Jean-Christophe Jameux
4 years ago
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# BTS 1 - DST 1 - Questions originales |
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a : -2,-3,-4,-5 |
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b : 2,4,6,8 |
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c : 1,3,5,7,9 |
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|
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\item L'ensemble des solutions de l'inéquation $#a# x+#b#<#c#$ est : |
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\begin{enumerate} |
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\item\MauvaiseReponse $\mathbb{R}$ |
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\item\BonneReponse $]#(c-b)/a#,+\infty[$ |
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\item\MauvaiseReponse $]-\infty, #(b-c)/a#]$ |
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\end{enumerate} |
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a : -2,-3,-4,-5 |
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b : 2,4,6,8 |
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c : 1,3,5,7,9 |
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|
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\item L'ensemble des solutions de l'inéquation $#a#x+#b# \geqslant #c#$ |
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\begin{enumerate} |
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\item\MauvaiseReponse $\mathbb{R}$ |
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\item\MauvaiseReponse $[#(c-b)/a#,+\infty[$ |
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\item\BonneReponse $]-\infty,#(c-b)/a#]$ |
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\end{enumerate} |
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a : 2,3,4 |
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b : 2,4,6,8 |
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c : 1,3,5,7,9 |
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|
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\item Le nombre $#1/b#$ |
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\begin{enumerate} |
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\item\MauvaiseReponse est solution de l'équation $#b#x+1=0$ |
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\item\MauvaiseReponse est solution de l'équation $x+#b#=0$ |
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\item\BonneReponse est solution de l'inéquation $#a#x+#c#>0$ |
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\end{enumerate} |
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a : 3,5,6,7 |
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b : 4,5,6 |
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c : 1,2,3,5 |
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\item Le nombre $\sqrt{#a#}$ |
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\begin{enumerate} |
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\item\MauvaiseReponse est solution de l'équation $x^{2}+#a#=0$ |
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\item\BonneReponse est solution de l'équation $x^{3}-#a#x=0$ |
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\item\MauvaiseReponse est solution de l'inéquation $-#b#x+#c#>0$ |
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\end{enumerate} |
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a : 8,9,10,11,12 |
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b : 2,4,6,8 |
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c : 1,3,5,7 |
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\item Le nombre $#1/a#$ |
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\begin{enumerate} |
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\item\MauvaiseReponse est solution de l'équation $#a-1#x+1=0$ |
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\item\BonneReponse est solution de l'équation $#a#x-1=0$ |
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\item\MauvaiseReponse est solution de l'inéquation $#b#x+#c#<0$ |
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\end{enumerate} |
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a : -2,-3,-4,2,3,5 |
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b : 2,4,-2,3,-3 |
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c : 3,5 |
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d : 2,5 |
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e : 6,8 |
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\item Le couple solution du système $\left\{\begin{array}{c}#c#x+#d#y=#c*a+d*b# \\ x-#e#y=#a-e*b#\end{array}\right.$ est |
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\begin{enumerate} |
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\item\MauvaiseReponse $(#-2*a#;#b#)$ |
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\item\MauvaiseReponse $(#b/2# ; #a#)$ |
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\item\BonneReponse $(#a# ;#b#)$ |
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\end{enumerate} |
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a : -2,-3,-4,2,3,5 |
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b : 2,4,3 |
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\item $u$ est la suite définie pour tout entier $n \geqslant 1$ par $u_{n}=\frac{#a#n^{2}-#b#}{n^{2}}$. |
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\begin{enumerate} |
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\item\MauvaiseReponse $u_{3}=3$ |
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\item\BonneReponse $u_{3}=#(a* 9-b)/9#$ |
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\item\MauvaiseReponse $u_{3} =#((a* 3)^2-b)/9#$ |
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\end{enumerate} |
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a : 3,5 |
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b : 1,2,3 |
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c : 2,3,4 |
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Soit $\left(u_{n}\right)$ la suite définie par: $u_{0}=#c#$ et, pour tout entier naturel $n$, |
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\item $u_{n+1}=#a# u_{n}-#b#$, alors : |
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\begin{enumerate} |
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\item\MauvaiseReponse $u_{3}=#c#$ |
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\item\MauvaiseReponse $u_{3}=#b/(a-1)+(c-b/(a-1))* a^2#$ |
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\item\BonneReponse $u_{3}=#b/(a-1)+(c-b/(a-1))* a^3#$ |
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\end{enumerate} |
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a : 3,4,5 |
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b : -1,-2,-3 |
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\item $v$ est la suite définie par $v_{0}=#b#$ et la relation de récurrence $v_{n+1}=#a#n-v_{n}$, alors : |
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\begin{enumerate} |
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\item\BonneReponse $v_{2}=#a+b#$ |
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\item\MauvaiseReponse $v_{2}=#b-3#$ |
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\item\MauvaiseReponse $v_{2}=#a+1#$ |
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\end{enumerate} |
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a : -3/4,-1/2,-2/3,-1/4,-1/3 |
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b : -1,-2,-3,-4,-5 |
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\item On considère la suite arithmétique $\left(u_{n}\right)$ de premier terme $u_{0}=#b#$ et de raison $r=#a#$. |
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\begin{enumerate} |
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\item\MauvaiseReponse $u_{3}=#b#$ |
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\item\MauvaiseReponse $u_{3}=#b+2* a#$ |
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\item\BonneReponse $u_{3}=#b+3* a#$ |
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\end{enumerate} |
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a : 3/4,1/2,2/3,1/4,1/3 |
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b : 5/8,3/7,4/9,2/5 |
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Soit $\left(u_{n}\right)$ une suite géométrique de raison $q=#a#$. |
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\item Sachant que $u_{3}=#b#$, le premier terme $\mathrm{u}_ {0}$ est : |
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\begin{enumerate} |
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\item\BonneReponse $#b*(a)^ -3#$ |
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\item\MauvaiseReponse $#b* (a)^ 3#$ |
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\item\MauvaiseReponse $#a* (b)^ -3#$ |
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\end{enumerate} |
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a : 2,3,4,5,6,8,9 |
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b : 10,12,15,18 |
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Soit la suite $\left(u_{n}\right)$ définie par $u_{n+1}=#a/b#u_n$. |
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\item Cette suite est : |
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\begin{enumerate} |
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\item\MauvaiseReponse croissante |
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\item\BonneReponse décroissante |
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\item\MauvaiseReponse constante |
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\end{enumerate} |
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|
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Soit la suite $\left(u_{n}\right)$ définie par $u_{n+1}=#b/a#u_n$. |
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\item Cette suite est : |
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\begin{enumerate} |
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\item\BonneReponse croissante |
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\item\MauvaiseReponse décroissante |
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\item\MauvaiseReponse constante |
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\end{enumerate} |
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a : 2,4 |
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b : 3,5,8 |
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c : 6,7,9 |
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\item On considère l'équation $#a#x^{2}-#b# x-#c#=0$ alors le discriminant $\Delta$ est égal à : |
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\begin{enumerate} |
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\item\BonneReponse $#b^2+4*a*c#$ |
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\item\MauvaiseReponse $#b^2-4*a*c#$ |
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\item\MauvaiseReponse $#-(b^2)+4* c#$ |
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\end{enumerate} |
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a : 2,3 |
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b : 1,2,3,4,5,6,7,8,9 |
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\item Le nombre de solutions de l'équation $#a#x^{2}-#2*a*b# x+#a* b^2#=0$ est |
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\begin{enumerate} |
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\item\MauvaiseReponse $0$ |
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\item\BonneReponse $1$ |
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\item\MauvaiseReponse $2$ |
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\end{enumerate} |
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a : 2,3,4,5 |
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b : 6,7,8,9 |
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\item L'ensemble des solutions de l'équation $x^{2}+#b-a# x-#a* b#=0$ est : |
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\begin{enumerate} |
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\item\MauvaiseReponse $\emptyset$ |
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\item\BonneReponse $\{#a# ;-#b#\}$ |
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\item\MauvaiseReponse $\{#a# ; #b#\}$ |
