210 lines
7.0 KiB
TeX
210 lines
7.0 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{18}
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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 $A = ( -8 x + 10 ) ( -8 - ( -1 x ) )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( -8 x + 10 ) ( -8 - ( -1 x ) ) \\
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A & = & ( - 8 x + 10 ) ( -8 - ( - 1 x ) ) \\
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A & = & ( - 8 x + 10 ) ( -8 - ( - x ) ) \\
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A & = & ( - 8 x + 10 ) ( - 8 - ( - x ) ) \\
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A & = & ( - 8 x + 10 ) ( - 8 + x ) \\
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A & = & - 8 x^{ 2 } + 74 x - 80
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\end{eqnarray*}
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\end{solution}
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\subpart $B = ( 2 x - 5 )^{ 2 } - 2$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( 2 x - 5 )^{ 2 } - 2 \\
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A & = & ( 2 x - 5 )^{ 2 } - 2 \\
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A & = & 2 x - 5^{ 2 } - 2 \\
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A & = & 2 x - 5 ( 2 x - 5 ) - 2 \\
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A & = & 2 \times 2 x^{ 2 } + ( -5 \times 2 + 2 \times ( -5 ) ) x - 5 \times ( -5 ) - 2 \\
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A & = & 4 x^{ 2 } + ( -10 - 10 ) x + 25 - 2 \\
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A & = & 4 x^{ 2 } - 20 x + 23
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\end{eqnarray*}
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\end{solution}
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\subpart $C = -4 x - 10 + 4 ( -7 x + 9 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & -4 x - 10 + 4 ( -7 x + 9 )^{ 2 } \\
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A & = & - 4 x - 10 + 4 ( - 7 x + 9 )^{ 2 } \\
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A & = & - 4 x - 10 + 4 ( - 7 x + 9 )^{ 2 } \\
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A & = & - 4 x - 10 + 4 ( - 7 x + 9 )^{ 2 } \\
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A & = & - 4 x - 10 + 4 ( - 7 x + 9 )^{ 2 } \\
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A & = & - 4 x - 10 + 4 ( - 7 x + 9 ) ( - 7 x + 9 ) \\
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A & = & - 4 x - 10 + 4 ( -7 \times ( -7 ) x^{ 2 } + ( 9 \times ( -7 ) - 7 \times 9 ) x + 9 \times 9 ) \\
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A & = & - 4 x - 10 + 4 ( 49 x^{ 2 } + ( -63 - 63 ) x + 81 ) \\
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A & = & - 4 x - 10 + 4 ( 49 x^{ 2 } - 126 x + 81 ) \\
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A & = & - 4 x - 10 + 4 ( 49 x^{ 2 } - 126 x + 81 ) \\
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A & = & - 4 x - 10 + 4 \times 49 x^{ 2 } + 4 \times ( -126 ) x + 4 \times 81 \\
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A & = & 196 x^{ 2 } - 508 x + 314
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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 $A = 1 x^{ 2 } - x$
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\subpart $B = 81 x^{ 2 } + 81 + 162 x$
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\subpart $C = 49 x^{ 2 } - 81$
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\subpart $D = 81 x^{ 2 } - 144 x + 64$
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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 $7 x + 1 = 0$
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\subpart $- 9 x + 1 = - 5 x - 3$
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\columnbreak
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\subpart $- 2 x^{ 2 } - 9 x - 5 = -2x^2$
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\subpart $( 9 x + 3 ) ( 9 x - 5 ) = 0$
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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 $A(-2 ; -3)$, $B(-2 ; -3)$, $C(-8 ; 3)$ et $D(8 ; 10)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(-8 ; 1)$, $B(-4 ; -5)$, $C(6 ; 4)$ et $D(2 ; 7)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(-3 ; 3)$, $B(-3 ; 3)$, $C(-6 ; 3)$ et $D(-4 ; -2)$. 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 $\displaystyle A = \frac{ -6 }{ 2 } \times 4$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ -6 }{ 2 } \times 4 \\
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A & = & \frac{ -6 \times 2 \times 2 }{ 1 \times 2 } \\
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A & = & \frac{ -12 \times 2 }{ 2 } \\
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A & = & -12
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle B = \frac{ 10 }{ 8 } + \frac{ 5 }{ -40 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 10 }{ 8 } + \frac{ 5 }{ -40 } \\
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A & = & \frac{ 10 \times ( -5 ) }{ 8 \times ( -5 ) } + \frac{ 5 \times 1 }{ -40 \times 1 } \\
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A & = & \frac{ -50 }{ -40 } + \frac{ 5 }{ -40 } \\
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A & = & \frac{ -50 + 5 }{ -40 } \\
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A & = & \frac{ -45 }{ -40 } \\
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A & = & \frac{ 45 }{ 40 } \\
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A & = & \frac{ 9 \times 5 }{ 8 \times 5 } \\
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A & = & \frac{ 9 }{ 8 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle C = \frac{ 8 }{ 3 } + \frac{ 1 }{ 10 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 8 }{ 3 } + \frac{ 1 }{ 10 } \\
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A & = & \frac{ 8 \times 10 }{ 3 \times 10 } + \frac{ 1 \times 3 }{ 10 \times 3 } \\
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A & = & \frac{ 80 }{ 30 } + \frac{ 3 }{ 30 } \\
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A & = & \frac{ 80 + 3 }{ 30 } \\
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A & = & \frac{ 83 }{ 30 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle D = \frac{ 6 }{ -8 } + 5$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 6 }{ -8 } + 5 \\
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A & = & \frac{ 6 \times 1 }{ -8 \times 1 } + \frac{ 5 \times ( -8 ) }{ 1 \times ( -8 ) } \\
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A & = & \frac{ 6 }{ -8 } + \frac{ -40 }{ -8 } \\
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A & = & \frac{ 6 - 40 }{ -8 } \\
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A & = & \frac{ -34 }{ -8 } \\
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A & = & \frac{ 34 }{ 8 } \\
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A & = & \frac{ 17 \times 2 }{ 4 \times 2 } \\
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A & = & \frac{ 17 }{ 4 }
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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 $\displaystyle A = \frac{ 5 }{ -2 x } \times 6$
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\subpart $\displaystyle B = \frac{ -1 }{ -5 } + \frac{ 8 x }{ -35 }$
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\subpart $\displaystyle C = \frac{ 1 x }{ -7 } + \frac{ 2 }{ 8 x }$
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\subpart $\displaystyle D = \frac{ 10 }{ -4 x } + 9$
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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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