18} = \frac{-4}{18} = -0.22 = -22\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/31_DM1.tex b/2nd/Evaluations/DM_2021-09-27/31_DM1.tex new file mode 100644 index 0000000..a365168 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/31_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill TELEGONE Angie} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{6}{9} + \dfrac{1}{9}$ + \item $\dfrac{3}{2} + 4$ + + \item $\dfrac{10}{8} + \dfrac{5}{80}$ + \item $\dfrac{8}{5} + \dfrac{3}{10}$ + + \item $\dfrac{7}{2} \times 7$ + \item $\dfrac{5}{9} \times \dfrac{6}{9}$ + + \item $\dfrac{8}{3} \times \dfrac{- 9}{9}$ + \item $\dfrac{\dfrac{2}{4}}{\dfrac{1}{6}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{6}{9} + \dfrac{1}{9}=\dfrac{6 + 1}{9}=\dfrac{7}{9} = \dfrac{7}{9}$ + \item $\dfrac{3}{2} + 4=\dfrac{3}{2} + \dfrac{4}{1}=\dfrac{3}{2} + \dfrac{4 \times 2}{1 \times 2}=\dfrac{3}{2} + \dfrac{8}{2}=\dfrac{3 + 8}{2}=\dfrac{11}{2} = \dfrac{11}{2}$ + \item $\dfrac{10}{8} + \dfrac{5}{80}=\dfrac{10 \times 10}{8 \times 10} + \dfrac{5}{80}=\dfrac{100}{80} + \dfrac{5}{80}=\dfrac{100 + 5}{80}=\dfrac{105}{80} = \dfrac{21}{16}$ + \item $\dfrac{8}{5} + \dfrac{3}{10}=\dfrac{8 \times 2}{5 \times 2} + \dfrac{3}{10}=\dfrac{16}{10} + \dfrac{3}{10}=\dfrac{16 + 3}{10}=\dfrac{19}{10} = \dfrac{19}{10}$ + + \item $\dfrac{7}{2} \times 7=\dfrac{7 \times 7}{2}=\dfrac{49}{2} = \dfrac{49}{2}$ + \item $\dfrac{5}{9} \times \dfrac{6}{9}=\dfrac{5 \times 6}{9 \times 9}=\dfrac{30}{81} = \dfrac{10}{27}$ + \item $\dfrac{8}{3} \times \dfrac{- 9}{9}=\dfrac{8(- 9)}{3 \times 9}=\dfrac{- 72}{27} = \dfrac{- 8}{3}$ + \item $\dfrac{\dfrac{2}{4}}{\dfrac{1}{6}}=\dfrac{2}{4} \times \dfrac{6}{1}=\dfrac{2 \times 6}{4 \times 1}=\dfrac{12}{4} = 3$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 59 photos prises dont 30 ratées. + \item en juillet, il y a eu 49 photos réussies et 31 ratées. + \item en août, il y a eu 59 photos dont une proportion de 0.24 de photos ratées. + \item en septembre, il y a eu 13 photos ratées, ce qui correspondait à 20.63\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 29 & 49 & 45 & 50 & 173\\ + \hline + Ratées & 30 & 31 & 14 & 13 & 88\\ + \hline + Total & 59 & 80 & 59 & 63 & 261\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{173}{261} = 0.66 = 66\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{31 - 30}{30} = \frac{1}{30} = 0.03 = 3\% + \] + \item De juillet à août + \[ + \frac{14 - 31}{31} = \frac{-17}{31} = -0.55 = -54\% + \] + \item De août à septembre + \[ + \frac{13 - 14}{14} = \frac{-1}{14} = -0.07 = -7\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git a/2nd/Evaluations/DM_2021-09-27/32_DM1.tex b/2nd/Evaluations/DM_2021-09-27/32_DM1.tex new file mode 100644 index 0000000..b6ad2b8 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/32_DM1.tex @@ -0,0 +1,123 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill ZERDOUNI Adam} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{9}{7} + \dfrac{2}{7}$ + \item $\dfrac{3}{9} + 5$ + + \item $\dfrac{5}{2} + \dfrac{4}{12}$ + \item $\dfrac{8}{6} + \dfrac{9}{7}$ + + \item $\dfrac{6}{10} \times 3$ + \item $\dfrac{4}{6} \times \dfrac{9}{6}$ + + \item $\dfrac{3}{10} \times \dfrac{- 9}{90}$ + \item $\dfrac{\dfrac{9}{5}}{\dfrac{10}{3}}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{9}{7} + \dfrac{2}{7}=\dfrac{9 + 2}{7}=\dfrac{11}{7} = \dfrac{11}{7}$ + \item $\dfrac{3}{9} + 5=\dfrac{3}{9} + \dfrac{5}{1}=\dfrac{3}{9} + \dfrac{5 \times 9}{1 \times 9}=\dfrac{3}{9} + \dfrac{45}{9}=\dfrac{3 + 45}{9}=\dfrac{48}{9} = \dfrac{16}{3}$ + \item $\dfrac{5}{2} + \dfrac{4}{12}=\dfrac{5 \times 6}{2 \times 6} + \dfrac{4}{12}=\dfrac{30}{12} + \dfrac{4}{12}=\dfrac{30 + 4}{12}=\dfrac{34}{12} = \dfrac{17}{6}$ + \item $\dfrac{8}{6} + \dfrac{9}{7}=\dfrac{8 \times 7}{6 \times 7} + \dfrac{9 \times 6}{7 \times 