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\end{enumerate} |
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@ -0,0 +1,354 @@ |
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Soit la suite |
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telle que |
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et |
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pour tout entier |
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, et soit |
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la suite définie par |
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pour tout entier |
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. |
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Montrer que la suite |
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est une suite géométrique dont on donnera la raison et le premier terme |
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puis donner une formule pour |
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puis pour |
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en fonction de l'entier naturel |
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Établir, en faisant apparaitre les calculs, le tableau de signe sur |
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de la fonction |
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et en déduire les solutions sur |
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de l'inéquation |
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. |
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(Si vous ne parvenez pas à le faire par le calcul, une résolution graphique |
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\documentclass[oneside,twocolumn,landscape]{book} |
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\usepackage[T1]{fontenc} |
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\usepackage[utf8]{inputenc} |
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\usepackage{geometry} |
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\usepackage{amsmath} |
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\begin{document} |
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\section*{Contrôle de Mathématiques} |
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\let\MauvaiseReponse\null |
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\let\BonneReponse\null |
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|
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{\bf Merci de répondre sur la grille fournie et de ne pas oublier de traiter les deux questions au verso en évitant de sortir des cadres. Vous prendrez soin de rendre le sujet avec cette grille.} |
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\vspace{2em} |
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\begin{enumerate} |
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\item L'ensemble des solutions de l'inéquation $-2 x+2<1$ est : |
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\begin{enumerate} |
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\item\BonneReponse $]\frac{1}{2},+\infty[$ |
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\item\MauvaiseReponse $\mathbb{R}$ |
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\item\MauvaiseReponse $]-\infty, -\frac{1}{2}]$ |
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\end{enumerate} |
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|
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|
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\item L'ensemble des solutions de l'inéquation $-2x+8 \geqslant 9$ |
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|
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\begin{enumerate} |
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|
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\item\MauvaiseReponse $\mathbb{R}$ |
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|
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|
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\item\BonneReponse $]-\infty,-\frac{1}{2}]$ |
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\item\MauvaiseReponse $[-\frac{1}{2},+\infty[$ |
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|
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\end{enumerate} |
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|
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|
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\item Le nombre $\frac{1}{2}$ |
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|
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\begin{enumerate} |
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|
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\item\MauvaiseReponse est solution de l'équation $x+2=0$ |
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\item\MauvaiseReponse est solution de l'équation $2x+1=0$ |
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|
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|
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\item\BonneReponse est solution de l'inéquation $3x+7>0$ |
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|
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\end{enumerate} |
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|
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|
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|
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\item Le nombre $\sqrt{5}$ |
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|
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\begin{enumerate} |
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|
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|
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\item\BonneReponse est solution de l'équation $x^{3}-5x=0$ |
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|
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\item\MauvaiseReponse est solution de l'inéquation $-5x+2>0$ |
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\item\MauvaiseReponse est solution de l'équation $x^{2}+5=0$ |
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|
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\end{enumerate} |
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|
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\newpage |
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|
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\item Le nombre $\frac{1}{8}$ |
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|
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\begin{enumerate} |
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|
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|
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\item\BonneReponse est solution de l'équation $8x-1=0$ |
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\item\MauvaiseReponse est solution de l'équation $7x+1=0$ |
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|
||||
\item\MauvaiseReponse est solution de l'inéquation $2x+7<0$ |
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|
||||
\end{enumerate} |
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|
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|
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|
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\item Le couple solution du système $\left\{\begin{array}{c}5x+5y=10 \\ x-8y=-34\end{array}\right.$ est |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $(4;4)$ |
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|
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\item\BonneReponse $(-2 ;4)$ |
||||
\item\MauvaiseReponse $(2 ; -2)$ |
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|
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|
||||
\end{enumerate} |
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|
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|
||||
\item $u$ est la suite définie pour tout entier $n \geqslant 1$ par $u_{n}=\frac{3n^{2}-2}{n^{2}}$. |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $u_{3}=3$ |
||||
|
||||
\item\BonneReponse $u_{3}=\frac{25}{9}$ |
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|
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\item\MauvaiseReponse $u_{3} =\frac{79}{9}$ |
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|
||||
\end{enumerate} |
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|
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|
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|
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|
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\item Soit $\left(u_{n}\right)$ la suite définie par: $u_{0}=4$ et, pour tout entier naturel $n$, $u_{n+1}=3 u_{n}-1$, alors : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $u_{3}=4$ |
||||
|
||||
\item\MauvaiseReponse $u_{3}=32$ |
||||
|
||||
\item\BonneReponse $u_{3}=95$ |
||||
|
||||
\end{enumerate} |
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|
||||
\newpage |
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|
||||
\item $v$ est la suite définie par $v_{0}=-2$ et la relation de récurrence\\ $v_{n+1}=5n-v_{n}$, alors : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $v_{2}=3$ |
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||||
\item\MauvaiseReponse $v_{2}=-5$ |
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|
||||
\item\MauvaiseReponse $v_{2}=6$ |
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||||
\end{enumerate} |
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\item On considère la suite arithmétique $\left(u_{n}\right)$ de premier terme $u_{0}=-4$\\ et de raison $r=-\frac{3}{4}$. |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $u_{3}=-4$ |
||||
|
||||
\item\MauvaiseReponse $u_{3}=-\frac{11}{2}$ |
||||
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||||
\item\BonneReponse $u_{3}=-\frac{25}{4}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
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||||
\item Soit $\left(u_{n}\right)$ une suite géométrique de raison $q=\frac{2}{3}$. Sachant que $u_{3}=\frac{5}{8}$,\\ le premier terme $\mathrm{u}_ {0}$ est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $\frac{135}{64}$ |
||||
|
||||
\item\MauvaiseReponse $\frac{5}{27}$ |
||||
|
||||
\item\MauvaiseReponse $\frac{1024}{375}$ |
||||
|
||||
\end{enumerate} |
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|
||||
\item Soit la suite $\left(u_{n}\right)$ définie par $u_{n+1}=\frac{2}{15}u_n$. Cette suite est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse croissante |
||||
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||||
\item\BonneReponse décroissante |
||||
|
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\item\MauvaiseReponse constante |
||||
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||||
\end{enumerate} |
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\newpage |
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|
||||
\item On considère l'équation $4x^{2}-3 x-9=0$ alors le discriminant $\Delta$ est égal à : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $153$ |
||||
|
||||
\item\MauvaiseReponse $-135$ |
||||
|
||||
\item\MauvaiseReponse $27$ |
||||
|
||||
\end{enumerate} |
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|
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|
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|
||||
\item Le nombre de solutions de l'équation $3x^{2}-12 x+12=0$ est |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $0$ |
||||
|
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\item\BonneReponse $1$ |
||||
|
||||
\item\MauvaiseReponse $2$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
\item L'ensemble des solutions de l'équation $x^{2}+4 x-45=0$ est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\emptyset$ |
||||
|
||||
\item\BonneReponse $\{5 ;-9\}$ |
||||
|
||||
\item\MauvaiseReponse $\{5 ; 9\}$ |
||||
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\end{enumerate} |
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\end{enumerate} |
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\end{document} |
