Devoir maison: 5

(1)

Devoir maison: 5

Troisième – À rendre le Mercredi 18 avril 2016

Sujet 44

Solution Exercice 1

1 Développer les expressions suivantes a. A= 7(7x+ 3)

Solution:

A = 7(7x+ 3) A = 7×7x+ 7×3 A = 49x+ 21

b. B= (6x+ 9)(2x+ 8)

Solution:

B = (6x+ 9)(2x+ 8)

B = 6×2x²+ 9×2x+ 6×8x+ 9×8 B = 6×2x²+ (9×2 + 6×8)x+ 9×8 B = 12x²+ (18 + 48)x+ 72

B = 12x²+ 66x+ 72

c. C = (10x+ 9)² Solution:

C = (10x+ 9)²

C = (10x+ 9)(10x+ 9)

C = 10×10x²+ 9×10x+ 10×9x+ 9×9 C = 10×10x²+ (9×10 + 10×9)x+ 9×9 C = 100x²+ (90 + 90)x+ 81

C = 100x²+ 180x+ 81

d. D = (5x−7)² Solution:

D = (5x−7)²

D = (5x−7)(5x−7)

D = 5×5x²−7×5x+ 5×(−7)x−7×(−7) D = 5×5x²+ (−7×5 + 5×(−7))x−7×(−7) D = 25x²+ (−35−35)x+ 49

D = 25x²−70x+ 49

2 Factoriser les expressions suivantes a. A= 20x²−45x

Solution:

A= 20x²−45x= 5x(4x−9)

(2)

À rendre le Mercredi 18 avril 2016 Devoir maison: 5 b. B= 48x²+ 6x

Solution:

B= 48x²+ 6x=−6x(−8x−1)

c. C = 80x²−20x Solution:

C = 80x²−20x=−10x(−8x+ 2)

d. D = 81x²+ 126x+ 49 Solution:

D = 81x²+ 126x+ 49 = (9x+ 7)²

Exercice 2

Résoudre les équations suivantes.

1 6x+ 9 = 0

Solution:

6x+ 9 = 0 6x+ 9−9 = 0−9 6x+ 9−9 =−9

6x=−9 6x

6 = −9 6 6

6x= −3×3 2×3 x= −3

2

2 ²⁵x+ 19 = 0

Solution:

25

22x+ 19 = 0 25

22x+ 19−19 = 0−19 25

22x+ 19−19 =−19 25

22x=−19

2522x

2522

= −19

2522 2522

2522

x=−19× 22 25 25

22 × 22

25x= −19×22 1×25 25×22

22×25x= −418 1 25

1x= −418 25 x= −418

25

(3)

À rendre le Mercredi 18 avril 2016 Devoir maison: 5 3 28x+ 38 = 39

(4)

À rendre le Mercredi 18 avril 2016 Devoir maison: 5

Solution:

28x+ 38 = 39 28x+ 38−38 = 39−38 28x+ 38−38 = 1

28x= 1 28x

28 = 1 28 28

28x= 1 28 x= 1

28

4 12x+ 5 =−8x−2

Solution:

12x+ 5 =−8x−2 12x+ 5−5 =−8x−2−5

12x=−8x−7

12x−(−8x) = −8x−7−(−8x) 12x+ 8x=−8x−7 + 8x (12 + 8)x=−8x+ 8x−7 20x= (−8 + 8)x−7 20x=−7

20x

20 = −7 20 20

20x= −7 20 x= −7 20

Exercice 3

Dans une urne, on a placé des boules colorées indiscernables au touché. Il y a 5 boules bleu, 4 boules jaunes, 2 boules vertes et 2 boules rouges.

1 a. Quelle est la probabilité de tirer une boule bleu ? Solution: 5

13 ≈0.38

b. Quelle est la probabilté de tirer une boule jaune ou bleu ? Solution: 9

13 ≈0.69

c. A-t-on plus de chance de tirer une boule verte ou une boule rouge ? Solution: Boules vertes : 2

13 ≈0.15 Boules rouges : 2

≈0.15

(5)

2 On effectue 14 tirages (avec remise) dans cette urne et on obtient les couleurs suivantes :

B R J B V J R R J B B J R J

a. Compléter le tableau des effectifs ci-dessous Couleur Bleu Jaune Vert Rouge

Effectif 4 5 1 4

b. Calculer la fréquence des boules vertes.

