diff --git a/2nd/01_Proportion_et_fractions/1_exercises_tech.tex b/2nd/01_Proportion_et_fractions/1_exercises_tech.tex new file mode 100644 index 0000000..1b37ba2 --- /dev/null +++ b/2nd/01_Proportion_et_fractions/1_exercises_tech.tex @@ -0,0 +1,64 @@ +\begin{exercise}[subtitle={Multiplication de fractions}, step={3}, origin={Création}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\searchMode}] + Faire les calculs suivants + \begin{multicols}{4} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{- 6}{3} + \dfrac{- 7}{3}$ + \item $\dfrac{- 10}{5} + \dfrac{6}{5}$ + + \item $\dfrac{7}{10} + \dfrac{3}{90}$ + \item $\dfrac{10}{81} + \dfrac{5}{9}$ + + \item $\dfrac{7}{9} + \dfrac{3}{10}$ + \item $\dfrac{8}{5} + \dfrac{3}{7}$ + + \item $\dfrac{1}{a} + \dfrac{1}{2a}$ + \item $\dfrac{3}{5a} + \dfrac{1}{4a}$ + \end{enumerate} + \end{multicols} + +\end{exercise} + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{- 6}{3} + \dfrac{- 7}{3}=\dfrac{- 6 - 7}{3}=\dfrac{- 13}{3} = \dfrac{- 13}{3}$ + \item $\dfrac{- 10}{5} + \dfrac{6}{5}=\dfrac{- 10 + 6}{5}=\dfrac{- 4}{5} = \dfrac{- 4}{5}$ + \item $\dfrac{7}{10} + \dfrac{3}{90}=\dfrac{7 \times 9}{10 \times 9} + \dfrac{3}{90}=\dfrac{63}{90} + \dfrac{3}{90}=\dfrac{63 + 3}{90}=\dfrac{66}{90} = \dfrac{11}{15}$ + \item $\dfrac{10}{81} + \dfrac{5}{9}=\dfrac{10}{81} + \dfrac{5 \times 9}{9 \times 9}=\dfrac{10}{81} + \dfrac{45}{81}=\dfrac{10 + 45}{81}=\dfrac{55}{81} = \dfrac{55}{81}$ + \item $\dfrac{7}{9} + \dfrac{3}{10}=\dfrac{7 \times 10}{9 \times 10} + \dfrac{3 \times 9}{10 \times 9}=\dfrac{70}{90} + \dfrac{27}{90}=\dfrac{70 + 27}{90}=\dfrac{97}{90} = \dfrac{97}{90}$ + \item $\dfrac{- 6}{3} + \dfrac{- 7}{3}=\dfrac{- 6 - 7}{3}=\dfrac{- 13}{3} = \dfrac{- 13}{3}$ + \item $\dfrac{1}{a} + \dfrac{1}{2a} = \dfrac{2}{2a} + \dfrac{1}{2a} = \dfrac{2+1}{2a} = \dfrac{3}{2a}$ + \item $\dfrac{3}{5a} + \dfrac{1}{4a} = \dfrac{12}{20a} + \dfrac{5}{20a} = \dfrac{12+5}{2a} = \dfrac{17}{2a}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Multiplication de fractions}, step={3}, origin={Création}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\searchMode}] + Faire les calculs suivants + \begin{multicols}{4} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{7}{8} \times \dfrac{- 10}{8}$ + \item $B = \dfrac{3}{10} \times \dfrac{7}{10}$ + + \item $\dfrac{3}{4} \times \dfrac{9}{12}$ + \item $\dfrac{2}{30} \times \dfrac{4}{10}$ + + \item $\dfrac{9}{3} \times \dfrac{9}{7}$ + \item $\dfrac{5}{4} \times \dfrac{3}{7}$ + + \item $\dfrac{1}{a} * \dfrac{1}{2a}$ + \item $\dfrac{3}{5a} * \dfrac{1}{4a}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{7}{8} \times \dfrac{- 10}{8}=\dfrac{7(- 10)}{8 \times 8}=\dfrac{- 70}{64} = \dfrac{- 35}{32}$ + \item $\dfrac{3}{10} \times \dfrac{7}{10}=\dfrac{3 \times 7}{10 \times 10}=\dfrac{21}{100} = \dfrac{21}{100}$ + \item $\dfrac{3}{4} \times \dfrac{9}{12}=\dfrac{3 \times 9}{4 \times 12}=\dfrac{27}{48} = \dfrac{9}{16}$ + \item $\dfrac{2}{30} \times \dfrac{4}{10}=\dfrac{2 \times 4}{30 \times 10}=\dfrac{8}{300} = \dfrac{2}{75}$ + \item $\dfrac{9}{3} \times \dfrac{9}{7}=\dfrac{9 \times 9}{3 \times 7}=\dfrac{81}{21} = \dfrac{27}{7}$ + \item $\dfrac{7}{8} \times \dfrac{- 10}{8}=\dfrac{7(- 10)}{8 \times 8}=\dfrac{- 70}{64} = \dfrac{- 35}{32}$ + \item $\dfrac{1}{a} \times \dfrac{1}{2a} = \dfrac{1\times 1}{a\times 2a} = \dfrac{1}{2a^2}$ + \item $\dfrac{3}{5a} \times \dfrac{1}{4a} = \dfrac{3\times 1}{5a\times 4a} = \dfrac{3}{20a^2}$ + \end{enumerate} +\end{solution} diff --git a/2nd/01_Proportion_et_fractions/all_exercises.pdf b/2nd/01_Proportion_et_fractions/all_exercises.pdf index 9fe4f56..c4da229 100644 Binary files a/2nd/01_Proportion_et_fractions/all_exercises.pdf and b/2nd/01_Proportion_et_fractions/all_exercises.pdf differ diff --git a/2nd/01_Proportion_et_fractions/all_exercises.tex b/2nd/01_Proportion_et_fractions/all_exercises.tex index 5044892..1cc2b68 100644 --- a/2nd/01_Proportion_et_fractions/all_exercises.tex +++ b/2nd/01_Proportion_et_fractions/all_exercises.tex @@ -22,5 +22,6 @@ \maketitle \input{exercises.tex} +\input{1_exercises_tech.tex} \end{document} diff --git a/2nd/01_Proportion_et_fractions/bopytex_config.py b/2nd/01_Proportion_et_fractions/bopytex_config.py new file mode 100644 index 0000000..599b6b5 --- /dev/null +++ b/2nd/01_Proportion_et_fractions/bopytex_config.py @@ -0,0 +1,12 @@ +# bopytex_config.py +from mapytex.calculus.random import expression as random_expression +from mapytex import render +import random + +random.seed(0) # Controlling the seed allows to make subject reproductible + +render.set_render("tex") + +direct_access = { + "random_expression": random_expression, +} diff --git a/2nd/01_Proportion_et_fractions/exercises.tex b/2nd/01_Proportion_et_fractions/exercises.tex index 814ce17..96216e7 100644 --- a/2nd/01_Proportion_et_fractions/exercises.tex +++ b/2nd/01_Proportion_et_fractions/exercises.tex @@ -43,16 +43,17 @@ \end{exercise} \begin{solution} + \def\arraystretch{2} \begin{enumerate} - \item $\frac{120}{150} = \frac{4}{5} = 0.8 = 80\%$ - \item $\frac{5}{22} \approx 0.22 = 22\%$ + \item $\dfrac{120}{150} = \dfrac{4}{5} = 0.8 = 80\%$ + \item $\dfrac{5}{22} \approx 0.22 = 22\%$ \item \begin{tabular}{|p{4cm}|*{4}{c|}} \hline Camping & Les flots bleu & Cascade magique & Le tronc dégarni & La vallée plate\\ \hline - Proportion en fraction & $\frac{0}{35}$ & $\frac{10}{15}$ & $\frac{40}{75}$ & $\frac{100}{200}$ \\ + Proportion en fraction & $\dfrac{0}{35}$ & $\dfrac{10}{15}$ & $\dfrac{40}{75}$ & $\dfrac{100}{200}$ \\ \hline Proportion en décimal & 0 & 0.66 & 0.53 & 0.5 \\ \hline @@ -60,6 +61,7 @@ \hline \end{tabular} \end{enumerate} + \def\arraystretch{1.5} \end{solution} @@ -106,29 +108,31 @@ \end{exercise} \begin{solution} + \def\arraystretch{2} \begin{tabular}{|*{4}{c|}} \hline Proportion & Fraction irréductible & Effectifs associés & Valeur décimale \\ \hline - 10\% & $\frac{1}{10}$ & 10 pour 100, c'est comme 1 pour 10 & 0.1\\ + 10\% & $\dfrac{1}{10}$ & 10 pour 100, c'est comme 1 pour 10 & 0.1\\ \hline - 20\% & $\frac{1}{5}$ & 20 pour 100, c'est comme 1 pour 5 & 0.2\\ + 20\% & $\dfrac{1}{5}$ & 20 pour 100, c'est comme 1 pour 5 & 0.2\\ \hline - 25\% & $\frac{1}{4}$ & 25 pour 100, c'est comme 1 pour 4 & 0.25\\ + 25\% & $\dfrac{1}{4}$ & 25 pour 100, c'est comme 1 pour 4 & 0.25\\ \hline - 33.3\% & $\frac{333}{1000}$ & 33.3 pour 100, c'est comme 333 pour 1000 & 0.333\\ + 33.3\% & $\dfrac{333}{1000}$ & 33.3 pour 100, c'est comme 333 pour 1000 & 0.333\\ \hline - 50\% & $\frac{1}{2}$ & 50 pour 100, c'est comme 1 pour 2 & 0.5 \\ + 50\% & $\dfrac{1}{2}$ & 50 pour 100, c'est comme 1 pour 2 & 0.5 \\ \hline - 60\% & $\frac{3}{5}$ & 60 pour 100, c'est comme 3 pour 5 & 0.6 \\ + 60\% & $\dfrac{3}{5}$ & 60 pour 100, c'est comme 3 pour 5 & 0.6 \\ \hline - 66.7\% & $\frac{667}{1000}$ & 66.7 pour 100, c'est comme 667 pour 1000 & 0.667\\ + 66.7\% & $\dfrac{667}{1000}$ & 66.7 pour 100, c'est comme 667 pour 1000 & 0.667\\ \hline - 75\% & $\frac{3}{4}$ & 75 pour 100, c'est comme 3 pour 4 & 0.75 \\ + 75\% & $\dfrac{3}{4}$ & 75 pour 100, c'est comme 3 pour 4 & 0.75 \\ \hline 100\% & 1 & 100 pour 100, c'est comme 1 pour 1 & 1\\ \hline \end{tabular} + \def\arraystretch{1.5} \end{solution} \begin{exercise}[subtitle={Techniques}, step={1}, origin={MEpC}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\trainMode}] @@ -148,19 +152,21 @@ \end{exercise} \begin{solution} - \begin{enumerate} - \item $\frac{20}{100} \times 190 = 38$ - \item $\frac{2}{3} \times 126 = 84$ - \item $\frac{42}{100} = \frac{31}{50} = 0.42$ - \item $\frac{78}{100} = \frac{39}{50} = 0.78$ - \item $\frac{1,5}{5} = \frac{3}{10} = 0.3$ - \item $\frac{1500}{2300} = \frac{15}{23} \approx 0.65$ - \item $\frac{30}{100} \times 400 = 120$ - \item $\frac{0.6}{100} \times \np{2 000 000} = \np{12 000}$ - \item $ \frac{14}{0.4} = 35$ - \item $ \frac{150 000}{0.75} = 200 000$ - \item $ \frac{5\times 30}{0.24} = 625$ - \end{enumerate} + \begin{multicols}{3} + \begin{enumerate} + \item $\dfrac{20}{100} \times 190 = 38$ + \item $\dfrac{2}{3} \times 126 = 84$ + \item $\dfrac{42}{100} = \dfrac{31}{50} = 0.42$ + \item $\dfrac{78}{100} = \dfrac{39}{50} = 