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\documentclass[oneside,twocolumn,landscape]{book} |
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\usepackage[T1]{fontenc} |
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\usepackage[utf8]{inputenc} |
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\usepackage{geometry} |
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\begin{document} |
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\section*{Contrôle de Mathématiques} |
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\let\MauvaiseReponse\null |
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\let\BonneReponse\null |
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|
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{\bf Merci de répondre sur la grille fournie et de ne pas oublier de traiter les deux questions au verso en évitant de sortir des cadres. Vous prendrez soin de rendre le sujet avec cette grille.} |
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\vspace{2em} |
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\begin{enumerate} |
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|
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\item L'ensemble des solutions de l'inéquation $-3 x+2<5$ est : |
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|
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\begin{enumerate} |
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|
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\item\MauvaiseReponse $\mathbb{R}$ |
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|
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\item\BonneReponse $]-1,+\infty[$ |
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|
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\item\MauvaiseReponse $]-\infty, 1]$ |
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|
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\end{enumerate} |
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|
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\item L'ensemble des solutions de l'inéquation $-3x+8 \geqslant 5$ |
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|
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\begin{enumerate} |
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|
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\item\MauvaiseReponse $\mathbb{R}$ |
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|
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\item\MauvaiseReponse $[1,+\infty[$ |
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|
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\item\BonneReponse $]-\infty,1]$ |
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|
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\end{enumerate} |
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|
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|
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|
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|
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\item Le nombre $\frac{1}{6}$ |
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|
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\begin{enumerate} |
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|
||||
\item\MauvaiseReponse est solution de l'équation $6x+1=0$ |
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|
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\item\MauvaiseReponse est solution de l'équation $x+6=0$ |
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|
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\item\BonneReponse est solution de l'inéquation $3x+3>0$ |
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|
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\end{enumerate} |
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|
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|
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|
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\item Le nombre $\sqrt{6}$ |
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|
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\begin{enumerate} |
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|
||||
\item\MauvaiseReponse est solution de l'équation $x^{2}+6=0$ |
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|
||||
\item\BonneReponse est solution de l'équation $x^{3}-6x=0$ |
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|
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\item\MauvaiseReponse est solution de l'inéquation $-6x+2>0$ |
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|
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\end{enumerate} |
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|
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\newpage |
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|
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\item Le nombre $\frac{1}{8}$ |
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|
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\begin{enumerate} |
||||
|
||||
\item\BonneReponse est solution de l'équation $8x-1=0$ |
||||
\item\MauvaiseReponse est solution de l'équation $7x+1=0$ |
||||
|
||||
|
||||
\item\MauvaiseReponse est solution de l'inéquation $8x+3<0$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Le couple solution du système $\left\{\begin{array}{c}5x+2y=-7 \\ x-8y=-35\end{array}\right.$ est |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $(6;4)$ |
||||
|
||||
\item\BonneReponse $(-3 ;4)$ |
||||
\item\MauvaiseReponse $(2 ; -3)$ |
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|
||||
|
||||
\end{enumerate} |
||||
|
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|
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|
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|
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|
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|
||||
\item $u$ est la suite définie pour tout entier $n \geqslant 1$ par $u_{n}=\frac{-2n^{2}-4}{n^{2}}$. |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $u_{3}=3$ |
||||
|
||||
|
||||
\item\MauvaiseReponse $u_{3} =\frac{32}{9}$ |
||||
\item\BonneReponse $u_{3}=-\frac{22}{9}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
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|
||||
\item Soit $\left(u_{n}\right)$ la suite définie par: $u_{0}=2$ et, pour tout entier naturel $n$, $u_{n+1}=3 u_{n}-3$, alors : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $u_{3}=2$ |
||||
|
||||
\item\BonneReponse $u_{3}=15$ |
||||
\item\MauvaiseReponse $u_{3}=6$ |
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|
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|
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\end{enumerate} |
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|
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|
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|
||||
\newpage |
||||
|
||||
\item $v$ est la suite définie par $v_{0}=-2$ et la relation de récurrence\\ $v_{n+1}=4n-v_{n}$, alors : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $v_{2}=-5$ |
||||
\item\BonneReponse $v_{2}=2$ |
||||
|
||||
\item\MauvaiseReponse $v_{2}=5$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
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|
||||
\item On considère la suite arithmétique $\left(u_{n}\right)$ de premier terme $u_{0}=-3$\\ et de raison $r=-\frac{1}{2}$. |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $u_{3}=-3$ |
||||
|
||||
\item\BonneReponse $u_{3}=-\frac{9}{2}$ |
||||
\item\MauvaiseReponse $u_{3}=-4$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Soit $\left(u_{n}\right)$ une suite géométrique de raison $q=\frac{1}{4}$. Sachant que $u_{3}=\frac{5}{8}$,\\ le premier terme $\mathrm{u}_ {0}$ est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $\frac{5}{512}$ |
||||
\item\BonneReponse $40$ |
||||
|
||||
\item\MauvaiseReponse $\frac{128}{125}$ |
||||
|
||||
\end{enumerate} |
||||
|
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|
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|
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\item Soit la suite $\left(u_{n}\right)$ définie par $u_{n+1}=\frac{1}{6}u_n$. Cette suite est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse décroissante |
||||
\item\MauvaiseReponse croissante |
||||
|
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|
||||
\item\MauvaiseReponse constante |
||||
|
||||
\end{enumerate} |
||||
|
||||
\newpage |
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|
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|
||||
\item On considère l'équation $2x^{2}-5 x-9=0$ alors le discriminant $\Delta$ est égal à : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $-47$ |
||||
\item\BonneReponse $97$ |
||||
|
||||
\item\MauvaiseReponse $11$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
\item Le nombre de solutions de l'équation $3x^{2}-48 x+192=0$ est |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $0$ |
||||
|
||||
|
||||
\item\MauvaiseReponse $2$ |
||||
\item\BonneReponse $1$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item L'ensemble des solutions de l'équation $x^{2}+3 x-28=0$ est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $\{4 ;-7\}$ |
||||
\item\MauvaiseReponse $\emptyset$ |
||||
|
||||
|
||||
\item\MauvaiseReponse $\{4 ; 7\}$ |
||||
|
||||
\end{enumerate} |
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\end{enumerate} |
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\end{document} |
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\documentclass[oneside,twocolumn,landscape]{book} |
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\usepackage[T1]{fontenc} |
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\usepackage[utf8]{inputenc} |
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\usepackage{geometry} |
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\geometry{verbose,tmargin=1cm,bmargin=1cm,lmargin=2cm,rmargin=2cm} |
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\setcounter{secnumdepth}{3} |
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\setcounter{tocdepth}{3} |
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\usepackage{amsmath} |
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\usepackage{amssymb} |
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\usepackage{amsfonts} |
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\pagestyle{empty} |
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|
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|
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\begin{document} |
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|
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\section*{Contrôle de Mathématiques} |
||||
|
||||
\let\MauvaiseReponse\null |
||||
\let\BonneReponse\null |
||||
|
||||
|
||||
|
||||
{\bf Merci de répondre sur la grille fournie et de ne pas oublier de traiter les deux questions au verso en évitant de sortir des cadres. Vous prendrez soin de rendre le sujet avec cette grille.} |
||||
\vspace{2em} |
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|
||||
|
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item L'ensemble des solutions de l'inéquation $-4 x+8<9$ est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\mathbb{R}$ |
||||
|
||||
|
||||
\item\MauvaiseReponse $]-\infty, \frac{1}{4}]$ |
||||
\item\BonneReponse $]-\frac{1}{4},+\infty[$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\item L'ensemble des solutions de l'inéquation $-5x+4 \geqslant 3$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\mathbb{R}$ |
||||
|
||||
\item\BonneReponse $]-\infty,\frac{1}{5}]$ |
||||
\item\MauvaiseReponse $[\frac{1}{5},+\infty[$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\item Le nombre $\frac{1}{4}$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse est solution de l'équation $4x+1=0$ |
||||
\item\BonneReponse est solution de l'inéquation $4x+5>0$ |
||||
|
||||
\item\MauvaiseReponse est solution de l'équation $x+4=0$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Le nombre $\sqrt{7}$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse est solution de l'équation $x^{3}-7x=0$ |
||||
\item\MauvaiseReponse est solution de l'équation $x^{2}+7=0$ |
