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module 2 corrigé des exercices
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Module 2Éléments d’algèbre
Exercices et corrigé
Version 3
MQT 1001
Mathématiques appliquées
à la gestion
Houda Affes
,Table des matières
Exercices ........................................................................................................................................................... 1
Section 1 ......................................................................................................................................................... 1
Section 2 ......................................................................................................................................................... 5
Section 3 ....................................................................................................................................................... 13
Section 4 ....................................................................................................................................................... 20
Corrigé des exercices ................................................................................................................................... 26
Section 1 ....................................................................................................................................................... 26
Section 2 ....................................................................................................................................................... 30
Section 3 ....................................................................................................................................................... 41
Section 4 ....................................................................................................................................................... 50
, MQT 1001 – Mathématiques appliquées à la gestion
Module 2 – Exercices et corrigé
Exercices
Section 1
( )
Déterminez la valeur de l’expression PV 1+ NI , lorsque les variables prennent les valeurs
suivantes :
PV = 2 000 , N = 2 et I = 0,05
PV = 5 000 , N = 5 et I = 8 %
1 1
PV = 10 000 000 , N = et I = 6 %
2 2
PV = 1 , N = 1 et I = 100 % I
3
PV = 10 456 , N = 7,375 et I = 16 %
4
La variable P = 3 000 , n = 3 et i = 0,1 i. Déterminez la valeur de chacune des expressions suivantes :
(
P 1+ ni )
( )
n
P 1+ i
(
P n+i )
P + n 1+ i( )
3P + 5ni
i
La variable indicée Xi est définie par X i = + i + 2 . Déterminez la valeur de :
2
X2
X 14
X7
X 21
X 5 432
1
, MQT 1001 – Mathématiques appliquées à la gestion
Module 2 – Exercices et corrigé
Si a = 3 et b = −4 , déterminez la valeur des expressions suivantes :
–a 2
( –a )
2
b2
–b2
( –b)
2
a 2 + b2
( a + b)
2
a 2 – b2
b2 – a 2
(b – a)2
Quelle valeur faut-il donner à la variable x pour que les expressions suivantes égalent 10?
x–6
2x
3
2x
x2 + 1
32x
⎛ 3 −4 5 0 ⎞
⎜ ⎟
Soit la matrice A = ⎜ −1 5 2 9 ⎟ ; déterminez la valeur des expressions suivantes :
⎜⎝ 4 −6 8 −7 ⎟⎠
a3,2
a2,3 + a3,4
a2,2
a1,1 +
a3,3
a2,1 + a1,2
a3,1 − a1,3
2
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