209 lines
6.9 KiB
TeX
209 lines
6.9 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{26}
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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 $A = ( -8 x + 3 ) ( -8 - 7 x )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( -8 x + 3 ) ( -8 - 7 x ) \\
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A & = & ( - 8 x + 3 ) ( -8 - 7 x ) \\
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A & = & ( - 8 x + 3 ) ( - 8 - 7 x ) \\
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A & = & ( - 8 x + 3 ) ( - 8 - 7 x ) \\
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A & = & 56 x^{ 2 } + 43 x - 24
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\end{eqnarray*}
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\end{solution}
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\subpart $B = ( -3 x - 9 )^{ 2 } - 6$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( -3 x - 9 )^{ 2 } - 6 \\
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A & = & ( - 3 x - 9 )^{ 2 } - 6 \\
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A & = & ( - 3 x - 9 )^{ 2 } - 6 \\
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A & = & - 3 x - 9^{ 2 } - 6 \\
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A & = & - 3 x - 9 ( - 3 x - 9 ) - 6 \\
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A & = & -3 \times ( -3 ) x^{ 2 } + ( -9 \times ( -3 ) - 3 \times ( -9 ) ) x - 9 \times ( -9 ) - 6 \\
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A & = & 9 x^{ 2 } + ( 27 + 27 ) x + 81 - 6 \\
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A & = & 9 x^{ 2 } + 54 x + 75
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\end{eqnarray*}
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\end{solution}
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\subpart $C = -1 x - 3 + 4 ( -6 x - 6 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & -1 x - 3 + 4 ( -6 x - 6 )^{ 2 } \\
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A & = & - 1 x - 3 + 4 ( - 6 x - 6 )^{ 2 } \\
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A & = & - x - 3 + 4 ( - 6 x - 6 )^{ 2 } \\
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A & = & - x - 3 + 4 ( - 6 x - 6 )^{ 2 } \\
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A & = & - x - 3 + 4 - 6 x - 6^{ 2 } \\
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A & = & - x - 3 + 4 - 6 x - 6^{ 2 } \\
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A & = & - x - 3 + 4 - 6 x - 6 ( - 6 x - 6 ) \\
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A & = & - x - 3 + 4 ( -6 \times ( -6 ) x^{ 2 } + ( -6 \times ( -6 ) - 6 \times ( -6 ) ) x - 6 \times ( -6 ) ) \\
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A & = & - x - 3 + 4 ( 36 x^{ 2 } + ( 36 + 36 ) x + 36 ) \\
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A & = & - x - 3 + 4 ( 36 x^{ 2 } + 72 x + 36 ) \\
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A & = & - x - 3 + 4 ( 36 x^{ 2 } + 72 x + 36 ) \\
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A & = & - x - 3 + 4 \times 36 x^{ 2 } + 4 \times 72 x + 4 \times 36 \\
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A & = & 144 x^{ 2 } + 287 x + 141
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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 $A = 3 x^{ 2 } - x$
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\subpart $B = 9 x^{ 2 } + 64 + 48 x$
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\subpart $C = 9 x^{ 2 } - 64$
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\subpart $D = 9 x^{ 2 } - 18 x + 9$
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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 $4 x + 5 = 0$
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\subpart $2 x + 1 = - 8 x + 6$
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\columnbreak
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\subpart $x^{ 2 } - 4 x + 3 = 1x^2$
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\subpart $( 5 x + 8 ) ( -6 x - 2 ) = 0$
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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 $A(7 ; 6)$, $B(-4 ; -5)$, $C(6 ; 9)$ et $D(-1 ; 2)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(-9 ; -6)$, $B(-7 ; 5)$, $C(-6 ; -6)$ et $D(10 ; 9)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(5 ; -9)$, $B(6 ; -8)$, $C(-8 ; -7)$ et $D(-10 ; -9)$. 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 $\displaystyle A = \frac{ 8 }{ -5 } \times 3$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 8 }{ -5 } \times 3 \\
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A & = & \frac{ 8 \times 3 }{ -5 } \\
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A & = & \frac{ 24 }{ -5 } \\
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A & = & \frac{ -24 }{ 5 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle B = \frac{ 9 }{ -6 } + \frac{ 3 }{ 18 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 9 }{ -6 } + \frac{ 3 }{ 18 } \\
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A & = & \frac{ 9 \times 3 }{ -6 \times 3 } + \frac{ 3 \times ( -1 ) }{ 18 \times ( -1 ) } \\
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A & = & \frac{ 27 }{ -18 } + \frac{ -3 }{ -18 } \\
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A & = & \frac{ 27 - 3 }{ -18 } \\
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A & = & \frac{ 24 }{ -18 } \\
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A & = & \frac{ -24 }{ 18 } \\
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A & = & \frac{ -4 \times 6 }{ 3 \times 6 } \\
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A & = & \frac{ -4 }{ 3 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle C = \frac{ 9 }{ -7 } + \frac{ -7 }{ 5 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 9 }{ -7 } + \frac{ -7 }{ 5 } \\
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A & = & \frac{ 9 \times 5 }{ -7 \times 5 } + \frac{ -7 \times ( -7 ) }{ 5 \times ( -7 ) } \\
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A & = & \frac{ 45 }{ -35 } + \frac{ 49 }{ -35 } \\
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A & = & \frac{ 45 + 49 }{ -35 } \\
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A & = & \frac{ 94 }{ -35 } \\
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A & = & \frac{ -94 }{ 35 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle D = \frac{ 9 }{ 2 } - 10$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 9 }{ 2 } - 10 \\
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A & = & \frac{ 9 \times 1 }{ 2 \times 1 } + \frac{ -10 \times 2 }{ 1 \times 2 } \\
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A & = & \frac{ 9 }{ 2 } + \frac{ -20 }{ 2 } \\
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A & = & \frac{ 9 - 20 }{ 2 } \\
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A & = & \frac{ -11 }{ 2 }
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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 $\displaystyle A = \frac{ 1 }{ 6 x } \times 7$
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\subpart $\displaystyle B = \frac{ -9 }{ 4 } + \frac{ -6 x }{ -12 }$
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\subpart $\displaystyle C = \frac{ -8 x }{ 7 } + \frac{ -2 }{ 6 x }$
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\subpart $\displaystyle D = \frac{ -5 }{ -2 x } - 9$
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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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