||||
|
||||
|
||||
\item\MauvaiseReponse est solution de l'inéquation $-5x+3>0$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
\newpage |
||||
|
||||
\item Le nombre $\frac{1}{10}$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse est solution de l'équation $9x+1=0$ |
||||
|
||||
|
||||
\item\MauvaiseReponse est solution de l'inéquation $2x+3<0$ |
||||
\item\BonneReponse est solution de l'équation $10x-1=0$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
\item Le couple solution du système $\left\{\begin{array}{c}3x+5y=-24 \\ x-6y=15\end{array}\right.$ est |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $(6;-3)$ |
||||
|
||||
\item\BonneReponse $(-3 ;-3)$ |
||||
\item\MauvaiseReponse $(-\frac{3}{2} ; -3)$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\item $u$ est la suite définie pour tout entier $n \geqslant 1$ par $u_{n}=\frac{-3n^{2}-4}{n^{2}}$. |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $u_{3}=3$ |
||||
|
||||
|
||||
\item\MauvaiseReponse $u_{3} =\frac{77}{9}$ |
||||
\item\BonneReponse $u_{3}=-\frac{31}{9}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
\item Soit $\left(u_{n}\right)$ la suite définie par: $u_{0}=3$ et, pour tout entier naturel $n$, $u_{n+1}=5 u_{n}-2$, alors : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $u_{3}=313$ |
||||
\item\MauvaiseReponse $u_{3}=3$ |
||||
|
||||
\item\MauvaiseReponse $u_{3}=63$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
\newpage |
||||
|
||||
\item $v$ est la suite définie par $v_{0}=-3$ et la relation de récurrence\\ $v_{n+1}=4n-v_{n}$, alors : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $v_{2}=-6$ |
||||
|
||||
\item\MauvaiseReponse $v_{2}=5$ |
||||
\item\BonneReponse $v_{2}=1$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item On considère la suite arithmétique $\left(u_{n}\right)$ de premier terme $u_{0}=-5$\\ et de raison $r=-\frac{2}{3}$. |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $u_{3}=-7$ |
||||
\item\MauvaiseReponse $u_{3}=-5$ |
||||
|
||||
\item\MauvaiseReponse $u_{3}=-\frac{19}{3}$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Soit $\left(u_{n}\right)$ une suite géométrique de raison $q=\frac{1}{3}$. Sachant que $u_{3}=\frac{4}{9}$,\\ le premier terme $\mathrm{u}_ {0}$ est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $\frac{4}{243}$ |
||||
|
||||
\item\MauvaiseReponse $\frac{243}{64}$ |
||||
\item\BonneReponse $12$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\item Soit la suite $\left(u_{n}\right)$ définie par $u_{n+1}=\frac{4}{15}u_n$. Cette suite est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse croissante |
||||
|
||||
|
||||
\item\MauvaiseReponse constante |
||||
\item\BonneReponse décroissante |
||||
|
||||
\end{enumerate} |
||||
|
||||
\newpage |
||||
|
||||
|
||||
\item On considère l'équation $4x^{2}-8 x-9=0$ alors le discriminant $\Delta$ est égal à : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $-80$ |
||||
|
||||
\item\MauvaiseReponse $-28$ |
||||
\item\BonneReponse $208$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Le nombre de solutions de l'équation $2x^{2}-20 x+50=0$ est |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $1$ |
||||
\item\MauvaiseReponse $0$ |
||||
|
||||
|
||||
\item\MauvaiseReponse $2$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item L'ensemble des solutions de l'équation $x^{2}+7 x-18=0$ est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\emptyset$ |
||||
|
||||
|
||||
\item\MauvaiseReponse $\{2 ; 9\}$ |
||||
\item\BonneReponse $\{2 ;-9\}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
\end{document} |
||||
|
||||
|
||||
|
||||
|
||||
@ -0,0 +1,265 @@ |
||||
# TSP - DST 1 - Questions originales |
||||
|
||||
a : -2,-3,-4,-5 |
||||
b : 2,4,6,8 |
||||
c : 1,3,5,7,9 |
||||
|
||||
\item L'ensemble des solutions de l'inéquation $#a# x+#b#<#c#$ est : |
||||
\begin{enumerate} |
||||
\item\MauvaiseReponse $\mathbb{R}$ |
||||
\item\BonneReponse $]#(c-b)/a#,+\infty[$ |
||||
\item\MauvaiseReponse $]-\infty, #(b-c)/a#]$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
a : -2,-3,-4,-5 |
||||
b : 2,4,6,8 |
||||
c : 1,3,5,7,9 |
||||
|
||||
\item L'ensemble des solutions de l'inéquation $#a#x+#b# \geqslant #c#$ |
||||
\begin{enumerate} |
||||
\item\MauvaiseReponse $\mathbb{R}$ |
||||
\item\MauvaiseReponse $[#(c-b)/a#,+\infty[$ |
||||
\item\BonneReponse $]-\infty,#(c-b)/a#]$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
a : 2,3,4 |
||||
b : 2,4,6,8 |
||||
c : 1,3,5,7,9 |
||||
|
||||
\item Le nombre $#1/b#$ |
||||
\begin{enumerate} |
||||
\item\MauvaiseReponse est solution de l'équation $#b#x+1=0$ |
||||
\item\MauvaiseReponse est solution de l'équation $x+#b#=0$ |
||||
\item\BonneReponse est solution de l'inéquation $#a#x+#c#>0$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
a : 3,5,6,7 |
||||
b : 4,5,6 |
||||
c : 1,2,3,5 |
||||
|
||||
\item Le nombre $\sqrt{#a#}$ |
||||
\begin{enumerate} |
||||
\item\MauvaiseReponse est solution de l'équation $x^{2}+#a#=0$ |
||||
\item\BonneReponse est solution de l'équation $x^{3}-#a#x=0$ |
||||
\item\MauvaiseReponse est solution de l'inéquation $-#b#x+#c#>0$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
a : 8,9,10,11,12 |
||||
b : 2,4,6,8 |
||||
c : 1,3,5,7 |
||||
|
||||
\item Le nombre $#1/a#$ |
||||
\begin{enumerate} |
||||
\item\MauvaiseReponse est solution de l'équation $#a-1#x+1=0$ |
||||
\item\BonneReponse est solution de l'équation $#a#x-1=0$ |
||||
\item\MauvaiseReponse est solution de l'inéquation $#b#x+#c#<0$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
a : -2,-3,-4,2,3,5 |
||||
b : 2,4,-2,3,-3 |
||||
c : 3,5 |
||||
d : 2,5 |
||||
e : 6,8 |
||||
|
||||
\item Le couple solution du système $\left\{\begin{array}{c}#c#x+#d#y=#c*a+d*b# \\ x-#e#y=#a-e*b#\end{array}\right.$ est |
||||
\begin{enumerate} |
||||
\item\MauvaiseReponse $(#-2*a#;#b#)$ |
||||
\item\MauvaiseReponse $(#b/2# ; #a#)$ |
||||
\item\BonneReponse $(#a# ;#b#)$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
a : 2,3,4,5 |
||||
b : 6,7,8,9 |
||||
|
||||
\item L'ensemble des solutions de l'équation $x^{2}+#b-a# x-#a* b#=0$ est : |
||||
\begin{enumerate} |
||||
\item\MauvaiseReponse $\emptyset$ |
||||
\item\BonneReponse $\{#a# ;-#b#\}$ |
||||
\item\MauvaiseReponse $\{#a# ; #b#\}$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
a : 15/2,12/5,6/7 |
||||
b : 3/4,3/8,5/4 |
||||
c : 2,3 |
||||
|
||||
\item $#a# - #b# \times#c#=$ |
||||
\begin{enumerate} |
||||
\item\MauvaiseReponse $#(a-b)* c#$ |
||||
\item\MauvaiseReponse $#a-b#$ |
||||
\item\BonneReponse $#a-b* c#$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
a : 13/2,9/5,5/7 |
||||
b : 1/4,1/8,1/3 |
||||
|
||||
\item $\frac{#a#-1}{#b#+1}=$ |
||||
\begin{enumerate} |
||||
\item\BonneReponse $#(a-1)/(b+1)#$ |
||||
\item\MauvaiseReponse $#a/b#$ |
||||
\item\MauvaiseReponse $#(a-1)* (b+1)#$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
a : 2,4,6,8 |
||||
b : 10,12,14,16,18,20 |
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $A$, si $AB=#a#$ et $BC=#b#$, alors |
||||
\begin{enumerate} |
||||
\item\MauvaiseReponse $\sin (\hat{B})=#a/b#$ |
||||
\item\BonneReponse $AC=\sqrt{#b^2-a^2#}$ |
||||
\item\MauvaiseReponse $\cos (\hat{C})=#a/b#$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
a : 2,4,6,8 |
||||
b : 10,12,14,16,18,20 |
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $A$, si $AB=#a#$ et $BC=#b#$, alors |
||||
\begin{enumerate} |
||||
\item\MauvaiseReponse $\tan (\hat{C})=#a/b#$ |
||||
\item\MauvaiseReponse $AC=\sqrt{#a^2+b^2#}$ |
||||
\item\BonneReponse $\cos (\hat{B})=#a/b#$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
a : 2,4,6,8 |
||||
b : 10,15,20,25,30,35,40 |
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $A$, si $AB=#a#\mathrm{cm}$ et $AC=#b#\mathrm{mm}$, alors $\hat{B}=$ : |
||||
\begin{enumerate} |
||||
\item\MauvaiseReponse $#10* a#\times\arctan\left(#b#\right)$ |
||||
\item\BonneReponse $\arctan\left(\frac{#b#}{#10* a#}\right)$ |
||||
\item\MauvaiseReponse $\frac{\arctan\left(#b/10#\right)}{#a#}$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
a : 10,15,20,25,30,35,40 |
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $B$, si $\widehat{A}=#a#^{\circ}$ alors |
||||
\begin{enumerate} |
||||
\item\MauvaiseReponse $\widehat{C}=#100-a#^{\circ}$ |
||||
\item\MauvaiseReponse $\widehat{C}=#a+45#^{\circ}$ |
||||
\item\BonneReponse $\widehat{C}=#90-a#^{\circ}$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
a : 50,55,60,65,70,75,80 |
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $B$, si $\widehat{A}=#a#^{\circ}$ alors |
||||
\begin{enumerate} |
||||
\item\MauvaiseReponse $\widehat{C}=#100-a#^{\circ}$ |
||||
\item\MauvaiseReponse $\widehat{C}=#a-45#^{\circ}$ |
||||
\item\BonneReponse $\widehat{C}=#90-a#^{\circ}$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
n : 3,4,5,6,7,8,9,10,11 |
||||
|
||||
\item Si $ABC$ est un triangle rectangle en $B$ tel que $AB=#n^2-1#\mathrm{cm}$ et $BC=#2*n#\mathrm{cm}$, alors le segment $\left[AC\right]$ mesure : |
||||
\begin{enumerate} |
||||
\item\BonneReponse $#n^2+1#\mathrm{cm}$ |
||||
\item\MauvaiseReponse $#n^2+2*n-1#\mathrm{cm}$ |
||||
\item\MauvaiseReponse $#n^2-2* n-1#\mathrm{cm}$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
n : 3,4,5,6,7,8,9,10,11 |
||||
|
||||
\item Si $ABC$ est un triangle rectangle en $B$ tel que $AB=#2*n+1#\mathrm{cm}$ et $AC=#2*n^2+2*n+1#\mathrm{cm}$, alors le segment $\left[BC\right]$ mesure : |
||||
\begin{enumerate} |
||||
\item\BonneReponse $#2*n^2+2*n#\mathrm{cm}$ |
||||
\item\MauvaiseReponse $#n^2+2*n-1#\mathrm{cm}$ |
||||
\item\MauvaiseReponse $#2*n^2+4* n+2#\mathrm{cm}$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
n : 3,4,5,6,7,8,9,10,11 |
||||
|
||||
|
||||
\item Dans quel cas le triangle $ABC$ est-il rectangle ? |
||||
\begin{enumerate} |
||||
\item\BonneReponse $AB=#n^2-1#\mathrm{cm}$, $AC=#n^2+1#\mathrm{cm}$ et $BC=#2* n#\mathrm{cm}$ |
||||
\item\MauvaiseReponse $AB=#n^2-1#\mathrm{cm}$, $AC=#n^2+2* n-1#\mathrm{cm}$ et $BC=#2* n#\mathrm{cm}$ |
||||
\item\MauvaiseReponse $AB=#n^2-1#\mathrm{cm}$, $AC=#n^2-2* n-1#\mathrm{cm}$ et $BC=#2* n#\mathrm{cm}$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
a : 6,18,30 |
||||
b : 12,24,36 |
||||
k : 2/3,3/2 |
||||
|
||||
\item On considère deux triangles non plat $ABC$ et $A^\prime B^\prime C^\prime$ tels que $\left(AB\right)//\left(A^{\prime}B^{\prime}\right)$, $\left(AC\right)//\left(A^{\prime}C^{\prime}\right)$ et $\left(CB\right)//\left(C^{\prime}B^{\prime}\right)$. Si on a $AB=#a#\mathrm{cm}$, $AC=#b#\mathrm{cm}$ et $A^{\prime}B^{\prime}=#a*k#\mathrm{mm}$, alors $A^{\prime}C^{\prime}=$ |
||||
\begin{enumerate} |
||||
\item\BonneReponse $#b*k#\mathrm{mm}$ |
||||
\item\MauvaiseReponse $#a/k#\mathrm{cm}$ |
||||
\item\MauvaiseReponse $#b/k#\mathrm{cm}$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
a : 5,15,25 |
||||
b : 10,20,30 |
||||
k : 2/5,5/2 |
||||
|
||||
\item On considère deux triangles non plat $ABC$ et $A^\prime B^\prime C^\prime$ tels que $\left(AB\right)//\left(A^{\prime}B^{\prime}\right)$, $\left(AC\right)//\left(A^{\prime}C^{\prime}\right)$ et $\left(CB\right)//\left(C^{\prime}B^{\prime}\right)$. Si on a $AB=#a#\mathrm{mm}$, $AC=#b#\mathrm{mm}$ et $A^{\prime}B^{\prime}=#a* k#\mathrm{cm}$, alors $A^{\prime}C^{\prime}=$ |
||||
\begin{enumerate} |
||||
\item\BonneReponse $#10*b*k#\mathrm{mm}$ |
||||
\item\MauvaiseReponse $#b/k#\mathrm{mm}$ |
||||
\item\MauvaiseReponse $#b/k#\mathrm{cm}$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
a : 21,63 |
||||
b : 42,84 |
||||
k : 3/7,7/3 |
||||
|
||||
|
||||
\item On considère deux triangles non plat $ABC$ et $A^\prime B^\prime C^\prime$ tels que $\left(AB\right)//\left(A^{\prime}B^{\prime}\right)$ et $\left(CB\right)//\left(C^{\prime}B^{\prime}\right)$. On a $\left(AC\right)//\left(A^{\prime}C^{\prime}\right)$ si on a : |
||||
\begin{enumerate} |
||||
\item\BonneReponse $AB=#a#\mathrm{m}$, $AC=#b#\mathrm{m}$, $A^{\prime}B^{\prime}=#a*k#\mathrm{cm}$ et $A^{\prime}C^{\prime}=#b*k#\mathrm{cm}$ |
||||
\item\MauvaiseReponse $AB=#a#\mathrm{m}$, $AC=#b#\mathrm{m}$, $A^{\prime}B^{\prime}=#a*k#\mathrm{cm}$ et $A^{\prime}C^{\prime}=#b/k#\mathrm{cm}$ |
||||
\item\MauvaiseReponse $AB=#a#\mathrm{m}$, $AC=#b#\mathrm{m}$, $A^{\prime}B^{\prime}=#a*k#\mathrm{cm}$ et $A^{\prime}C^{\prime}=#a/k#\mathrm{cm}$ |
||||
\end{enumerate} |
||||
|
||||
Binary file not shown.