Solution: Fréquence de boules vertes : ₁₄¹

À chaque couleur, on associe des points. Une boule bleu rapporte 10 points, une boule jaune 5 points, une boule verte 2 points et une boule rouge 0 points.

c. Combien de points a-t-on gagné ? Solution: 17

d. Calculer la moyenne des gains.

Solution: 4.25

e. Calculer la médiane des gains.

Solution: 6

(6)

Devoir maison: 5

Sujet 07

Solution Exercice 1

1 Développer les expressions suivantes a. A=−9(2x+ 7)

Solution:

A = −9(2x+ 7) A = −9×2x−9×7 A = −18x−63

b. B= (2x+ 6)(6x+ 9)

Solution:

B = (2x+ 6)(6x+ 9)

B = 2×6x²+ 6×6x+ 2×9x+ 6×9 B = 2×6x²+ (6×6 + 2×9)x+ 6×9 B = 12x²+ (36 + 18)x+ 54

B = 12x²+ 54x+ 54

C = (7x+ 3)²

C = (7x+ 3)(7x+ 3)

C = 7×7x²+ 3×7x+ 7×3x+ 3×3 C = 7×7x²+ (3×7 + 7×3)x+ 3×3 C = 49x²+ (21 + 21)x+ 9

C = 49x²+ 42x+ 9

D = (5x−5)²

D = (5x−5)(5x−5)

D = 5×5x²−5×5x+ 5×(−5)x−5×(−5) D = 5×5x²+ (−5×5 + 5×(−5))x−5×(−5) D = 25x²+ (−25−25)x+ 25

D = 25x²−50x+ 25

2 Factoriser les expressions suivantes a. A=−60x²+ 70x

Solution:

A=−60x²+ 70x= 10x(−6x+ 7)

(7)

À rendre le Mercredi 18 avril 2016 Devoir maison: 5 b. B=−10x²−10x

Solution:

B=−10x²−10x= 10x(−1x−1)

C = 3x²−27x= 3x(1x−9)

d. D = 4x²+ 36x+ 81 Solution:

D = 4x²+ 36x+ 81 = (2x+ 9)²

Exercice 2

1 −6x+ 1 = 0

Solution:

−6x+ 1 = 0

−6x+ 1−1 = 0−1

−6x+ 1−1 =−1

−6x=−1

−6x

−6 = −1

−6

−6x= 1 6 x= 1 6

2 ²⁷₂₉x+ 10 = 0

Solution:

27

29x+ 10 = 0 27

29x+ 10−10 = 0−10 27

29x+ 10−10 =−10 27

29x=−10

2729x

2729

= −10

2729 2729

2729

x=−10× 29 27 27

29 × 29

27x= −10×29 1×27 27×29

29×27x= −290 1 27

1x= −290 27 x= −290

27

(8)

(9)

Solution:

24x+ 29 = 4 24x+ 29−29 = 4−29 24x+ 29−29 =−25

24x=−25 24x

24 = −25 24 24

24x= −25 24 x= −25

24

4 16x−3 =−1x−6

Solution:

16x−3 =−1x−6 16x−3 =−x−6

16x−3−(−3) =−x−6−(−3) 16x−3 + 3 =−x−6 + 3

16x=−x−3

16x−(−x) =−x−3−(−x) 16x+x=−x−3 +x (16 + 1)x=−x+x−3

17x= (−1 + 1)x−3 17x=−3

17x

17 = −3 17 17

17x= −3 17 x= −3 17

Exercice 3

18 ≈0.17

18 ≈0.44

18 ≈0.39

(10)

Une boule rouge

V V R J J R J B R B B V R V

Effectif 3 3 4 4

Solution: Fréquence de boules vertes : ₁₄⁴

Solution: 4.25

Solution: 6

(11)

Devoir maison: 5

Sujet 53

Solution Exercice 1

1 Développer les expressions suivantes a. A= 8(−9x−3)

Solution:

A = 8(−9x−3)

A = 8×(−9)x+ 8×(−3) A = −72x−24

b. B= (7x+ 7)(10x+ 4)

Solution:

B = (7x+ 7)(10x+ 4)

B = 7×10x²+ 7×10x+ 7×4x+ 7×4 B = 7×10x²+ (7×10 + 7×4)x+ 7×4 B = 70x²+ (70 + 28)x+ 28

