192 lines
8.0 KiB
TeX
192 lines
8.0 KiB
TeX
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\documentclass[a5paper,10pt, table]{/media/documents/Cours/Prof/Enseignements/2015-2016/tools/style/classDS}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2015-2016/2015_2016}
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%\geometry{left=10mm,right=10mm, top=10mm, bottom=10mm}
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% Title Page
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\titre{1}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Troisième}
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\date{7 decembre 2015}
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%\duree{1 heure}
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\sujet{\Var{infos.num}}
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% DS DSCorr DM DMCorr Corr
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\typedoc{DM}
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\geometry{left=10mm,right=10mm, bottom= 10mm, top=10mm}
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%\printanswers
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\begin{document}
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\maketitle
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\ifprintanswers
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\begin{center}
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\Large Solution
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\end{center}
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\normalsize
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\else
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\textbf{Vous devez rendre le sujet avec la copie.}
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\fi
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\begin{questions}
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\question Completer ces opérations à trous pour qu'il y est égalité.
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\begin{multicols}{2}
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\begin{parts}
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\Block{set a,b,ans,c = random_str("{a},{b},{a*c},{b*c}", conditions = ["{a} != {b}"], val_min = 2, val_max = 10).split(',')}%
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\part $\dfrac{\Var{a}}{\Var{b}} = \dfrac{\quad \ldots \quad}{\Var{c}}$
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\begin{solution}
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$\dfrac{\Var{a}}{\Var{b}} = \dfrac{\Var{ans}}{\Var{c}}$
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\end{solution}
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\Block{set a,b,ans,c = random_str("{a*c},{b*c},{a},{b}", conditions = ["{a} != {b}"], val_min = 2, val_max = 10).split(',')}%
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\part $\dfrac{\Var{a}}{\Var{b}} = \dfrac{\quad \cdots \quad}{\Var{c}}$
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\begin{solution}
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$\dfrac{\Var{a}}{\Var{b}} = \dfrac{\Var{ans}}{\Var{c}}$
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\end{solution}
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% Facile
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\Block{set a,b,tot,ans,c = random_str("{a},{b},{a+b},{a+b-c},{c}", val_min = 25, val_max = 200).split(',')}
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\part $\Var{a} + \Var{b} = \quad \cdots \quad + \Var{c}$
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\begin{solution}
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$\Var{a} + \Var{b} = \Var{ans} + \Var{c} = \Var{tot}$
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\end{solution}
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% Soustration à gauche
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\Block{set a,b,tot,ans,c = random_str("{a},{b},{a-b},{a-b-c},{c}", conditions = ["{a-b-c}>0"], val_min = 25, val_max = 200).split(',')}
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\part $\Var{a} - \Var{b} = \quad \cdots \quad + \Var{c}$
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\begin{solution}
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$\Var{a} - \Var{b} = \Var{ans} + \Var{c} = \Var{tot}$
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\end{solution}
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% Soustration des deux côtés
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\Block{set a,b,tot,ans,c = random_str("{a},{b},{a-b},{a-b+c},{c}", conditions = ["{a-b+c}>0"], val_min = 25, val_max = 200).split(',')}
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\part $\Var{a} - \Var{b} = \quad \cdots \quad - \Var{c}$
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\begin{solution}
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$\Var{a} - \Var{b} = \Var{ans} - \Var{c} = \Var{tot}$
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\end{solution}
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% Trou négatif
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\Block{set a,b,tot,ans,c = random_str("{a},{b},{a+b},{a+b-c},{c}", conditions = ["{a+b-c}<0"], val_min = 25, val_max = 200).split(',')}
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\part $\Var{a} + \Var{b} = \quad \cdots \quad + \Var{c}$
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\begin{solution}
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$\Var{a} + \Var{b} = \Var{ans} + \Var{c} = \Var{tot}$
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\end{solution}
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% Multiplications
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\Block{set a,b,tot,ans,c = random_str("{a}, {7*b}, {a*7*b}, {b}, {a*7}", val_min=2, val_max=14).split(',')}
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\part $\Var{a} \times \Var{b} = \quad \cdots \quad \times \Var{c}$
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\begin{solution}
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$\Var{a} \times \Var{b} = \Var{ans} \times \Var{c} = \Var{tot}$
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\end{solution}
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% Multiplications
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\Block{set a,b,tot,ans,c = random_str("{a}, {4*b}, {a*4*b}, {b}, {a*4}", val_min=2, val_max=20).split(',')}
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\part $\Var{a} \times \Var{b} = \quad \cdots \quad \times \Var{c}$
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\begin{solution}
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$\Var{a} \times \Var{b} = \Var{ans} \times \Var{c} = \Var{tot}$
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\end{solution}
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\end{parts}
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\end{multicols}
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\question Construire les deux triangles suivant en respectant les mesures.