@ -0,0 +1,340 @@ |
||||
\documentclass[oneside,twoside]{book} |
||||
\usepackage[T1]{fontenc} |
||||
\usepackage[utf8]{inputenc} |
||||
\usepackage{geometry} |
||||
\geometry{verbose,tmargin=2cm,bmargin=2cm,lmargin=2cm,rmargin=2cm} |
||||
\setcounter{secnumdepth}{3} |
||||
\setcounter{tocdepth}{3} |
||||
\usepackage{amsmath} |
||||
\usepackage{amssymb} |
||||
\usepackage{stmaryrd} |
||||
\PassOptionsToPackage{version=3}{mhchem} |
||||
\usepackage{mhchem} |
||||
|
||||
\makeatletter |
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands. |
||||
\usepackage{amsfonts} |
||||
\usepackage{bbold} |
||||
|
||||
\raggedbottom |
||||
|
||||
\AtBeginDocument{ |
||||
\def\labelitemi{\(\triangleright\)} |
||||
\def\labelitemii{\(\triangleright\)} |
||||
\def\labelitemiii{\(\triangleright\)} |
||||
\def\labelitemiv{\(\triangleright\)} |
||||
} |
||||
|
||||
\makeatother |
||||
|
||||
\begin{document} |
||||
|
||||
\chapter*{Contrôle de Mathématiques} |
||||
|
||||
\let\MauvaiseReponse\null |
||||
\let\BonneReponse\null |
||||
|
||||
{\bf Merci de répondre sur la grille fournie et de rendre le sujet avec la grille.} |
||||
\vspace{2em} |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\item L'ensemble des solutions de l'inéquation $-2 x+2<1$ est : |
||||
\begin{enumerate} |
||||
\item\BonneReponse $]\frac{1}{2},+\infty[$ |
||||
\item\MauvaiseReponse $\mathbb{R}$ |
||||
\item\MauvaiseReponse $]-\infty, -\frac{1}{2}]$ |
||||
\end{enumerate} |
||||
|
||||
|
||||
\item L'ensemble des solutions de l'inéquation $-2x+8 \geqslant 9$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\mathbb{R}$ |
||||
|
||||
|
||||
\item\BonneReponse $]-\infty,-\frac{1}{2}]$ |
||||
\item\MauvaiseReponse $[-\frac{1}{2},+\infty[$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\item Le nombre $\frac{1}{2}$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse est solution de l'équation $x+2=0$ |
||||
\item\MauvaiseReponse est solution de l'équation $2x+1=0$ |
||||
|
||||
|
||||
\item\BonneReponse est solution de l'inéquation $3x+7>0$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Le nombre $\sqrt{5}$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\BonneReponse est solution de l'équation $x^{3}-5x=0$ |
||||
|
||||
\item\MauvaiseReponse est solution de l'inéquation $-5x+2>0$ |
||||
\item\MauvaiseReponse est solution de l'équation $x^{2}+5=0$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Le nombre $\frac{1}{8}$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\BonneReponse est solution de l'équation $8x-1=0$ |
||||
\item\MauvaiseReponse est solution de l'équation $7x+1=0$ |
||||
|
||||
\item\MauvaiseReponse est solution de l'inéquation $2x+7<0$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
\newpage |
||||
|
||||
\item Le couple solution du système $\left\{\begin{array}{c}5x+5y=10 \\ x-8y=-34\end{array}\right.$ est |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $(4;4)$ |
||||
|
||||
\item\BonneReponse $(-2 ;4)$ |
||||
\item\MauvaiseReponse $(2 ; -2)$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item L'ensemble des solutions de l'équation $x^{2}+4 x-32=0$ est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\emptyset$ |
||||
|
||||
\item\BonneReponse $\{4 ;-8\}$ |
||||
|
||||
\item\MauvaiseReponse $\{4 ; 8\}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\item $\frac{15}{2} - \frac{3}{8} \times3=$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\frac{171}{8}$ |
||||
|
||||
\item\MauvaiseReponse $\frac{57}{8}$ |
||||
|
||||
\item\BonneReponse $\frac{51}{8}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item $\displaystyle\frac{\frac{5}{7}-1}{\frac{1}{8}+1}=$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $-\frac{16}{63}$ |
||||
|
||||
\item\MauvaiseReponse $\frac{40}{7}$ |
||||
|
||||
\item\MauvaiseReponse $-\frac{9}{28}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $A$, si $AB=2$ et $BC=14$, alors |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\sin (\hat{B})=\frac{1}{7}$ |
||||
|
||||
\item\BonneReponse $AC=\sqrt{192}$ |
||||
|
||||
\item\MauvaiseReponse $\cos (\hat{C})=\frac{1}{7}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $A$, si $AB=2$ et $BC=20$, alors |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\tan (\hat{C})=\frac{1}{10}$ |
||||
|
||||
\item\MauvaiseReponse $AC=\sqrt{404}$ |
||||
|
||||
\item\BonneReponse $\cos (\hat{B})=\frac{1}{10}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $A$, si $AB=2\mathrm{cm}$ et $AC=20\mathrm{mm}$, alors $\hat{B}=$ : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $20\times\arctan\left(20\right)$ |
||||
|
||||
\item\BonneReponse $\arctan\left(\frac{20}{20}\right)$ |
||||
|
||||
\item\MauvaiseReponse $\frac{\arctan\left(2\right)}{2}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $B$, si $\widehat{A}=10^{\circ}$ alors |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\widehat{C}=90^{\circ}$ |
||||
|
||||
\item\MauvaiseReponse $\widehat{C}=55^{\circ}$ |
||||
|
||||
\item\BonneReponse $\widehat{C}=80^{\circ}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $B$, si $\widehat{A}=50^{\circ}$ alors |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\widehat{C}=50^{\circ}$ |
||||
|
||||
\item\MauvaiseReponse $\widehat{C}=5^{\circ}$ |
||||
|
||||
\item\BonneReponse $\widehat{C}=40^{\circ}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Si $ABC$ est un triangle rectangle en $B$ tel que $AB=15\mathrm{cm}$ et $BC=8\mathrm{cm}$, alors le segment $\left[AC\right]$ mesure : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $17\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $23\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $7\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Si $ABC$ est un triangle rectangle en $B$ tel que $AB=9\mathrm{cm}$ et $AC=41\mathrm{cm}$, alors le segment $\left[BC\right]$ mesure : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $23\mathrm{cm}$ |
||||
\item\BonneReponse $40\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $50\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Dans quel cas le triangle $ABC$ est-il rectangle ? |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $AB=24\mathrm{cm}$, $AC=34\mathrm{cm}$ et $BC=10\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $AB=24\mathrm{cm}$, $AC=14\mathrm{cm}$ et $BC=10\mathrm{cm}$ |
||||
\item\BonneReponse $AB=24\mathrm{cm}$, $AC=26\mathrm{cm}$ et $BC=10\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item On considère deux triangles non plat $ABC$ et $A^\prime B^\prime C^\prime$ tels que $\left(AB\right)//\left(A^{\prime}B^{\prime}\right)$, $\left(AC\right)//\left(A^{\prime}C^{\prime}\right)$ et $\left(CB\right)//\left(C^{\prime}B^{\prime}\right)$. Si on a $AB=6\mathrm{cm}$, $AC=24\mathrm{cm}$ et $A^{\prime}B^{\prime}=4\mathrm{mm}$, alors $A^{\prime}C^{\prime}=$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $9\mathrm{cm}$ |
||||
|
||||
\item\BonneReponse $16\mathrm{mm}$ |
||||
\item\MauvaiseReponse $36\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item On considère deux triangles non plat $ABC$ et $A^\prime B^\prime C^\prime$ tels que $\left(AB\right)//\left(A^{\prime}B^{\prime}\right)$, $\left(AC\right)//\left(A^{\prime}C^{\prime}\right)$ et $\left(CB\right)//\left(C^{\prime}B^{\prime}\right)$. Si on a $AB=5\mathrm{mm}$, $AC=20\mathrm{mm}$ et $A^{\prime}B^{\prime}=2\mathrm{cm}$, alors $A^{\prime}C^{\prime}=$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $50\mathrm{mm}$ |
||||
\item\BonneReponse $80\mathrm{mm}$ |
||||
|
||||
\item\MauvaiseReponse $50\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\item On considère deux triangles non plat $ABC$ et $A^\prime B^\prime C^\prime$ tels que $\left(AB\right)//\left(A^{\prime}B^{\prime}\right)$ et $\left(CB\right)//\left(C^{\prime}B^{\prime}\right)$. On a $\left(AC\right)//\left(A^{\prime}C^{\prime}\right)$ si on a : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $AB=63\mathrm{m}$, $AC=42\mathrm{m}$, $A^{\prime}B^{\prime}=147\mathrm{cm}$ et $A^{\prime}C^{\prime}=98\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $AB=63\mathrm{m}$, $AC=42\mathrm{m}$, $A^{\prime}B^{\prime}=147\mathrm{cm}$ et $A^{\prime}C^{\prime}=18\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $AB=63\mathrm{m}$, $AC=42\mathrm{m}$, $A^{\prime}B^{\prime}=147\mathrm{cm}$ et $A^{\prime}C^{\prime}=27\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
\end{document} |
||||
Binary file not shown.