6}=\dfrac{56}{42} + \dfrac{54}{42}=\dfrac{56 + 54}{42}=\dfrac{110}{42} = \dfrac{55}{21}$ + + \item $\dfrac{6}{10} \times 3=\dfrac{6 \times 3}{10}=\dfrac{18}{10} = \dfrac{9}{5}$ + \item $\dfrac{4}{6} \times \dfrac{9}{6}=\dfrac{4 \times 9}{6 \times 6}=\dfrac{36}{36} = 1$ + \item $\dfrac{3}{10} \times \dfrac{- 9}{90}=\dfrac{3(- 9)}{10 \times 90}=\dfrac{- 27}{900} = \dfrac{- 3}{100}$ + \item $\dfrac{\dfrac{9}{5}}{\dfrac{10}{3}}=\dfrac{9}{5} \times \dfrac{3}{10}=\dfrac{9 \times 3}{5 \times 10}=\dfrac{27}{50} = \dfrac{27}{50}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + \item en juin, il y a eu 54 photos prises dont 30 ratées. + \item en juillet, il y a eu 44 photos réussies et 48 ratées. + \item en août, il y a eu 53 photos dont une proportion de 0.23 de photos ratées. + \item en septembre, il y a eu 10 photos ratées, ce qui correspondait à 17.86\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & 24 & 44 & 41 & 46 & 155\\ + \hline + Ratées & 30 & 48 & 12 & 10 & 100\\ + \hline + Total & 54 & 92 & 53 & 56 & 255\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{155}{255} = 0.61 = 60\% + \] + \item + \begin{itemize} + \item De juin à juillet + \[ + \frac{48 - 30}{30} = \frac{18}{30} = 0.6 = 60\% + \] + \item De juillet à août + \[ + \frac{12 - 48}{48} = \frac{-36}{48} = -0.75 = -75\% + \] + \item De août à septembre + \[ + \frac{10 - 12}{12} = \frac{-2}{12} = -0.17 = -16\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document} \ No newline at end of file diff --git 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a/2nd/Evaluations/DM_2021-09-27/tpl_DM1.tex b/2nd/Evaluations/DM_2021-09-27/tpl_DM1.tex new file mode 100644 index 0000000..9de0018 --- /dev/null +++ b/2nd/Evaluations/DM_2021-09-27/tpl_DM1.tex @@ -0,0 +1,149 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +% Title Page +\title{DM1 \hfill \Var{Nom}} +\tribe{2nd6} +\date{À rendre pour Vendredi 1 octobre 2021} + +\xsimsetup{ + solution/print = false +} + +\begin{document} +\maketitle + +\begin{exercise}[subtitle={Calculs avec des fractions}] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \begin{multicols}{3} + \begin{enumerate}[label={\Alph*=}] + %- set A = Expression.random("{a} / {b} + {c} / {b}", ["a!=b", "c!=b", "b > 1"], min_max=(1, 10)) + \item $\Var{A}$ + %- set B = Expression.random("{a} / {b} + {c}", ["a!=b", "b > 1"], min_max=(1, 10)) + \item $\Var{B}$ + + %- set C = Expression.random("{a} / {b} + {c} / {k*b}", ["a!=b", "c!=b", "b > 1"], min_max=(1, 10)) + \item $\Var{C}$ + %- set D = Expression.random("{a} / {b} + {c} / {d}", ["a!=b", "c!=d", "b > 1", "d > 1"], min_max=(0, 10)) + \item $\Var{D}$ + + %- set E = Expression.random("{a} / {b} * {c}", ["a!=b", "b > 1"], min_max=(1, 10)) + \item $\Var{E}$ + %- set F = Expression.random("{a} / {b} * {c} / {b}", ["a!=b", "c!=b", "b > 1"], min_max=(1, 10)) + \item $\Var{F}$ + + %- set G = Expression.random("{a} / {b} * {c} / {k*b}", ["a!=b", "c!=b", "b > 1", "k > 1"], min_max=(-10, 10)) + \item $\Var{G}$ + %- set H = Expression.random("({a} / {b}) / ({c} / {d})", ["a!=b", "c!=d", "b > 1", "d > 1"], min_max=(0, 10)) + \item $\Var{H}$ + \end{enumerate} + \end{multicols} +\end{exercise} + + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\Var{A.simplify().explain() | join('=')} = \Var{A.simplify().simplified}$ + \item $\Var{B.simplify().explain() | join('=')} = \Var{B.simplify().simplified}$ + \item $\Var{C.simplify().explain() | join('=')} = \Var{C.simplify().simplified}$ + \item $\Var{D.simplify().explain() | join('=')} = \Var{D.simplify().simplified}$ + + \item $\Var{E.simplify().explain() | join('=')} = \Var{E.simplify().simplified}$ + \item $\Var{F.simplify().explain() | join('=')} = \Var{F.simplify().simplified}$ + \item $\Var{G.simplify().explain() | join('=')} = \Var{G.simplify().simplified}$ + \item $\Var{H.simplify().explain() | join('=')} = \Var{H.simplify().simplified}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Radars}] + Un radar de la sécurité routière prend en photo les véhicules en ecvès de vitesse. Sur certaines photos, il n'est pas possible de lire le numéro d'immatriculation du véhicule., on dit alors que la photo est ratée; dans le cas contraire, on dit qu'elle est réussie. + + Le radar a pris des photos pendant l'été: + \begin{itemize} + %- set juin_reu, juin_rat = random_list(["a", "b"], min_max=(20, 30)) + %- set juin_tot = juin_reu + juin_rat + \item en juin, il y a eu \Var{juin_tot} photos prises dont \Var{juin_rat} ratées. + %- set juil_reu, juil_rat = random_list(["a", "b"], min_max=(30, 50)) + %- set juil_tot = juil_reu + juil_rat + \item en juillet, il y a eu \Var{juil_reu} photos réussies et \Var{juil_rat} ratées. + %- set aout_rat = random_list(["a"], min_max=(10, 20))[0] + %- set aout_reu = random_list(["a"], min_max=(40, 50))[0] + %- set aout_tot = aout_reu + aout_rat + %- set aout_prop_rat = aout_rat / aout_tot + \item en août, il y a eu \Var{aout_tot} photos dont une proportion de \Var{aout_prop_rat | round(2)} de photos ratées. + %- set sept_rat = random_list(["a"], min_max=(5, 15))[0] + %- set sept_reu = random_list(["a"], min_max=(40, 50))[0] + %- set sept_tot = sept_reu + sept_rat + %- set sept_prop_rat = sept_rat / sept_tot + \item en septembre, il y a eu \Var{sept_rat} photos ratées, ce qui correspondait à \Var{ (sept_prop_rat*100) | round(2)}\% des photos prises. + \end{itemize} + + \begin{enumerate} + \item Compléter le tableau suivant. + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & & & & &\\ + \hline + Ratées & & & & &\\ + \hline + Total & & & & & \\ + \hline + \end{tabular} + \end{center} + \item Sur l'ensemble de ces 4 mois, quel a été le pourcentage de photos réussies? + \item Décrire l'évolution relative du nombre de photos ratées mois par mois. + \end{enumerate} +\end{exercise} + +\begin{solution} + \textit{La correction est automatique, il peut y avoir des problèmes d'arrondis.} + \begin{enumerate} + \item ~ + %- set reu_tot = juin_reu + juil_reu + aout_reu + sept_reu + %- set rat_tot = juin_rat + juil_rat + aout_rat + sept_rat + %- set tot_tot = juin_tot + juil_tot + aout_tot + sept_tot + \begin{center} + \begin{tabular}{|c|*{5}{c|}} + \hline + & Juin & Juillet & Août & Septembre & Total\\ + \hline + Réussies & \Var{juin_reu} & \Var{juil_reu} & \Var{aout_reu} & \Var{sept_reu} & \Var{reu_tot}\\ + \hline + Ratées & \Var{juin_rat} & \Var{juil_rat} & \Var{aout_rat} & \Var{sept_rat} & \Var{rat_tot}\\ + \hline + Total & \Var{juin_tot} & \Var{juil_tot} & \Var{aout_tot} & \Var{sept_tot} & \Var{tot_tot}\\ + \hline + \end{tabular} + \end{center} + \item Proportion de photos réussies + \[ + \frac{\Var{reu_tot}}{\Var{tot_tot}} = \Var{(reu_tot / tot_tot) | round(2)} = \Var{(reu_tot / tot_tot * 100) | int}\% + \] + \item + \begin{itemize} + \item De juin à juillet + %- set juin_juil = (juil_rat - juin_rat) / juin_rat + \[ + \frac{\Var{juil_rat} - \Var{juin_rat}}{\Var{juin_rat}} = \frac{\Var{juil_rat - juin_rat}}{\Var{juin_rat}} = \Var{juin_juil | round(2)} = \Var{(juin_juil*100) | int }\% + \] + \item De juillet à août + %- set juil_aout = (aout_rat - juil_rat) / juil_rat + \[ + \frac{\Var{aout_rat} - \Var{juil_rat}}{\Var{juil_rat}} = \frac{\Var{aout_rat - juil_rat}}{\Var{juil_rat}} = \Var{juil_aout | round(2)} = \Var{(juil_aout*100) | int }\% + \] + \item De août à septembre + %- set aout_sept = (sept_rat - aout_rat) / aout_rat + \[ + \frac{\Var{sept_rat} - \Var{aout_rat}}{\Var{aout_rat}} = \frac{\Var{sept_rat - aout_rat}}{\Var{aout_rat}} = \Var{aout_sept | round(2)} = \Var{(aout_sept*100) | int }\% + \] + \end{itemize} + \end{enumerate} +\end{solution} + + +\printsolutionstype{exercise} + +\end{document}

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