LTETT - 9STP1 – Corrigé du Devoir en classe de mathématiques II,1
Exercice 1
a) 6 2 32 7 4 4 192
6 64 7 4 19 6 8 28 19 48 47 1
⋅ − ⋅ −
= − ⋅ −
= ⋅ − −
= −
=
( ) ( )
c) 3 2 2 3 2 2 4 3 3 2
3 2 3 2 3 2 2 4 3 2 2 3 2
6 2 3 8 6 6 2 7 6 6 12 6 7 6
− − −
= ⋅ − ⋅ − ⋅ + ⋅
= − ⋅ − + ⋅
= − − +
= −
d) 300 2 48 3 100 3 2 16 3 3 100 3 2 16 3 3 10 3 2 4 3 3 10 3 8 3 3 17 3
+ −
= ⋅ + ⋅ −
= ⋅ + ⋅ −
= + ⋅ −
= + −
=
( )( )
( ) ( )
b) A= 5 3 1 2 3 5 5 2 3 3 3 2 3 5 10 3 3 6
1 9 3
P 2 5 3 2 1 2 3 2 5 2 3 2 1 2 2 3 10 2 3 2 4 3 12 2 3
− +
= + ⋅ − − ⋅
= + − −
= − +
= − + +
= ⋅ − ⋅ + ⋅ + ⋅
= − + +
= +
( )
22 2
e) 2 5
2 2 2 5 5 4 4 5 9 9 4 5
+
= + ⋅ ⋅ +
= + +
= +
Exercice 2
a) (2x + 1)2 + (4x – 3)2 b) 0,2x(0,1x + 1,2) – 0,2x2
= (2x)2 + 2⋅2x⋅1 + 12 + (4x)2 – 2⋅4x⋅3 + 32 = 0,2x⋅0,1x + 0,2x⋅1,2 – 0,2x2
= 4x2 + 4x + 1 + 16x2 – 24x + 9 = 0,02x2 + 0,24x – 0,2x2
= 20x2 – 20x + 10 = -0,18x2 + 0,24x
Exercice 3 a)14
2 ⋅104⋅213 10-7 49
⋅ 3 3 ( 5) 2
5 -5
1
2 3 10 6 10 6 10 600 10 10
− − − −
−
= ⋅ ⋅ = ⋅ = ⋅ =
⋅ c) 112 = 121 = 1,21⋅102
b) 8
2⋅1016⋅255 10-2 20
⋅ 14 14 12 2 3
3 4 12 1
2 5 10
10 10 10 10 1 10 1000 10
(10 )
⋅ ⋅ −
= = ⋅ = ⋅ = ⋅ =
⋅
Exercice 4
1° voir ci-contre Æ 2° p(A) = 0,4 = 40%
p(B) = 0,4 ⋅ 0,3 = 0,12 = 12%
p(C) = 0,2 ⋅ 0,1 + 0,4 ⋅ 0,3 + 0,4 ⋅ 0,6 = 0,02 + 0,12 + 0,24 = 0,38 = 38%
p(D) [= p(non C)] = 100% - 38% = 62%
p(E) = 0,1 = 10%
Exercice 5
a) 2 ⋅ (-4) + 4 = -8 + 4 = 12 et -3 ⋅ (-4) - 16 = 12 – 16 = -4 donc vrai ! b) (-3)2 + 9 = 9 + 9 = 18 ≠ 0 donc faux !
c) 180° - 65° - 65° = 50°≠ 57,5° donc faux !
d) 1 1 1 1 1 16 1 1 2 2 4 6 3 1
1 16 16 8 8 4 16 16 8 4
− − − − −
− − − − − = = = ≠ donc faux !
e) Vrai, car 1
4= 25%.
f) 1 1 1 1 2 4 7 1
16 8 4 16 16 2
+ + = + + = ≠ donc faux !
même exercice que dans le devoir I,3 !!!
exercice du travail de vacances de Noël !!!
exercice de la feuille traitée la semaine avant le devoir !!!
Attention ! Il faut écrire des parenthèses
autour du -3 ! -32 = -9 et (-3)2 = 9