@ -0,0 +1,328 @@ |
||||
\documentclass[oneside,twoside]{book} |
||||
\usepackage[T1]{fontenc} |
||||
\usepackage[utf8]{inputenc} |
||||
\usepackage{geometry} |
||||
\geometry{verbose,tmargin=2cm,bmargin=2cm,lmargin=2cm,rmargin=2cm} |
||||
\setcounter{secnumdepth}{3} |
||||
\setcounter{tocdepth}{3} |
||||
\usepackage{amsmath} |
||||
\usepackage{amssymb} |
||||
\usepackage{stmaryrd} |
||||
\PassOptionsToPackage{version=3}{mhchem} |
||||
\usepackage{mhchem} |
||||
|
||||
\makeatletter |
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands. |
||||
\usepackage{amsfonts} |
||||
\usepackage{bbold} |
||||
|
||||
\raggedbottom |
||||
|
||||
\AtBeginDocument{ |
||||
\def\labelitemi{\(\triangleright\)} |
||||
\def\labelitemii{\(\triangleright\)} |
||||
\def\labelitemiii{\(\triangleright\)} |
||||
\def\labelitemiv{\(\triangleright\)} |
||||
} |
||||
|
||||
\makeatother |
||||
|
||||
\begin{document} |
||||
|
||||
\chapter*{Contrôle de Mathématiques} |
||||
|
||||
\let\MauvaiseReponse\null |
||||
\let\BonneReponse\null |
||||
|
||||
{\bf Merci de répondre sur la grille fournie et de rendre le sujet avec la grille.} |
||||
\vspace{2em} |
||||
\begin{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
\item L'ensemble des solutions de l'inéquation $-3 x+2<5$ est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\mathbb{R}$ |
||||
|
||||
\item\BonneReponse $]-1,+\infty[$ |
||||
|
||||
\item\MauvaiseReponse $]-\infty, 1]$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
\item L'ensemble des solutions de l'inéquation $-3x+8 \geqslant 5$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\mathbb{R}$ |
||||
|
||||
\item\MauvaiseReponse $[1,+\infty[$ |
||||
|
||||
\item\BonneReponse $]-\infty,1]$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\item Le nombre $\frac{1}{6}$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse est solution de l'équation $6x+1=0$ |
||||
|
||||
\item\MauvaiseReponse est solution de l'équation $x+6=0$ |
||||
|
||||
\item\BonneReponse est solution de l'inéquation $3x+3>0$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Le nombre $\sqrt{6}$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse est solution de l'équation $x^{2}+6=0$ |
||||
|
||||
\item\BonneReponse est solution de l'équation $x^{3}-6x=0$ |
||||
|
||||
\item\MauvaiseReponse est solution de l'inéquation $-6x+2>0$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
\newpage |
||||
|
||||
\item Le nombre $\frac{1}{8}$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse est solution de l'équation $8x-1=0$ |
||||
\item\MauvaiseReponse est solution de l'équation $7x+1=0$ |
||||
|
||||
|
||||
\item\MauvaiseReponse est solution de l'inéquation $8x+3<0$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Le couple solution du système $\left\{\begin{array}{c}5x+2y=-7 \\ x-8y=-35\end{array}\right.$ est |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $(6;4)$ |
||||
|
||||
\item\BonneReponse $(-3 ;4)$ |
||||
\item\MauvaiseReponse $(2 ; -3)$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item L'ensemble des solutions de l'équation $x^{2}+2 x-24=0$ est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $\{4 ;-6\}$ |
||||
\item\MauvaiseReponse $\emptyset$ |
||||
|
||||
|
||||
\item\MauvaiseReponse $\{4 ; 6\}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item $\frac{12}{5} - \frac{5}{4} \times2=$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\frac{23}{10}$ |
||||
\item\BonneReponse $-\frac{1}{10}$ |
||||
|
||||
\item\MauvaiseReponse $\frac{23}{20}$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item $\displaystyle\frac{\frac{9}{5}-1}{\frac{1}{8}+1}=$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $\frac{72}{5}$ |
||||
\item\BonneReponse $\frac{32}{45}$ |
||||
|
||||
\item\MauvaiseReponse $\frac{9}{10}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $A$, si $AB=4$ et $BC=10$, alors |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\sin (\hat{B})=\frac{2}{5}$ |
||||
|
||||
|
||||
\item\MauvaiseReponse $\cos (\hat{C})=\frac{2}{5}$ |
||||
\item\BonneReponse $AC=\sqrt{84}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $A$, si $AB=4$ et $BC=14$, alors |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\tan (\hat{C})=\frac{2}{7}$ |
||||
|
||||
\item\BonneReponse $\cos (\hat{B})=\frac{2}{7}$ |
||||
\item\MauvaiseReponse $AC=\sqrt{212}$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $A$, si $AB=2\mathrm{cm}$ et $AC=35\mathrm{mm}$, alors $\hat{B}=$ : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $\arctan\left(\frac{35}{20}\right)$ |
||||
\item\MauvaiseReponse $20\times\arctan\left(35\right)$ |
||||
|
||||
|
||||
\item\MauvaiseReponse $\frac{\arctan\left(\frac{7}{2}\right)}{2}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $B$, si $\widehat{A}=20^{\circ}$ alors |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\widehat{C}=80^{\circ}$ |
||||
|
||||
\item\MauvaiseReponse $\widehat{C}=65^{\circ}$ |
||||
|
||||
\item\BonneReponse $\widehat{C}=70^{\circ}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $B$, si $\widehat{A}=60^{\circ}$ alors |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\widehat{C}=40^{\circ}$ |
||||
|
||||
\item\BonneReponse $\widehat{C}=30^{\circ}$ |
||||
\item\MauvaiseReponse $\widehat{C}=15^{\circ}$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Si $ABC$ est un triangle rectangle en $B$ tel que $AB=35\mathrm{cm}$ et $BC=12\mathrm{cm}$, alors le segment $\left[AC\right]$ mesure : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $47\mathrm{cm}$ |
||||
|
||||
\item\BonneReponse $37\mathrm{cm}$ |
||||
\item\MauvaiseReponse $23\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Si $ABC$ est un triangle rectangle en $B$ tel que $AB=13\mathrm{cm}$ et $AC=85\mathrm{cm}$, alors le segment $\left[BC\right]$ mesure : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $47\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $98\mathrm{cm}$ |
||||
\item\BonneReponse $84\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
\newpage |
||||
|
||||
\item Dans quel cas le triangle $ABC$ est-il rectangle ? |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $AB=48\mathrm{cm}$, $AC=50\mathrm{cm}$ et $BC=14\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $AB=48\mathrm{cm}$, $AC=62\mathrm{cm}$ et $BC=14\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $AB=48\mathrm{cm}$, $AC=34\mathrm{cm}$ et $BC=14\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item On considère deux triangles non plat $ABC$ et $A^\prime B^\prime C^\prime$ tels que $\left(AB\right)//\left(A^{\prime}B^{\prime}\right)$, $\left(AC\right)//\left(A^{\prime}C^{\prime}\right)$ et $\left(CB\right)//\left(C^{\prime}B^{\prime}\right)$. Si on a $AB=6\mathrm{cm}$, $AC=36\mathrm{cm}$ et $A^{\prime}B^{\prime}=9\mathrm{mm}$, alors $A^{\prime}C^{\prime}=$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $54\mathrm{mm}$ |
||||
|
||||
\item\MauvaiseReponse $4\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $24\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item On considère deux triangles non plat $ABC$ et $A^\prime B^\prime C^\prime$ tels que $\left(AB\right)//\left(A^{\prime}B^{\prime}\right)$, $\left(AC\right)//\left(A^{\prime}C^{\prime}\right)$ et $\left(CB\right)//\left(C^{\prime}B^{\prime}\right)$. Si on a $AB=5\mathrm{mm}$, $AC=30\mathrm{mm}$ et $A^{\prime}B^{\prime}=\frac{25}{2}\mathrm{cm}$, alors $A^{\prime}C^{\prime}=$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $12\mathrm{mm}$ |
||||
\item\BonneReponse $750\mathrm{mm}$ |
||||
|
||||
\item\MauvaiseReponse $12\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\item On considère deux triangles non plat $ABC$ et $A^\prime B^\prime C^\prime$ tels que $\left(AB\right)//\left(A^{\prime}B^{\prime}\right)$ et $\left(CB\right)//\left(C^{\prime}B^{\prime}\right)$. On a $\left(AC\right)//\left(A^{\prime}C^{\prime}\right)$ si on a : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $AB=21\mathrm{m}$, $AC=84\mathrm{m}$, $A^{\prime}B^{\prime}=49\mathrm{cm}$ et $A^{\prime}C^{\prime}=36\mathrm{cm}$ |
||||
\item\BonneReponse $AB=21\mathrm{m}$, $AC=84\mathrm{m}$, $A^{\prime}B^{\prime}=49\mathrm{cm}$ et $A^{\prime}C^{\prime}=196\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $AB=21\mathrm{m}$, $AC=84\mathrm{m}$, $A^{\prime}B^{\prime}=49\mathrm{cm}$ et $A^{\prime}C^{\prime}=9\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
\end{document} |
||||
Binary file not shown.