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\begin{parts}
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\Block{set a,b,c = random_str("{a},{b},{c}",conditions = ["{c} > {b} + {a}"], val_min = 1).split(',')}
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\part Le triangle $ABC$ tel que $AB = \Var{a}$, $AC = \Var{b}$ et $BC = \Var{c}$.
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\Block{set a,b,c = random_str("{a},{b*10},{c*10}",conditions = ["{b} + {c} < 16"], val_min = 3).split(',')}
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\part Le triangle $IJK$ tel que $IJ = \Var{a}$, $\widehat{JIK} = \Var{b}^o$ et $\widehat{IJK} = \Var{c}^o$.
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\end{parts}
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\question Faire les calculs suivants en \textbf{détaillant les étapes}.
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\begin{multicols}{2}
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\begin{parts}
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\Block{set e = Expression.random("{a}+{b}*{c}", val_min = 2, val_max = 20)}
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\part $A = \Var{e}$
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\begin{solution}
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$\Var{e.simplify().explain() | join('=')}$
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\end{solution}
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\Block{set e = Expression.random("{a}*{b}+{c}", val_min = 2, val_max = 20)}
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\part $B = \Var{e}$
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\begin{solution}
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$\Var{e.simplify().explain() | join('=')}$
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\end{solution}
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\Block{set e = Expression.random("{a}*({b}+{c})", val_min = 2, val_max = 20)}
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\part $C = \Var{e}$
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\begin{solution}
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$\Var{e.simplify().explain() | join('=')}$
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\end{solution}
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\Block{set e = Expression.random("{a}*{b}-{c}", val_min = 2, val_max = 20)}
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\part $C = \Var{e}$
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\begin{solution}
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$\Var{e.simplify().explain() | join('=')}$
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\end{solution}
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\Block{set e = Expression.random("{a}+{b}+{c}", val_min = 2, val_max = 20)}
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\part $D = \Var{e}$
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\begin{solution}
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$\Var{e.simplify().explain() | join('=')}$
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\end{solution}
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\Block{set e = Expression.random("{a}+{b}-{c}", val_min = 2, val_max = 20)}
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\part $E = \Var{e}$
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\begin{solution}
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$\Var{e.simplify().explain() | join('=')}$
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\end{solution}
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\end{parts}
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\end{multicols}
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\question Résoudre les problèmes suivants en détaillant les calculs et écrivant une phrase de conclusion.
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\Block{set a,b = random_str("{a}, {b}", conditions=["{a}>{2*b}", "gcd({a},{b})==1", "gcd({b},10)==1"], val_min=2, val_max=30).split(",")}
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\begin{parts}
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\part Le père d'une famille de $\Var{b}$ enfants à fait construire $\Var{a}$ maisons. Il veut les donner équitablement à tous ces enfants. Comment peut-il faire?
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\begin{solution}
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Il va donner $\Var{int(a)//int(b)}$ maisons à chacun de ses enfants et il lui en restera $\Var{int(a)%int(b)}$
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\end{solution}
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\part Roukaya a mis dans le four $\Var{a}$ rangées de $\Var{b}$ gâteaux. Combien de gâteaux a-t-elle mis au four?
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\begin{solution}
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Roukaya a mis $\Var{a} \times \Var{b} = \Var{int(a)*int(b)}$ gâteaux au four.
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\end{solution}
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\part Abdallah a $\Var{a}$\euro qui veut partager entre ces $\Var{b}$ copains. Combien peut-il donner à chacun de ses amis?
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\begin{solution}
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\Block{set donne = floor(int(a)/int(b)*100)/100}
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\Block{set reste = round(int(a) - donne*int(b),2)}
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Abdallah va donner $\Var{donne}$\euro à chacun de ses amis et il lui restera $\Var{a} - \Var{donne}\times\Var{b} = \Var{reste}$\euro.
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\end{solution}
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\part Un segment mesure $\Var{a}$ unités. On le partage en $\Var{b}$ parties égales. Combien chaque partie mesure-t-elle exactement?
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\begin{solution}
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Si l'on essaye de faire la division de $\Var{a}$ par $\Var{b}$, on se rend compte, qu'on ne trouve jamais de reste nul. Aucun nombre décimal ne pourra représenter cette longueur. La longueur d'une seule partie sera $\dfrac{\Var{a}}{\Var{b}}$ (nombre que l'on ne pourra pas écrire avec des virgules).
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\end{solution}
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\end{parts}
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\end{questions}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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