0.78$ + \item $\dfrac{1,5}{5} = \dfrac{3}{10} = 0.3$ + \item $\dfrac{1500}{2300} = \dfrac{15}{23} \approx 0.65$ + \item $\dfrac{30}{100} \times 400 = 120$ + \item $\dfrac{0.6}{100} \times \np{2 000 000} = \np{12 000}$ + \item $ \dfrac{14}{0.4} = 35$ + \item $ \dfrac{150 000}{0.75} = 200 000$ + \item $ \dfrac{5\times 30}{0.24} = 625$ + \end{enumerate} + \end{multicols} \end{solution} \begin{exercise}[subtitle={Radars}, step={1}, origin={MEpC}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\groupMode}] @@ -187,11 +193,11 @@ \begin{enumerate} \item Est-il possible de trouver deux nombres entiers distincts $a$ et $b$ tels que: \[ - \frac{1}{a} + \frac{1}{b} = 1 + \dfrac{1}{a} + \dfrac{1}{b} = 1 \] \item Est-il possible de trouver deux nombres entiers distincts $a$, $b$ et $c$ tels que: \[ - \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1 + \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} = 1 \] \item Avec 4 nombres? 5? Et plus? \end{enumerate} @@ -213,11 +219,11 @@ \end{multicols} \item Indiquez sur les disques les fractions correspondantes \[ - \frac{1}{2} \qquad - \frac{1}{3} \qquad - \frac{1}{4} \qquad - \frac{1}{8} \qquad - \frac{1}{12} \qquad + \dfrac{1}{2} \qquad + \dfrac{1}{3} \qquad + \dfrac{1}{4} \qquad + \dfrac{1}{8} \qquad + \dfrac{1}{12} \qquad \] \item Reconstituez un disque complet à l'aide de 3 portions. \item Reconstituez un disque complet à l'aide de 4 portions. diff --git a/2nd/01_Proportion_et_fractions/solutions.pdf b/2nd/01_Proportion_et_fractions/solutions.pdf index 5d18ea9..92aa79a 100644 Binary files a/2nd/01_Proportion_et_fractions/solutions.pdf and b/2nd/01_Proportion_et_fractions/solutions.pdf differ diff --git a/2nd/01_Proportion_et_fractions/solutions.tex b/2nd/01_Proportion_et_fractions/solutions.tex index 69496cc..5322452 100644 --- a/2nd/01_Proportion_et_fractions/solutions.tex +++ b/2nd/01_Proportion_et_fractions/solutions.tex @@ -22,7 +22,6 @@ \maketitle \input{exercises.tex} -%\printcollection{banque} -%\printsolutions{exercises} +\input{1_exercises_tech.tex} \end{document} diff --git a/2nd/01_Proportion_et_fractions/tpl_exercises_tech.tex b/2nd/01_Proportion_et_fractions/tpl_exercises_tech.tex new file mode 100644 index 0000000..c1bda40 --- /dev/null +++ b/2nd/01_Proportion_et_fractions/tpl_exercises_tech.tex @@ -0,0 +1,76 @@ +\begin{exercise}[subtitle={Multiplication de fractions}, step={3}, origin={Création}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\searchMode}] + Faire les calculs suivants + \begin{multicols}{4} + \begin{enumerate}[label={\Alph*=}] + %- set A = random_expression("{a} / {b} + {c} / {b}", ["a!=b", "c!