118 lines
4.1 KiB
TeX
118 lines
4.1 KiB
TeX
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\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/2014-2015/Archive/2014-2015/tools/style/classDS}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2014-2015/Archive/2014-2015/2014_2015}
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\usepackage{multicol}
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% Title Page
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\titre{Octobre 1}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{\premiereS}
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\date{6 octobre 2014}
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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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\begin{document}
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\maketitle
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Vous collerez le sujet sur votre copie.
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\begin{questions}
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\question[6]
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Tracer un repère orthonormé sur votre copie et tracer les droites suivantes dessus.
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\begin{parts}
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\Block{set A = RdExpression("A({a};{b})", ["{a*b}>0"])()}
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\Block{set cA = RdExpression("{a}", ["{a} > 0", "{a} < 5"])()}
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\part Droite $d_1$ passant par $\Var{A}$ et de coefficient directeur $\Var{cA}$.
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\Block{set B = RdExpression("B({a};{b})", ["{a*b}<0"])()}
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\Block{set cB = RdExpression("{a}", ["{a} < 0", "{a} > -5"])()}
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\part Droite $d_2$ passant par $\Var{B}$ et de coefficient directeur $\Var{cB}$.
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\Block{set C = RdExpression("C({a};{b})", ["{a*b}>0"])()}
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\Block{set cC = RdExpression("\\frac{a}{b}", ["{a} > 1", "{b} > 1", "gcd({a},{b}) == 1"])()}
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\part Droite $d_3$ passant par $\Var{C}$ et de coefficient directeur $\Var{cC}$.
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\Block{set d4 = RdExpression("y = {a}x + {b}", ["{b} > 0"])()}
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\part Droite $d_4$ d'équation \Var{d4}.
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\Block{set d5 = RdExpression("y = {a}x - {b}", ["{b} > 0"])()}
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\part Droite $d_5$ d'équation \Var{d5}.
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\Block{set d6 = RdExpression("y = {a}x - {b}", ["{b} > 0"])()}
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\part Droite $d_6$ d'équation \Var{d6}.
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\end{parts}
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\question[5]
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À partir du graphique suivant, déterminer l'équation des droites $\mathcal{D}_1$,$\mathcal{D}_2$,$\mathcal{D}_3$,$\mathcal{D}_4$.
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\begin{tikzpicture}[scale=0.5]
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\draw[very thin, gray] (-10,-10) grid (10,10);
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\draw[->, thick] (-10,0) -- (10,0) node[below right] {$x$};
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\draw[->, very thick] (0,-10) -- (0,10) node[above] {$y$};
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\draw (0,0) node[below left] {$O$};
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\draw (0,1) node {-} node[left] {$J$};
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\draw (1,0) node[rotate=90] {-} node[below] {$I$};
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\Block{set D1 = RdExpression("(-10,{a}) -- (10,{b})", ["{b} > -9", "{a} < 10"])()}
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\draw[very thick] \Var{D1} node[above right] {$\mathcal{D}_1$};
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\Block{set D2 = RdExpression("(-10,{a}) -- ({b}, 10)", ["{b} > 0", "{a} <10 "])()}
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\draw[very thick] \Var{D2} node[above right] {$\mathcal{D}_2$};
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\Block{set D3 = RdExpression("({a}, -10) -- (10,{b})",["{a} < 0", "{b} > -10"])()}
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\draw[very thick] \Var{D3} node[above right] {$\mathcal{D}_3$};
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\Block{set D4 = RdExpression("(-10,{a}) -- (10,{b})", ["{b} < 10", "{a} > -10"])()}
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\draw[very thick] \Var{D4} node[above right] {$\mathcal{D}_4$};
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\end{tikzpicture}
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\question[5]
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\Block{set f = RdExpression("{a}x^2 + x - {b}", ["{a} not in [-1,1]","{b} > 0"])()}
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Soit $f : x \mapsto \Var{f}$.
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Calculer les quantités suivantes (simplifier quand c'est possible)
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\begin{parts}
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\begin{multicols}{2}
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\part $f(0)$
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\part $f(0 + h)$
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\part $f'(0)$
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\columnbreak
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\part $f(2)$
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\part $f(2 + h)$
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\part $f'(2)$
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\end{multicols}
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\end{parts}
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\question[4]
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Factoriser les quantités suivantes
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\Block{set A = RdExpression("{a} h^2 + {b}h", ["{b} > 0"])()}
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\Block{set B = RdExpression("({d}x + {e})({a}x + {b})+({a}x + {b})({c}x + {d})", ["{b} > 1", "{d} > 1, {e} > 1", "{a} > 1", "{b} > 1"])()}
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\Block{set C = RdExpression("({d}x + {e})({a}x + {b})-({a}x + {b})({c}x + {d})", ["{b} > 1", "{d} > 1, {e} > 1", "{a} > 1", "{b} > 1"])()}
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\Block{set D = RdExpression(" x^2 - {b**2}")()}
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\Block{set E = RdExpression(" x^2 + {2*b}x + {b**2}", ["{b} > 0"])()}
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\begin{parts}
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\part $A = \Var{ A }$
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\part $B = \Var{ B }$
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Avec identité remarquable
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\part $C = \Var{ D }$
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\part $D = \Var{ E }$
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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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