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{21}
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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 $A = ( 2 x - 5 ) ( 2 - ( -3 x ) )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( 2 x - 5 ) ( 2 - ( -3 x ) ) \\
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A & = & ( 2 x - 5 ) ( 2 - ( - 3 x ) ) \\
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A & = & ( 2 x - 5 ) ( 2 - ( - 3 x ) ) \\
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A & = & 2 x - 5 ( 2 + 3 x ) \\
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A & = & 6 x^{ 2 } - 11 x - 10
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\end{eqnarray*}
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\end{solution}
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\subpart $B = ( -6 x - 8 )^{ 2 } + 2$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( -6 x - 8 )^{ 2 } + 2 \\
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A & = & ( - 6 x - 8 )^{ 2 } + 2 \\
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A & = & ( - 6 x - 8 )^{ 2 } + 2 \\
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A & = & - 6 x - 8^{ 2 } + 2 \\
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A & = & - 6 x - 8 ( - 6 x - 8 ) + 2 \\
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A & = & -6 \times ( -6 ) x^{ 2 } + ( -8 \times ( -6 ) - 6 \times ( -8 ) ) x - 8 \times ( -8 ) + 2 \\
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A & = & 36 x^{ 2 } + ( 48 + 48 ) x + 64 + 2 \\
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A & = & 36 x^{ 2 } + 96 x + 66
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\end{eqnarray*}
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\end{solution}
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\subpart $C = -8 x - 8 + 4 ( -9 x - 5 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & -8 x - 8 + 4 ( -9 x - 5 )^{ 2 } \\
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A & = & - 8 x - 8 + 4 ( - 9 x - 5 )^{ 2 } \\
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A & = & - 8 x - 8 + 4 ( - 9 x - 5 )^{ 2 } \\
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A & = & - 8 x - 8 + 4 - 9 x - 5^{ 2 } \\
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A & = & - 8 x - 8 + 4 - 9 x - 5^{ 2 } \\
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A & = & - 8 x - 8 + 4 - 9 x - 5 ( - 9 x - 5 ) \\
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A & = & - 8 x - 8 + 4 ( -9 \times ( -9 ) x^{ 2 } + ( -5 \times ( -9 ) - 9 \times ( -5 ) ) x - 5 \times ( -5 ) ) \\
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A & = & - 8 x - 8 + 4 ( 81 x^{ 2 } + ( 45 + 45 ) x + 25 ) \\
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A & = & - 8 x - 8 + 4 ( 81 x^{ 2 } + 90 x + 25 ) \\
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A & = & - 8 x - 8 + 4 ( 81 x^{ 2 } + 90 x + 25 ) \\
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A & = & - 8 x - 8 + 4 \times 81 x^{ 2 } + 4 \times 90 x + 4 \times 25 \\
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A & = & 324 x^{ 2 } + 352 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 $A = -5 x^{ 2 } - x$
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\subpart $B = 100 x^{ 2 } + 1 + 20 x$
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\subpart $C = 49 x^{ 2 } - 9$
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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 $- 7 x + 2 = 0$
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\subpart $5 x + 7 = 5 x + 6$
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\columnbreak
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\subpart $6 x^{ 2 } + 5 x + 2 = 6x^2$
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\subpart $( -5 x + 5 ) ( -6 x - 4 ) = 0$
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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 $A(-5 ; 9)$, $B(7 ; -3)$, $C(3 ; -6)$ et $D(2 ; -5)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(4 ; 7)$, $B(-10 ; -6)$, $C(8 ; -10)$ et $D(4 ; 1)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(-3 ; 9)$, $B(1 ; 1)$, $C(8 ; -2)$ et $D(6 ; 2)$. 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 $\displaystyle A = \frac{ -8 }{ -4 } \times ( -7 )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ -8 }{ -4 } \times ( -7 ) \\
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A & = & \frac{ -8 \times 7 \times ( -1 ) }{ 4 \times ( -1 ) } \\
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A & = & \frac{ -56 \times ( -1 ) }{ -4 } \\
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A & = & \frac{ 56 }{ -4 } \\
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A & = & -14
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle B = \frac{ -10 }{ 4 } + \frac{ 3 }{ 12 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ -10 }{ 4 } + \frac{ 3 }{ 12 } \\
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A & = & \frac{ -10 \times 3 }{ 4 \times 3 } + \frac{ 3 \times 1 }{ 12 \times 1 } \\
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A & = & \frac{ -30 }{ 12 } + \frac{ 3 }{ 12 } \\
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A & = & \frac{ -30 + 3 }{ 12 } \\
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A & = & \frac{ -27 }{ 12 } \\
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A & = & \frac{ -9 \times 3 }{ 4 \times 3 } \\
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A & = & \frac{ -9 }{ 4 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle C = \frac{ -10 }{ -5 } + \frac{ -6 }{ 7 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ -10 }{ -5 } + \frac{ -6 }{ 7 } \\
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A & = & \frac{ -10 \times 7 }{ -5 \times 7 } + \frac{ -6 \times ( -5 ) }{ 7 \times ( -5 ) } \\
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A & = & \frac{ -70 }{ -35 } + \frac{ 30 }{ -35 } \\
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A & = & \frac{ -70 + 30 }{ -35 } \\
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A & = & \frac{ -40 }{ -35 } \\
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A & = & \frac{ 40 }{ 35 } \\
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A & = & \frac{ 8 \times 5 }{ 7 \times 5 } \\
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A & = & \frac{ 8 }{ 7 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle D = \frac{ 6 }{ 7 } - 8$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 6 }{ 7 } - 8 \\
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A & = & \frac{ 6 \times 1 }{ 7 \times 1 } + \frac{ -8 \times 7 }{ 1 \times 7 } \\
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A & = & \frac{ 6 }{ 7 } + \frac{ -56 }{ 7 } \\
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A & = & \frac{ 6 - 56 }{ 7 } \\
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A & = & \frac{ -50 }{ 7 }
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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 $\displaystyle A = \frac{ -2 }{ 5 x } \times ( -10 )$
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\subpart $\displaystyle B = \frac{ 5 }{ 6 } + \frac{ -8 x }{ 12 }$
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\subpart $\displaystyle C = \frac{ 4 x }{ 1 } + \frac{ 8 }{ -4 x }$
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\subpart $\displaystyle D = \frac{ -8 }{ 10 x } - 1$
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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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