=b", "b > 1"], global_config={"rejected":[-1, 0, 1]}) + \item $\Var{A}$ + %- set B = random_expression("{a} / {b} + {c} / {b}", ["a!=b", "c!=b", "b > 1"], global_config={"rejected":[-1, 0, 1]}) + \item $\Var{B}$ + + %- set C = random_expression("{a} / {b} + {c} / {d*b}", ["a!=b", "c!=b", "b > 1"], global_config={"min_max":(1, 10)}) + \item $\Var{C}$ + %- set D = random_expression("{a} / {d*b} + {c} / {b}", ["a!=b", "c!=b", "b > 1"], global_config={"min_max":(1, 10)}) + \item $\Var{D}$ + + %- set E = random_expression("{a} / {b} + {c} / {d}", ["a!=b", "c!=b", "gcd(b, d) == 1"], global_config={"min_max":(1, 10)}) + \item $\Var{E}$ + %- set F = random_expression("{a} / {b} + {c} / {d}", ["a!=b", "c!=b", "gcd(b, d) == 1"], global_config={"min_max":(1, 10)}) + \item $\Var{F}$ + + \item $\dfrac{1}{a} + \dfrac{1}{2a}$ + \item $\dfrac{3}{5a} + \dfrac{1}{4a}$ + \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 $\Var{A.simplify().explain() | join('=')} = \Var{A.simplify().simplified}$ + \item $\dfrac{1}{a} + \dfrac{1}{2a} = \dfrac{2}{2a} + \dfrac{1}{2a} = \dfrac{2+1}{2a} = \dfrac{3}{2a}$ + \item $\dfrac{3}{5a} + \dfrac{1}{4a} = \dfrac{12}{20a} + \dfrac{5}{20a} = \dfrac{12+5}{2a} = \dfrac{17}{2a}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Multiplication de fractions}, step={3}, origin={Création}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\searchMode}] + Faire les calculs suivants + \begin{multicols}{4} + \begin{enumerate}[label={\Alph*=}] + %- set A = random_expression("{a} / {b} * {c} / {b}", ["a!=b", "c!=b", "b > 1"], global_config={"rejected":[-1, 0, 1]}) + \item $\Var{A}$ + %- set B = random_expression("{a} / {b} * {c} / {b}", ["a!=b", "c!=b", "b > 1"], global_config={"rejected":[-1, 0, 1]}) + \item $B = \Var{B}$ + + %- set C = random_expression("{a} / {b} * {c} / {d*b}", ["a!=b", "c!=b", "b > 1"], global_config={"min_max":(1, 10)}) + \item $\Var{C}$ + %- set D = random_expression("{a} / {d*b} * {c} / {b}", ["a!=b", "c!=b", "b > 1"], global_config={"min_max":(1, 10)}) + \item $\Var{D}$ + + %- set E = random_expression("{a} / {b} * {c} / {d}", ["a!=b", "c!=b", "gcd(b, d) == 1"], global_config={"min_max":(1, 10)}) + \item $\Var{E}$ + %- set F = random_expression("{a} / {b} * {c} / {d}", ["a!=b", "c!=b", "gcd(b, d) == 1"], global_config={"min_max":(1, 10)}) + \item $\Var{F}$ + + \item $\dfrac{1}{a} * \dfrac{1}{2a}$ + \item $\dfrac{3}{5a} * \dfrac{1}{4a}$ + \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 $\Var{A.simplify().explain() | join('=')} = \Var{A.simplify().simplified}$ + \item $\dfrac{1}{a} \times \dfrac{1}{2a} = \dfrac{1\times 1}{a\times 2a} = \dfrac{1}{2a^2}$ + \item $\dfrac{3}{5a} \times \dfrac{1}{4a} = \dfrac{3\times 1}{5a\times 4a} = \dfrac{3}{20a^2}$ + \end{enumerate} +\end{solution}