206 lines
6.8 KiB
TeX
206 lines
6.8 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{11}
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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 $A = ( -9 x + 1 ) ( -9 - 5 x )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( -9 x + 1 ) ( -9 - 5 x ) \\
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A & = & ( - 9 x + 1 ) ( -9 - 5 x ) \\
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A & = & ( - 9 x + 1 ) ( - 9 - 5 x ) \\
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A & = & ( - 9 x + 1 ) ( - 9 - 5 x ) \\
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A & = & 45 x^{ 2 } + 76 x - 9
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\end{eqnarray*}
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\end{solution}
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\subpart $B = ( 5 x + 8 )^{ 2 } + 7$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( 5 x + 8 )^{ 2 } + 7 \\
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A & = & ( 5 x + 8 ) ( 5 x + 8 ) + 7 \\
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A & = & 5 \times 5 x^{ 2 } + ( 8 \times 5 + 5 \times 8 ) x + 8 \times 8 + 7 \\
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A & = & 25 x^{ 2 } + ( 40 + 40 ) x + 64 + 7 \\
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A & = & 25 x^{ 2 } + 80 x + 71
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\end{eqnarray*}
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\end{solution}
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\subpart $C = 3 x - 8 + 4 ( -10 x + 5 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & 3 x - 8 + 4 ( -10 x + 5 )^{ 2 } \\
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A & = & 3 x - 8 + 4 ( - 10 x + 5 )^{ 2 } \\
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A & = & 3 x - 8 + 4 ( - 10 x + 5 )^{ 2 } \\
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A & = & 3 x - 8 + 4 ( - 10 x + 5 )^{ 2 } \\
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A & = & 3 x - 8 + 4 ( - 10 x + 5 )^{ 2 } \\
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A & = & 3 x - 8 + 4 ( - 10 x + 5 ) ( - 10 x + 5 ) \\
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A & = & 3 x - 8 + 4 ( -10 \times ( -10 ) x^{ 2 } + ( 5 \times ( -10 ) - 10 \times 5 ) x + 5 \times 5 ) \\
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A & = & 3 x - 8 + 4 ( 100 x^{ 2 } + ( -50 - 50 ) x + 25 ) \\
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A & = & 3 x - 8 + 4 ( 100 x^{ 2 } - 100 x + 25 ) \\
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A & = & 3 x - 8 + 4 ( 100 x^{ 2 } - 100 x + 25 ) \\
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A & = & 3 x - 8 + 4 \times 100 x^{ 2 } + 4 \times ( -100 ) x + 4 \times 25 \\
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A & = & 400 x^{ 2 } - 397 x + 92
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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 $A = 7 x^{ 2 } - x$
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\subpart $B = 64 x^{ 2 } + 64 + 128 x$
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\subpart $C = 36 x^{ 2 } - 1$
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\subpart $D = 81 x^{ 2 } - 72 x + 16$
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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 $6 x + 6 = 0$
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\subpart $- 4 x + 4 = - 8 x + 6$
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\columnbreak
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\subpart $3 x^{ 2 } + 5 x + 10 = 3x^2$
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\subpart $( 5 x + 2 ) ( 2 x - 7 ) = 0$
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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 $A(-5 ; -3)$, $B(-8 ; 1)$, $C(-4 ; 8)$ et $D(-1 ; 4)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(2 ; 1)$, $B(8 ; 5)$, $C(3 ; 4)$ et $D(1 ; 3)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(10 ; 3)$, $B(8 ; 2)$, $C(-8 ; -10)$ et $D(2 ; -5)$. 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 $\displaystyle A = \frac{ -6 }{ -3 } \times ( -1 )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ -6 }{ -3 } \times ( -1 ) \\
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A & = & \frac{ -6 \times 1 \times ( -1 ) }{ 3 \times ( -1 ) } \\
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A & = & \frac{ -6 \times ( -1 ) }{ -3 } \\
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A & = & \frac{ 6 }{ -3 } \\
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A & = & -2
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle B = \frac{ 10 }{ -9 } + \frac{ -1 }{ 27 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 10 }{ -9 } + \frac{ -1 }{ 27 } \\
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A & = & \frac{ 10 \times 3 }{ -9 \times 3 } + \frac{ -1 \times ( -1 ) }{ 27 \times ( -1 ) } \\
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A & = & \frac{ 30 }{ -27 } + \frac{ 1 }{ -27 } \\
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A & = & \frac{ 30 + 1 }{ -27 } \\
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A & = & \frac{ 31 }{ -27 } \\
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A & = & \frac{ -31 }{ 27 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle C = \frac{ 10 }{ 4 } + \frac{ -10 }{ 1 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 10 }{ 4 } + \frac{ -10 }{ 1 } \\
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A & = & \frac{ 10 }{ 4 } - 10 \\
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A & = & \frac{ 10 \times 1 }{ 4 \times 1 } + \frac{ -10 \times 4 }{ 1 \times 4 } \\
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A & = & \frac{ 10 }{ 4 } + \frac{ -40 }{ 4 } \\
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A & = & \frac{ 10 - 40 }{ 4 } \\
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A & = & \frac{ -30 }{ 4 } \\
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A & = & \frac{ -15 \times 2 }{ 2 \times 2 } \\
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A & = & \frac{ -15 }{ 2 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle D = \frac{ 10 }{ 3 } - 7$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 10 }{ 3 } - 7 \\
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A & = & \frac{ 10 \times 1 }{ 3 \times 1 } + \frac{ -7 \times 3 }{ 1 \times 3 } \\
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A & = & \frac{ 10 }{ 3 } + \frac{ -21 }{ 3 } \\
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A & = & \frac{ 10 - 21 }{ 3 } \\
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A & = & \frac{ -11 }{ 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 $\displaystyle A = \frac{ 5 }{ 2 x } \times 10$
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\subpart $\displaystyle B = \frac{ 7 }{ -9 } + \frac{ 1 x }{ -9 }$
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\subpart $\displaystyle C = \frac{ -6 x }{ 8 } + \frac{ 10 }{ 1 x }$
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\subpart $\displaystyle D = \frac{ -2 }{ -4 x } - 2$
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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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