B = 70x²+ 98x+ 28

C = (2x+ 7)²

C = (2x+ 7)(2x+ 7)

C = 2×2x²+ 7×2x+ 2×7x+ 7×7 C = 2×2x²+ (7×2 + 2×7)x+ 7×7 C = 4x²+ (14 + 14)x+ 49

C = 4x²+ 28x+ 49

D = (7x−9)²

D = (7x−9)(7x−9)

D = 7×7x²−9×7x+ 7×(−9)x−9×(−9) D = 7×7x²+ (−9×7 + 7×(−9))x−9×(−9) D = 49x²+ (−63−63)x+ 81

D = 49x²−126x+ 81

2 Factoriser les expressions suivantes a. A= 20x²+ 45x

Solution:

A= 20x²+ 45x= 5x(4x+ 9)

(12)

Solution:

B= 64x²+ 40x= 8x(8x+ 5)

c. C =−36x²+ 24x Solution:

C =−36x²+ 24x=−6x(6x−4)

D = 9x²+ 54x+ 81 = (3x+ 9)²

Exercice 2

1 −10x−5 = 0

Solution:

−10x−5 = 0

−10x−5−(−5) = 0−(−5)

−10x−5 + 5 = 0 + 5

−10x−5 + 5 = 5

−10x= 5

−10x

−10 = 5

−10

−10x= −5 10 x= −1×5

2×5 x= −1

2

2 ²⁴₇ x+ 11 = 0

Solution:

24

7 x+ 11 = 0 24

7 x+ 11−11 = 0−11 24

7 x+ 11−11 =−11 24

7 x=−11

247 x

247

= −11

247 247

247

x=−11× 7 24 24

7 × 7

24x= −11×7 1×24 24×7

7×24x= −77 1 24

1×1x= −77 1 24

1x= −77

−2477

(13)

3 36x+ 41 = 50

Solution:

36x+ 41 = 50 36x+ 41−41 = 50−41 36x+ 41−41 = 9

36x= 9 36x

36 = 9 36 36

36x= 1×9 4×9 x= 1

4

4 5x+ 8 =−4x+ 16

Solution:

5x+ 8 =−4x+ 16 5x+ 8−8 =−4x+ 16−8

5x=−4x+ 8

5x−(−4x) = −4x+ 8−(−4x) 5x+ 4x=−4x+ 8 + 4x (5 + 4)x=−4x+ 4x+ 8 9x= (−4 + 4)x+ 8 9x= 8

9x 9 = 8 9 9

9x= 8 9 x= 8 9

Exercice 3

33 ≈0.27

33 ≈0.58

33 ≈0.24 Une boule rouge

(14)

V V V V J B R R J B J R R J

Effectif 2 4 4 4

Solution: 4.25

Solution: 6

(15)

Devoir maison: 5

Sujet 41

Solution Exercice 1

1 Développer les expressions suivantes a. A=−8(−1x−2)

Solution:

A = −8(−1x−2) A = −8(−x−2)

A = −8×(−1)x−8×(−2) A = 8x+ 16

b. B= (2x+ 10)(2x+ 8)

Solution:

B = (2x+ 10)(2x+ 8)

B = 2×2x²+ 10×2x+ 2×8x+ 10×8 B = 2×2x²+ (10×2 + 2×8)x+ 10×8 B = 4x²+ (20 + 16)x+ 80

B = 4x²+ 36x+ 80

C = (9x+ 10)²

C = (9x+ 10)(9x+ 10)

C = 9×9x²+ 10×9x+ 9×10x+ 10×10 C = 9×9x²+ (10×9 + 9×10)x+ 10×10 C = 81x²+ (90 + 90)x+ 100

C = 81x²+ 180x+ 100

D = (6x−5)²

D = (6x−5)(6x−5)

D = 6×6x²−5×6x+ 6×(−5)x−5×(−5) D = 6×6x²+ (−5×6 + 6×(−5))x−5×(−5) D = 36x²+ (−30−30)x+ 25

D = 36x²−60x+ 25

2 Factoriser les expressions suivantes a. A=−81x²−90x

Solution:

A=−81x²−90x= 9x(−9x−10)

(16)

Solution:

B=−21x²−28x=−7x(3x+ 4)

C =−6x²+ 6x=−2x(3x−3)

d. D = 100x²+ 180x+ 81 Solution:

D = 100x²+ 180x+ 81 = (10x+ 9)²

Exercice 2

1 −10x−1 = 0

Solution:

−10x−1 = 0

−10x−1−(−1) = 0−(−1)

−10x−1 + 1 = 0 + 1

−10x−1 + 1 = 1

−10x= 1

−10x

−10 = 1

−10

−10x= −1 10 x= −1 10

27

Solution:

27

13x+ 19 = 0 27

13x+ 19−19 = 0−19 27

13x+ 19−19 =−19 27

13x=−19

2713x

2713

= −19

2713 2713

2713

x=−19× 13 27 27

13 × 13

27x= −19×13 1×27 27×13

13×27x= −247 1 27

1×1x= −247 1 27

1x= −247

−27247

(17)

(18)

Solution:

2x+ 27 = 22 2x+ 27−27 = 22−27 2x+ 27−27 =−5

2x=−5 2x

2 = −5 2 2

2x= −5 2 x= −5

2

4 12x−8 = 19x−8

Solution:

12x−8 = 19x−8

12x−8−(−8) = 19x−8−(−8) 12x−8 + 8 = 19x−8 + 8

12x= 19x

12x−19x= 19x−19x (12−19)x= (19−19)x

−7x= 0

−7x

−7 = 0

−7

−7x= 0 x= 0

Exercice 3

18 ≈0.5

18 ≈0.72

18 ≈0.11 Une boule verte

(19)

V B B J B J R B B J B R B J

Effectif 7 4 1 2

Solution: 4.25

Solution: 6

(20)

Devoir maison: 5

Sujet 65

Solution Exercice 1

1 Développer les expressions suivantes a. A= 4(7x−2)

Solution:

A = 4(7x−2)

A = 4×7x+ 4×(−2) A = 28x−8

b. B= (10x+ 9)(5x+ 3)

Solution:

B = (10x+ 9)(5x+ 3)

B = 10×5x²+ 9×5x+ 10×3x+ 9×3 B = 10×5x²+ (9×5 + 10×3)x+ 9×3 B = 50x²+ (45 + 30)x+ 27

B = 50x²+ 75x+ 27

C = (6x+ 7)²

C = (6x+ 7)(6x+ 7)

C = 6×6x²+ 7×6x+ 6×7x+ 7×7 C = 6×6x²+ (7×6 + 6×7)x+ 7×7 C = 36x²+ (42 + 42)x+ 49

C = 36x²+ 84x+ 49

D = (7x−4)²

D = (7x−4)(7x−4)

D = 7×7x²−4×7x+ 7×(−4)x−4×(−4) D = 7×7x²+ (−4×7 + 7×(−4))x−4×(−4) D = 49x²+ (−28−28)x+ 16

D = 49x²−56x+ 16

Solution:

A=−14x²+ 28x= 7x(−2x+ 4)

(21)

Solution:

B=−63x²−54x= 9x(−7x−6)

c. C = 48x²+ 72x Solution:

C = 48x²+ 72x=−8x(−6x−9)

D = 9x²+ 54x+ 81 = (3x+ 9)²

Exercice 2

1 −9x−9 = 0

Solution:

−9x−9 = 0

−9x−9−(−9) = 0−(−9)

−9x−9 + 9 = 0 + 9

−9x−9 + 9 = 9

−9x= 9

−9x

−9 = 9

−9

−9x=−1 x=−1

2 ²²₂₉x+ 20 = 0

Solution:

22

29x+ 20 = 0 22

29x+ 20−20 = 0−20 22

29x+ 20−20 =−20 22

29x=−20

2229x

2229

= −20

2229 2229

2229

x=−20× 29 22 22

29 × 29

22x= 2×(−10)×29 1×2×11 22×29

29×22x= −10×29 1×11 1

1x= −290 11 x= −290

11

(22)

(23)

Solution:

14x+ 37 = 23 14x+ 37−37 = 23−37 14x+ 37−37 =−14

14x=−14 14x

14 = −14 14 14

14x=−1 x=−1

4 16x−6 = 7x−10

Solution:

16x−6 = 7x−10

16x−6−(−6) = 7x−10−(−6) 16x−6 + 6 = 7x−10 + 6

16x= 7x−4 16x−7x= 7x−4−7x (16−7)x= 7x−7x−4 9x= (7−7)x−4 9x=−4

9x

9 = −4 9 9

9x= −4 9 x= −4

9

Exercice 3

34 ≈0.21

34 ≈0.5

34 ≈0.24 Une boule verte

(24)