@ -0,0 +1,341 @@ |
||||
\documentclass[oneside,twoside]{book} |
||||
\usepackage[T1]{fontenc} |
||||
\usepackage[utf8]{inputenc} |
||||
\usepackage{geometry} |
||||
\geometry{verbose,tmargin=2cm,bmargin=2cm,lmargin=2cm,rmargin=2cm} |
||||
\setcounter{secnumdepth}{3} |
||||
\setcounter{tocdepth}{3} |
||||
\usepackage{amsmath} |
||||
\usepackage{amssymb} |
||||
\usepackage{stmaryrd} |
||||
\PassOptionsToPackage{version=3}{mhchem} |
||||
\usepackage{mhchem} |
||||
|
||||
\makeatletter |
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands. |
||||
\usepackage{amsfonts} |
||||
\usepackage{bbold} |
||||
|
||||
\raggedbottom |
||||
|
||||
\AtBeginDocument{ |
||||
\def\labelitemi{\(\triangleright\)} |
||||
\def\labelitemii{\(\triangleright\)} |
||||
\def\labelitemiii{\(\triangleright\)} |
||||
\def\labelitemiv{\(\triangleright\)} |
||||
} |
||||
|
||||
\makeatother |
||||
|
||||
\begin{document} |
||||
|
||||
\chapter*{Contrôle de Mathématiques} |
||||
|
||||
\let\MauvaiseReponse\null |
||||
\let\BonneReponse\null |
||||
|
||||
|
||||
{\bf Merci de répondre sur la grille fournie et de rendre le sujet avec la grille.} |
||||
\vspace{2em} |
||||
|
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item L'ensemble des solutions de l'inéquation $-4 x+8<9$ est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\mathbb{R}$ |
||||
|
||||
|
||||
\item\MauvaiseReponse $]-\infty, \frac{1}{4}]$ |
||||
\item\BonneReponse $]-\frac{1}{4},+\infty[$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\item L'ensemble des solutions de l'inéquation $-5x+4 \geqslant 3$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\mathbb{R}$ |
||||
|
||||
\item\BonneReponse $]-\infty,\frac{1}{5}]$ |
||||
\item\MauvaiseReponse $[\frac{1}{5},+\infty[$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\item Le nombre $\frac{1}{4}$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse est solution de l'équation $4x+1=0$ |
||||
\item\BonneReponse est solution de l'inéquation $4x+5>0$ |
||||
|
||||
\item\MauvaiseReponse est solution de l'équation $x+4=0$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Le nombre $\sqrt{7}$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse est solution de l'équation $x^{3}-7x=0$ |
||||
\item\MauvaiseReponse est solution de l'équation $x^{2}+7=0$ |
||||
|
||||
|
||||
\item\MauvaiseReponse est solution de l'inéquation $-5x+3>0$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Le nombre $\frac{1}{10}$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse est solution de l'équation $9x+1=0$ |
||||
|
||||
|
||||
\item\MauvaiseReponse est solution de l'inéquation $2x+3<0$ |
||||
\item\BonneReponse est solution de l'équation $10x-1=0$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
\newpage |
||||
|
||||
\item Le couple solution du système $\left\{\begin{array}{c}3x+5y=-24 \\ x-6y=15\end{array}\right.$ est |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $(6;-3)$ |
||||
|
||||
\item\BonneReponse $(-3 ;-3)$ |
||||
\item\MauvaiseReponse $(-\frac{3}{2} ; -3)$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
\item L'ensemble des solutions de l'équation $x^{2}+3 x-40=0$ est : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\emptyset$ |
||||
|
||||
\item\BonneReponse $\{5 ;-8\}$ |
||||
|
||||
\item\MauvaiseReponse $\{5 ; 8\}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item $\frac{6}{7} - \frac{5}{4} \times2=$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $-\frac{23}{14}$ |
||||
\item\MauvaiseReponse $-\frac{11}{14}$ |
||||
|
||||
\item\MauvaiseReponse $-\frac{11}{28}$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item $\displaystyle\frac{\frac{13}{2}-1}{\frac{1}{8}+1}=$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $52$ |
||||
|
||||
\item\BonneReponse $\frac{44}{9}$ |
||||
\item\MauvaiseReponse $\frac{99}{16}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $A$, si $AB=4$ et $BC=20$, alors |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\sin (\hat{B})=\frac{1}{5}$ |
||||
|
||||
|
||||
\item\MauvaiseReponse $\cos (\hat{C})=\frac{1}{5}$ |
||||
\item\BonneReponse $AC=\sqrt{384}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $A$, si $AB=6$ et $BC=10$, alors |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $\cos (\hat{B})=\frac{3}{5}$ |
||||
\item\MauvaiseReponse $\tan (\hat{C})=\frac{3}{5}$ |
||||
|
||||
\item\MauvaiseReponse $AC=\sqrt{136}$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $A$, si $AB=4\mathrm{cm}$ et $AC=35\mathrm{mm}$, alors $\hat{B}=$ : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $40\times\arctan\left(35\right)$ |
||||
|
||||
|
||||
\item\MauvaiseReponse $\frac{\arctan\left(\frac{7}{2}\right)}{4}$ |
||||
\item\BonneReponse $\arctan\left(\frac{35}{40}\right)$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $B$, si $\widehat{A}=30^{\circ}$ alors |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\widehat{C}=70^{\circ}$ |
||||
|
||||
\item\BonneReponse $\widehat{C}=60^{\circ}$ |
||||
\item\MauvaiseReponse $\widehat{C}=75^{\circ}$ |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
\item Dans un triangle $ABC$ rectangle en $B$, si $\widehat{A}=75^{\circ}$ alors |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\MauvaiseReponse $\widehat{C}=25^{\circ}$ |
||||
|
||||
\item\MauvaiseReponse $\widehat{C}=30^{\circ}$ |
||||
|
||||
\item\BonneReponse $\widehat{C}=15^{\circ}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Si $ABC$ est un triangle rectangle en $B$ tel que $AB=63\mathrm{cm}$ et $BC=16\mathrm{cm}$, alors le segment $\left[AC\right]$ mesure : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
\item\BonneReponse $65\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $79\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $47\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Si $ABC$ est un triangle rectangle en $B$ tel que $AB=19\mathrm{cm}$ et $AC=181\mathrm{cm}$, alors le segment $\left[BC\right]$ mesure : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $98\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $200\mathrm{cm}$ |
||||
\item\BonneReponse $180\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item Dans quel cas le triangle $ABC$ est-il rectangle ? |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $AB=99\mathrm{cm}$, $AC=119\mathrm{cm}$ et $BC=20\mathrm{cm}$ |
||||
\item\BonneReponse $AB=99\mathrm{cm}$, $AC=101\mathrm{cm}$ et $BC=20\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $AB=99\mathrm{cm}$, $AC=79\mathrm{cm}$ et $BC=20\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
\item On considère deux triangles non plat $ABC$ et $A^\prime B^\prime C^\prime$ tels que $\left(AB\right)//\left(A^{\prime}B^{\prime}\right)$, $\left(AC\right)//\left(A^{\prime}C^{\prime}\right)$ et $\left(CB\right)//\left(C^{\prime}B^{\prime}\right)$. Si on a $AB=30\mathrm{cm}$, $AC=12\mathrm{cm}$ et $A^{\prime}B^{\prime}=45\mathrm{mm}$, alors $A^{\prime}C^{\prime}=$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $20\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $8\mathrm{cm}$ |
||||
\item\BonneReponse $18\mathrm{mm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
\item On considère deux triangles non plat $ABC$ et $A^\prime B^\prime C^\prime$ tels que $\left(AB\right)//\left(A^{\prime}B^{\prime}\right)$, $\left(AC\right)//\left(A^{\prime}C^{\prime}\right)$ et $\left(CB\right)//\left(C^{\prime}B^{\prime}\right)$. Si on a $AB=15\mathrm{mm}$, $AC=20\mathrm{mm}$ et $A^{\prime}B^{\prime}=6\mathrm{cm}$, alors $A^{\prime}C^{\prime}=$ |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $50\mathrm{mm}$ |
||||
|
||||
\item\BonneReponse $80\mathrm{mm}$ |
