201 lines
6.5 KiB
TeX
201 lines
6.5 KiB
TeX
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\documentclass[a4paper,12pt, table]{/media/documents/Cours/Prof/Enseignements/2014-2015/tools/style/classDS}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2014-2015/2014_2015}
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%\geometry{left=10mm,right=10mm, top=10mm, bottom=10mm}
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% Title Page
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\titre{4}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{\seconde}
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\date{6 mai 2015}
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%\duree{1 heure}
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\sujet{24}
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% DS DSCorr DM DMCorr Corr
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\typedoc{DM}
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%\printanswers
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\begin{document}
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\maketitle
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Vous devez rendre le sujet avec la copie.
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\begin{questions}
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\question
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\begin{parts}
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\part Développer et simplifier les expressions suivantes
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\begin{subparts}
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\begin{multicols}{2}
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\subpart $A = ( -1 x - 2 ) ( -1 - 8 x )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( -1 x - 2 ) ( -1 - 8 x ) \\
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A & = & ( - 1 x - 2 ) ( -1 - 8 x ) \\
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A & = & ( - x - 2 ) ( -1 - 8 x ) \\
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A & = & ( - x - 2 ) ( - 1 - 8 x ) \\
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A & = & - x - 2 ( - 1 - 8 x ) \\
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A & = & 8 x^{ 2 } + 17 x + 2
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\end{eqnarray*}
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\end{solution}
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\subpart $B = ( 5 x + 7 )^{ 2 } + 5$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( 5 x + 7 )^{ 2 } + 5 \\
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A & = & ( 5 x + 7 ) ( 5 x + 7 ) + 5 \\
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A & = & 5 \times 5 x^{ 2 } + ( 7 \times 5 + 5 \times 7 ) x + 7 \times 7 + 5 \\
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A & = & 25 x^{ 2 } + ( 35 + 35 ) x + 49 + 5 \\
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A & = & 25 x^{ 2 } + 70 x + 54
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\end{eqnarray*}
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\end{solution}
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\subpart $C = 6 x - 7 + 4 ( 5 x + 4 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & 6 x - 7 + 4 ( 5 x + 4 )^{ 2 } \\
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A & = & 6 x - 7 + 4 ( 5 x + 4 )^{ 2 } \\
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A & = & 6 x - 7 + 4 ( 5 x + 4 )^{ 2 } \\
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A & = & 6 x - 7 + 4 ( 5 x + 4 )^{ 2 } \\
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A & = & 6 x - 7 + 4 ( 5 x + 4 ) ( 5 x + 4 ) \\
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A & = & 6 x - 7 + 4 ( 5 \times 5 x^{ 2 } + ( 4 \times 5 + 5 \times 4 ) x + 4 \times 4 ) \\
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A & = & 6 x - 7 + 4 ( 25 x^{ 2 } + ( 20 + 20 ) x + 16 ) \\
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A & = & 6 x - 7 + 4 ( 25 x^{ 2 } + 40 x + 16 ) \\
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A & = & 6 x - 7 + 4 ( 25 x^{ 2 } + 40 x + 16 ) \\
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A & = & 6 x - 7 + 4 \times 25 x^{ 2 } + 4 \times 40 x + 4 \times 16 \\
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A & = & 100 x^{ 2 } + 166 x + 57
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\end{eqnarray*}
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\end{solution}
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\end{multicols}
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\end{subparts}
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\part Factoriser les expressions suivantes
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\begin{subparts}
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\begin{multicols}{2}
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\subpart $A = 2 x^{ 2 } - x$
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\subpart $B = 9 x^{ 2 } + 4 + 12 x$
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\subpart $C = 81 x^{ 2 } - 4$
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\subpart $D = 49 x^{ 2 } - 28 x + 4$
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\end{multicols}
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\end{subparts}
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\part Résoudre les équations suivantes
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\begin{subparts}
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\begin{multicols}{2}
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\subpart $x + 4 = 0$
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\subpart $- 9 x - 4 = 6 x - 5$
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\columnbreak
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\subpart $- x^{ 2 } - 2 x - 9 = -1x^2$
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\subpart $( 3 x + 7 ) ( 2 x - 4 ) = 0$
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\end{multicols}
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\end{subparts}
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\end{parts}
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\question
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\begin{parts}
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\part Soit $A(-7 ; 2)$, $B(-10 ; 8)$, $C(-10 ; -2)$ et $D(-8 ; -6)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(6 ; 4)$, $B(-3 ; -9)$, $C(10 ; 1)$ et $D(-4 ; -9)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(-9 ; 5)$, $B(-5 ; -7)$, $C(-2 ; 8)$ et $D(3 ; -7)$. Est-ce que les droites $(AC)$ et $(BD)$ sont colinéaires?
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\end{parts}
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\question
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\begin{parts}
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\part Faire les calculs suivants en \textbf{détaillant les étapes} et en simplifiant les fractions.
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\begin{multicols}{2}
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\begin{subparts}
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\subpart $\displaystyle A = \frac{ -7 }{ -2 } \times 1$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ -7 }{ -2 } \times 1 \\
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A & = & \frac{ -7 }{ -2 } \\
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A & = & \frac{ 7 }{ 2 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle B = \frac{ 10 }{ 2 } + \frac{ 7 }{ 4 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 10 }{ 2 } + \frac{ 7 }{ 4 } \\
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A & = & \frac{ 10 \times 2 }{ 2 \times 2 } + \frac{ 7 \times 1 }{ 4 \times 1 } \\
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A & = & \frac{ 20 }{ 4 } + \frac{ 7 }{ 4 } \\
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A & = & \frac{ 20 + 7 }{ 4 } \\
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A & = & \frac{ 27 }{ 4 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle C = \frac{ 7 }{ 2 } + \frac{ 8 }{ 7 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 7 }{ 2 } + \frac{ 8 }{ 7 } \\
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A & = & \frac{ 7 \times 7 }{ 2 \times 7 } + \frac{ 8 \times 2 }{ 7 \times 2 } \\
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A & = & \frac{ 49 }{ 14 } + \frac{ 16 }{ 14 } \\
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A & = & \frac{ 49 + 16 }{ 14 } \\
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A & = & \frac{ 65 }{ 14 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle D = \frac{ -8 }{ -3 } + 7$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ -8 }{ -3 } + 7 \\
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A & = & \frac{ -8 \times 1 }{ -3 \times 1 } + \frac{ 7 \times ( -3 ) }{ 1 \times ( -3 ) } \\
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A & = & \frac{ -8 }{ -3 } + \frac{ -21 }{ -3 } \\
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A & = & \frac{ -8 - 21 }{ -3 } \\
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A & = & \frac{ -29 }{ -3 } \\
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A & = & \frac{ 29 }{ 3 }
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\end{eqnarray*}
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\end{solution}
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\end{subparts}
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\end{multicols}
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\part Mettre les expressions suivantes sur le même dénominateur
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\begin{multicols}{2}
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\begin{subparts}
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\subpart $\displaystyle A = \frac{ -10 }{ -8 x } \times 9$
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\subpart $\displaystyle B = \frac{ -2 }{ 2 } + \frac{ -6 x }{ 2 }$
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\subpart $\displaystyle C = \frac{ -8 x }{ -1 } + \frac{ 2 }{ 1 x }$
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\subpart $\displaystyle D = \frac{ -3 }{ -9 x } - 4$
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\end{subparts}
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\end{multicols}
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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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