J V B V J V R R J R B V V V

Effectif 2 3 6 3

Solution: Fréquence de boules vertes : ₁₄⁶

Solution: 4.25

Solution: 6

(25)

Devoir maison: 5

Sujet 18

Solution Exercice 1

1 Développer les expressions suivantes a. A=−6(−1x+ 5)

Solution:

A = −6(−1x+ 5) A = −6(−x+ 5)

A = −6×(−1)x−6×5 A = 6x−30

b. B= (2x+ 10)(9x+ 7)

Solution:

B = (2x+ 10)(9x+ 7)

B = 2×9x²+ 10×9x+ 2×7x+ 10×7 B = 2×9x²+ (10×9 + 2×7)x+ 10×7 B = 18x²+ (90 + 14)x+ 70

B = 18x²+ 104x+ 70

C = (6x+ 5)²

C = (6x+ 5)(6x+ 5)

C = 6×6x²+ 5×6x+ 6×5x+ 5×5 C = 6×6x²+ (5×6 + 6×5)x+ 5×5 C = 36x²+ (30 + 30)x+ 25

C = 36x²+ 60x+ 25

D = (4x−7)²

D = (4x−7)(4x−7)

D = 4×4x²−7×4x+ 4×(−7)x−7×(−7) D = 4×4x²+ (−7×4 + 4×(−7))x−7×(−7) D = 16x²+ (−28−28)x+ 49

D = 16x²−56x+ 49

Solution:

A=−50x²+ 25x= 5x(−10x+ 5)

(26)

À rendre le Mercredi 18 avril 2016 Devoir maison: 5 b. B=−40x²+ 30x

Solution:

B=−40x²+ 30x= 10x(−4x+ 3)

C = 14x²−10x=−2x(−7x+ 5)

d. D = 100x²+ 80x+ 16 Solution:

D = 100x²+ 80x+ 16 = (10x+ 4)²

Exercice 2

1 −1x+ 3 = 0

Solution:

−1x+ 3 = 0

−x+ 3 = 0

−x+ 3−3 = 0−3

−x+ 3−3 =−3

−x=−3

−x

−1 = −3

−1

−1x= 3 x= 3

2 ⁷ x+ 30 = 0

Solution:

7

13x+ 30 = 0 7

13x+ 30−30 = 0−30 7

13x+ 30−30 =−30 7

13x=−30

137 x

137

= −30

137 137

137

x=−30× 13 7 7

13 × 13

7 x= −30×13 1×7 7×13

13×7x= −390 1 7

1x= −390 7 x= −390

7

(27)

(28)

Solution:

23x+ 14 = 44 23x+ 14−14 = 44−14 23x+ 14−14 = 30

23x= 30 23x

23 = 30 23 23

23x= 30 23 x= 30 23

4 −4x−4 = 13x+ 18

Solution:

−4x−4 = 13x+ 18

−4x−4−(−4) = 13x+ 18−(−4)

−4x−4 + 4 = 13x+ 18 + 4

−4x= 13x+ 22

−4x−13x= 13x+ 22−13x (−4−13)x= 13x−13x+ 22

−17x= (13−13)x+ 22

−17x= 22

−17x

−17 = 22

−17

−17x= −22 17 x= −22

17

Exercice 3

23 ≈0.22

23 ≈0.52

≈0.35

(29)

V B B J B J R R R R J R J J

Effectif 3 5 1 5

Solution: 4.25

Solution: 6

(30)

Devoir maison: 5

Sujet 14

Solution Exercice 1

Solution:

A = 6(7x+ 10) A = 6×7x+ 6×10 A = 42x+ 60

b. B= (9x+ 10)(5x+ 2)

Solution:

B = (9x+ 10)(5x+ 2)

B = 9×5x²+ 10×5x+ 9×2x+ 10×2 B = 9×5x²+ (10×5 + 9×2)x+ 10×2 B = 45x²+ (50 + 18)x+ 20

B = 45x²+ 68x+ 20

C = (9x+ 4)²

C = (9x+ 4)(9x+ 4)

