211 lines
7.1 KiB
TeX
211 lines
7.1 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{30}
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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 $A = ( -6 x - 8 ) ( -6 - ( -8 x ) )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( -6 x - 8 ) ( -6 - ( -8 x ) ) \\
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A & = & ( - 6 x - 8 ) ( -6 - ( - 8 x ) ) \\
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A & = & ( - 6 x - 8 ) ( - 6 - ( - 8 x ) ) \\
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A & = & - 6 x - 8 ( - 6 + 8 x ) \\
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A & = & - 48 x^{ 2 } - 28 x + 48
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\end{eqnarray*}
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\end{solution}
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\subpart $B = ( -3 x + 3 )^{ 2 } - 10$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( -3 x + 3 )^{ 2 } - 10 \\
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A & = & ( - 3 x + 3 )^{ 2 } - 10 \\
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A & = & ( - 3 x + 3 ) ( - 3 x + 3 ) - 10 \\
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A & = & -3 \times ( -3 ) x^{ 2 } + ( 3 \times ( -3 ) - 3 \times 3 ) x + 3 \times 3 - 10 \\
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A & = & 9 x^{ 2 } + ( -9 - 9 ) x + 9 - 10 \\
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A & = & 9 x^{ 2 } - 18 x - 1
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\end{eqnarray*}
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\end{solution}
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\subpart $C = 6 x - 9 + 4 ( -5 x + 10 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & 6 x - 9 + 4 ( -5 x + 10 )^{ 2 } \\
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A & = & 6 x - 9 + 4 ( - 5 x + 10 )^{ 2 } \\
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A & = & 6 x - 9 + 4 ( - 5 x + 10 )^{ 2 } \\
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A & = & 6 x - 9 + 4 ( - 5 x + 10 )^{ 2 } \\
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A & = & 6 x - 9 + 4 ( - 5 x + 10 )^{ 2 } \\
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A & = & 6 x - 9 + 4 ( - 5 x + 10 ) ( - 5 x + 10 ) \\
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A & = & 6 x - 9 + 4 ( -5 \times ( -5 ) x^{ 2 } + ( 10 \times ( -5 ) - 5 \times 10 ) x + 10 \times 10 ) \\
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A & = & 6 x - 9 + 4 ( 25 x^{ 2 } + ( -50 - 50 ) x + 100 ) \\
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A & = & 6 x - 9 + 4 ( 25 x^{ 2 } - 100 x + 100 ) \\
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A & = & 6 x - 9 + 4 ( 25 x^{ 2 } - 100 x + 100 ) \\
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A & = & 6 x - 9 + 4 \times 25 x^{ 2 } + 4 \times ( -100 ) x + 4 \times 100 \\
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A & = & 100 x^{ 2 } - 394 x + 391
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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 $A = 8 x^{ 2 } - x$
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\subpart $B = 4 x^{ 2 } + 100 + 40 x$
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\subpart $C = 36 x^{ 2 } - 9$
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\subpart $D = 36 x^{ 2 } - 84 x + 49$
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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 $10 x + 4 = 0$
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\subpart $- 4 x - 2 = 6 x + 8$
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\columnbreak
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\subpart $4 x^{ 2 } - 5 x - 9 = 4x^2$
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\subpart $( -7 x + 5 ) ( -3 x - 10 ) = 0$
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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 $A(-5 ; -10)$, $B(-7 ; -5)$, $C(4 ; 8)$ et $D(8 ; -2)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(3 ; 4)$, $B(-4 ; 5)$, $C(2 ; -6)$ et $D(-2 ; -5)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(-10 ; -2)$, $B(-3 ; 5)$, $C(-10 ; -8)$ et $D(-9 ; -7)$. 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 $\displaystyle A = \frac{ 2 }{ 10 } \times ( -8 )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 2 }{ 10 } \times ( -8 ) \\
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A & = & \frac{ 2 \times ( -4 ) \times 2 }{ 5 \times 2 } \\
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A & = & \frac{ -8 \times 2 }{ 10 } \\
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A & = & \frac{ -16 }{ 10 } \\
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A & = & \frac{ -8 \times 2 }{ 5 \times 2 } \\
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A & = & \frac{ -8 }{ 5 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle B = \frac{ 6 }{ 6 } + \frac{ 3 }{ -36 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 6 }{ 6 } + \frac{ 3 }{ -36 } \\
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A & = & \frac{ 6 \times ( -6 ) }{ 6 \times ( -6 ) } + \frac{ 3 \times 1 }{ -36 \times 1 } \\
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A & = & \frac{ -36 }{ -36 } + \frac{ 3 }{ -36 } \\
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A & = & \frac{ -36 + 3 }{ -36 } \\
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A & = & \frac{ -33 }{ -36 } \\
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A & = & \frac{ 33 }{ 36 } \\
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A & = & \frac{ 11 \times 3 }{ 12 \times 3 } \\
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A & = & \frac{ 11 }{ 12 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle C = \frac{ -9 }{ -10 } + \frac{ -1 }{ 3 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ -9 }{ -10 } + \frac{ -1 }{ 3 } \\
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A & = & \frac{ -9 \times 3 }{ -10 \times 3 } + \frac{ -1 \times ( -10 ) }{ 3 \times ( -10 ) } \\
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A & = & \frac{ -27 }{ -30 } + \frac{ 10 }{ -30 } \\
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A & = & \frac{ -27 + 10 }{ -30 } \\
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A & = & \frac{ -17 }{ -30 } \\
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A & = & \frac{ 17 }{ 30 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle D = \frac{ -6 }{ -8 } + 9$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ -6 }{ -8 } + 9 \\
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A & = & \frac{ -6 \times 1 }{ -8 \times 1 } + \frac{ 9 \times ( -8 ) }{ 1 \times ( -8 ) } \\
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A & = & \frac{ -6 }{ -8 } + \frac{ -72 }{ -8 } \\
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A & = & \frac{ -6 - 72 }{ -8 } \\
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A & = & \frac{ -78 }{ -8 } \\
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A & = & \frac{ 78 }{ 8 } \\
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A & = & \frac{ 39 \times 2 }{ 4 \times 2 } \\
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A & = & \frac{ 39 }{ 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 $\displaystyle A = \frac{ 9 }{ 9 x } \times 5$
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\subpart $\displaystyle B = \frac{ 4 }{ 7 } + \frac{ 3 x }{ -42 }$
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\subpart $\displaystyle C = \frac{ 6 x }{ -7 } + \frac{ 4 }{ 1 x }$
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\subpart $\displaystyle D = \frac{ -1 }{ -10 x } - 7$
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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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