||||
\item\MauvaiseReponse $50\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\item On considère deux triangles non plat $ABC$ et $A^\prime B^\prime C^\prime$ tels que $\left(AB\right)//\left(A^{\prime}B^{\prime}\right)$ et $\left(CB\right)//\left(C^{\prime}B^{\prime}\right)$. On a $\left(AC\right)//\left(A^{\prime}C^{\prime}\right)$ si on a : |
||||
|
||||
\begin{enumerate} |
||||
|
||||
|
||||
\item\MauvaiseReponse $AB=21\mathrm{m}$, $AC=42\mathrm{m}$, $A^{\prime}B^{\prime}=49\mathrm{cm}$ et $A^{\prime}C^{\prime}=18\mathrm{cm}$ |
||||
|
||||
\item\MauvaiseReponse $AB=21\mathrm{m}$, $AC=42\mathrm{m}$, $A^{\prime}B^{\prime}=49\mathrm{cm}$ et $A^{\prime}C^{\prime}=9\mathrm{cm}$ |
||||
\item\BonneReponse $AB=21\mathrm{m}$, $AC=42\mathrm{m}$, $A^{\prime}B^{\prime}=49\mathrm{cm}$ et $A^{\prime}C^{\prime}=98\mathrm{cm}$ |
||||
|
||||
\end{enumerate} |
||||
|
||||
|
||||
\end{enumerate} |
||||
|
||||
\end{document} |
||||
|
||||
|
||||
|
||||
|
||||
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@ -0,0 +1,307 @@ |
||||
module ParserTest exposing (..) |
||||
|
||||
-- Press buttons to increment and decrement a counter. |
||||
-- |
||||
-- Read how it works: |
||||
-- https://guide.elm-lang.org/architecture/buttons.html |
||||
-- |
||||
|
||||
import Parser exposing (..) |
||||
import Browser |
||||
import Html exposing (Html, button, div, text) |
||||
import Html.Events exposing (onClick) |
||||
import Maybe exposing (Maybe) |
||||
import Result exposing (Result) |
||||
|
||||
|
||||
|
||||
-- MAIN |
||||
|
||||
|
||||
main = |
||||
Browser.sandbox { init = init, update = update, view = view } |
||||
|
||||
|
||||
|
||||
-- MODEL |
||||
|
||||
|
||||
type alias Model = Int |
||||
|
||||
|
||||
init : Model |
||||
init = |
||||
0 |
||||
|
||||
|
||||
|
||||
-- UPDATE |
||||
|
||||
|
||||
type Msg |
||||
= Increment |
||||
| Decrement |
||||
|
||||
|
||||
update : Msg -> Model -> Model |
||||
update msg model = |
||||
case msg of |
||||
Increment -> |
||||
model + 1 |
||||
|
||||
Decrement -> |
||||
model - 1 |
||||
|
||||
|
||||
|
||||
-- VIEW |
||||
|
||||
|
||||
view : Model -> Html Msg |
||||
view model = |
||||
div [] [ text texte ] |
||||
|
||||
|
||||
texte = voirArbreParse <| run arbre "*\n *" |
||||
{-- |
||||
""" |
||||
* |
||||
* |
||||
* |
||||
* |
||||
* |
||||
* |
||||
* |
||||
* |
||||
* |
||||
* |
||||
* |
||||
* |
||||
* |
||||
* |
||||
* |
||||
""" |
||||
--} |
||||
|
||||
unArbre = |
||||
Arbre |
||||
[ Arbre [] |
||||
, Arbre |
||||
[ Arbre [] |
||||
] |
||||
] |
||||
|
||||
voirArbreParse arbreParsePotentiel = |
||||
case arbreParsePotentiel of |
||||
Err erreurs -> deadEndsToString erreurs |
||||
Ok arbreParse -> voirArbre arbreParse |
||||
|
||||
{-- |
||||
parser = |
||||
succeed identity |
||||
|. mangeDesEspaces 2 |
||||
|= ( |
||||
chompUntil "\n" |
||||
|> getChompedString |
||||
) |
||||
|
||||
mangeDesEspaces ind = |
||||
token <| String.repeat ind " " |
||||
|
||||
|
||||
mangeDesEspacesBis = |
||||
let |
||||
ind = |
||||
case getIndent of |
||||
Ok indent -> indent |
||||
Err _ -> 0 |
||||
in |
||||
token <| String.repeat ind " " |
||||
--} |
||||
|
||||
type Arbre = Arbre (List Arbre) |
||||
|
||||
voirArbre arbr = |
||||
case arbr of |
||||
Arbre [] -> "[]" |
||||
Arbre arbrs -> "[" ++ String.concat (List.map voirArbre arbrs) ++ "]" |
||||
|
||||
{-- |
||||
parserArbre = parserArbreInd 0 |
||||
|
||||
parserArbreInd ind = |
||||
succeed Arbre |
||||
|. token <| String.repeat ind " " |
||||
| |
||||
|. symbol "*" |
||||
|= oneOF [fin, sousArbre] |
||||
|. token "\n" |
||||
|. spaces |
||||
|= |
||||
|
||||
type Ligne = |
||||
LigneVide |
||||
| Ligne Indentation |
||||
|
||||
type alias Indentation = |
||||
{ indentation : Int |
||||
, ligne : String |
||||
} |
||||
|
||||
parserArborescence chaine = |
||||
chaine |
||||
|> String.lines |
||||
|> List.map profondeur |
||||
|> construireArbre |
||||
|
||||
construireArbre : List Ligne -> Result Arbre |
||||
construireArbre lgns = |
||||
case lgns of |
||||
[] -> Ok <| Arbre [] |
||||
LigneVide :: lgnss -> Ok <| construireArbre lgnss |
||||
Ligne ind :: lgnss -> |
||||
construireArbreBis ind.indentation ( Arbre [] ) lgnss |
||||
|
||||
construireArbreBis prfdr arbrs lgns = |
||||
case |
||||
|
||||
profondeur : String -> Ligne |
||||
profondeur ligne = |
||||
Indentation 0 ligne |
||||
|> profondeurBis |
||||
|
||||
profondeurBis ind = |
||||
if String.isEmpty ind.ligne then |
||||
LigneVide |
||||
else if String.startsWith " " then |
||||
{ ind |
||||
| indentation = ind.indentation + 1 |
||||
, ligne = String.dropLeft 1 ind.ligne |
||||
} |
||||
else |
||||
ind |
||||
--} |
||||
|
||||
|
||||
{-| Ce parser change l'indentation courante, cré un arbre puis |
||||
y intègre ses branches grâce à une boucle |
||||
-} |
||||
arbre : Parser Arbre |
||||
arbre = |
||||
let |
||||
suite = |
||||
flip withIndent |
||||
<| succeed Arbre |
||||
|. symbol "*" |
||||
|= loop [] arbres -- (Etat ind []) remplacé par [] |
||||
in |
||||
getCol |
||||
|> andThen suite |
||||
|
||||
flip f a b = f b a |
||||
|
||||
|
||||
type alias Etat = |
||||
{ indentation : Int |
||||
, arborescence : List Arbre |
||||
} |
||||
|
||||
arbres arbrs = |
||||
let |
||||
suite col_ind = |
||||
if Tuple.first col_ind > Tuple.second col_ind then -- if col > ind |
||||
succeed ( \arbr -> Loop (arbr :: arbrs) ) |
||||
|= lazy (\_ -> arbre) |
||||
else |
||||
succeed () |
||||
|> map (\_ -> Done (List.reverse arbrs)) |
||||
in |
||||
succeed Tuple.pair |
||||
|. spaces |
||||
|= getCol |
||||
|= getIndent |
||||
|> andThen suite |
||||
{-- |
||||
oneOf |
||||
[ succeed ( \arbr -> Loop { etat | arborescence = arbr :: etat.arborescence } ) |
||||
|= arbresBis |
||||
|. spaces |
||||
, succeed () |
||||
|> map (\_ -> Done (List.reverse etat.arborescence)) |
||||
] |
||||
--} |
||||
|
||||
{-- |
||||
arbresBis typeInd = |
||||
case typeInd of |
||||
MemeIndentation -> |
||||
succeed ( \arbr -> Loop { etat | arborescence = arbr :: etat.arborescence } ) |
||||
|. symbol "*" |
||||
|. spaces |
||||
|= regarderIndentation |
||||
|
||||
type Indentation = |
||||
MemeIndentation |
||||
| MoinsIndentee |
||||
| PlusIndentee |
||||
|
||||
regarderIndentation : Parser Indentation |
||||
regarderIndentation = |
||||
succeed pair |
||||
|= getCol |
||||
|= getIndent |
||||
|> andThen regarderIndentationBis |
||||
|
||||
regarderIndentationBis col_ind = |
||||
let |
||||
col = first col_ind |
||||
ind = second col_ind |
||||
if col == ind then MemeIndentation |
||||
else if col < ind then MoinsIndentee |
||||
else PlusIndentee |
||||
|
||||
arbresBis : Parser Arbre |
||||
arbresBis = |
||||
memeIndentation |
||||
|> andThen arbresTer |
||||
|
||||
arbresTer : Bool -> Parser Arbre |
||||
arbresTer mmInd = |
||||
if mmInd then |
||||
succeed Arbre |
||||
else |
||||
problem "expecting more spaces" |
||||
|
||||
plusIndentee : Parser Bool |
||||
plusIndentee = |
||||
succeed (>=) |
||||
|= getCol |
||||
|= getIndent |
||||
|
||||
moinsIndentee : Parser Bool |
||||
moinsIndentee = |
||||
succeed (<=) |
||||
|= getCol |
||||
|= getIndent |
||||
|
||||
parser = |
||||
succeed (x -> Arbre ) |
||||
|= oneOf |
||||
[ getChompedString <| chompUntil "\n" |
||||
, succeed "" |
||||
] |
||||
|. token "\n" |
||||
|. spaces |
||||
|= changerIndentation parser |
||||
|
||||
parserBis = |
||||
getChompedString <| chompUntil "\n" |
||||
|. token "\n" |
||||
|. spaces |
||||
|= changerIndentation parser |
||||
|
||||
|
||||
changerIndentation prsr |
||||
succeed (col -> withIndent col prsr) |
||||
|= getCol |
||||
--} |
||||
Loading…
Reference in new issue