C = 9×9x²+ 4×9x+ 9×4x+ 4×4 C = 9×9x²+ (4×9 + 9×4)x+ 4×4 C = 81x²+ (36 + 36)x+ 16

C = 81x²+ 72x+ 16

D = (9x−5)²

D = (9x−5)(9x−5)

D = 9×9x²−5×9x+ 9×(−5)x−5×(−5) D = 9×9x²+ (−5×9 + 9×(−5))x−5×(−5) D = 81x²+ (−45−45)x+ 25

D = 81x²−90x+ 25

2 Factoriser les expressions suivantes a. A=−18x²−9x

Solution:

A=−18x²−9x= 3x(−6x−3)

(31)

Solution:

B=−7x²+ 5x= 1x(−7x+ 5)

c. C = 8x²+ 5x Solution:

C = 8x²+ 5x=−1x(−8x−5)

D = 36x²+ 60x+ 25 = (6x+ 5)²

Exercice 2

1 5x−9 = 0

Solution:

5x−9 = 0

5x−9−(−9) = 0−(−9) 5x−9 + 9 = 0 + 9 5x−9 + 9 = 9

5x= 9 5x

5 = 9 5 5

5x= 9 5 x= 9 5

2 ²⁴₂₉x+ 24 = 0

Solution:

24

29x+ 24 = 0 24

29x+ 24−24 = 0−24 24

29x+ 24−24 =−24 24

29x=−24

2429x

2429

= −24

2429 2429

2429

x=−24× 29 24 24

29 × 29

24x= 24×(−1)×29 1×24 24×29

29×24x= −1×29 1×1 1

1x= −29 1 x=−29

(32)

(33)

Solution:

15x+ 46 = 49 15x+ 46−46 = 49−46 15x+ 46−46 = 3

15x= 3 15x

15 = 3 15 15

15x= 1×3 5×3 x= 1

5

4 15x+ 3 = 19x+ 2

Solution:

15x+ 3 = 19x+ 2 15x+ 3−3 = 19x+ 2−3

15x= 19x−1

15x−19x= 19x−1−19x (15−19)x= 19x−19x−1

−4x= (19−19)x−1

−4x=−1

−4x

−4 = −1

−4

−4x= 1 4 x= 1 4

Exercice 3

29 ≈0.34

29 ≈0.48

(34)

V B B J B B B V J R B R J R

Effectif 6 3 2 3

Solution: Fréquence de boules vertes : ₁₄²

Solution: 4.25

Solution: 6

(35)

Devoir maison: 5

Sujet 30

Solution Exercice 1

Solution:

A = 8(8x+ 3) A = 8×8x+ 8×3 A = 64x+ 24

b. B= (3x+ 5)(7x+ 6)

Solution:

B = (3x+ 5)(7x+ 6)

B = 3×7x²+ 5×7x+ 3×6x+ 5×6 B = 3×7x²+ (5×7 + 3×6)x+ 5×6 B = 21x²+ (35 + 18)x+ 30

B = 21x²+ 53x+ 30

C = (7x+ 4)²

C = (7x+ 4)(7x+ 4)

C = 7×7x²+ 4×7x+ 7×4x+ 4×4 C = 7×7x²+ (4×7 + 7×4)x+ 4×4 C = 49x²+ (28 + 28)x+ 16

C = 49x²+ 56x+ 16

D = (2x−4)²

D = (2x−4)(2x−4)

D = 2×2x²−4×2x+ 2×(−4)x−4×(−4) D = 2×2x²+ (−4×2 + 2×(−4))x−4×(−4) D = 4x²+ (−8−8)x+ 16

D = 4x²−16x+ 16

Solution:

A=−24x²+ 24x= 3x(−8x+ 8)

(36)

Solution:

B=−42x²−42x=−7x(6x+ 6)

c. C =−7x²−56x Solution:

C =−7x²−56x= 7x(−1x−8)

D = 9x²+ 60x+ 100 = (3x+ 10)²

Exercice 2

1 9x−8 = 0

Solution:

9x−8 = 0

9x−8−(−8) = 0−(−8) 9x−8 + 8 = 0 + 8 9x−8 + 8 = 8

9x= 8 9x

9 = 8 9 9

9x= 8 9 x= 8 9

3

Solution:

3

17x+ 9 = 0 3

17x+ 9−9 = 0−9 3

17x+ 9−9 =−9 3

17x=−9

173 x

173

= −9

173 173

173

x=−9× 17 3 3

17 × 17

3 x= 3×(−3)×17 1×3 3×17

17×3x= −3×17 1×1 1

1×1x= −51 1 1

1x=−51

= 51

(37)

(38)

Solution:

13x+ 15 = 32 13x+ 15−15 = 32−15 13x+ 15−15 = 17

13x= 17 13x

13 = 17 13 13

13x= 17 13 x= 17 13

4 16x+ 14 =−4x−4

Solution:

16x+ 14 =−4x−4 16x+ 14−14 =−4x−4−14

16x=−4x−18

16x−(−4x) =−4x−18−(−4x) 16x+ 4x=−4x−18 + 4x (16 + 4)x=−4x+ 4x−18 20x= (−4 + 4)x−18 20x=−18

20x

20 = −18 20 20

20x= −9×2 10×2 x= −9

10

Exercice 3

24 ≈0.33

24 ≈0.75

≈0.08

(39)

B J J R B R J B J J J J V J

Effectif 3 8 1 2

Solution: 4.25

Solution: 6

(40)

Devoir maison: 5

Sujet 36

Solution Exercice 1

1 Développer les expressions suivantes a. A= 10(−9x−7)

Solution:

A = 10(−9x−7)

A = 10×(−9)x+ 10×(−7) A = −90x−70

b. B= (2x+ 2)(8x+ 5)

Solution:

B = (2x+ 2)(8x+ 5)

B = 2×8x²+ 2×8x+ 2×5x+ 2×5 B = 2×8x²+ (2×8 + 2×5)x+ 2×5 B = 16x²+ (16 + 10)x+ 10

B = 16x²+ 26x+ 10

C = (6x+ 5)²

C = (6x+ 5)(6x+ 5)

C = 6×6x²+ 5×6x+ 6×5x+ 5×5 C = 6×6x²+ (5×6 + 6×5)x+ 5×5 C = 36x²+ (30 + 30)x+ 25

C = 36x²+ 60x+ 25

D = (8x−5)²

D = (8x−5)(8x−5)

D = 8×8x²−5×8x+ 8×(−5)x−5×(−5) D = 8×8x²+ (−5×8 + 8×(−5))x−5×(−5) D = 64x²+ (−40−40)x+ 25

D = 64x²−80x+ 25

Solution:

A=−18x²+ 2x= 2x(−9x+ 1)

(41)

Solution:

B=−6x²−10x= 2x(−3x−5)

C =−63x²−72x=−9x(7x+ 8)

D = 16x²+ 24x+ 9 = (4x+ 3)²

Exercice 2

1 −8x+ 2 = 0

Solution:

−8x+ 2 = 0

−8x+ 2−2 = 0−2

−8x+ 2−2 =−2

−8x=−2

−8x

−8 = −2

−8

−8x= 2 8 x= 1×2

4×2 x= 1

4

2 ²⁹₈ x+ 21 = 0

Solution:

29

8 x+ 21 = 0 29

8 x+ 21−21 = 0−21 29

8 x+ 21−21 =−21 29

8 x=−21

298 x

298

= −21

298 298

298

x=−21× 8 29 29

8 × 8

29x= −21×8 1×29 29×8

8×29x= −168 1 29

1×1x= −168 1 29

1x= −168 29 x= −168

29

(42)

(43)

Solution:

18x+ 41 = 50 18x+ 41−41 = 50−41 18x+ 41−41 = 9

18x= 9 18x

18 = 9 18 18

18x= 1×9 2×9 x= 1

2

4 11x−2 = 4x−3

Solution:

11x−2 = 4x−3

11x−2−(−2) = 4x−3−(−2) 11x−2 + 2 = 4x−3 + 2

11x= 4x−1 11x−4x= 4x−1−4x (11−4)x= 4x−4x−1 7x= (4−4)x−1 7x=−1

7x

7 = −1 7 7

7x= −1 7 x= −1

7

Exercice 3

24 ≈0.33

24 ≈0.62

(44)

V B R B R B B R V V B J B V

Effectif 6 1 4 3

Solution: 4.25

Solution: 6

(45)

Devoir maison: 5

Sujet 63

Solution Exercice 1

Solution:

A = −1(−9x+ 6)

A = −1×(−9)x−1×6 A = 9x−6

b. B= (6x+ 10)(6x+ 8)

Solution:

B = (6x+ 10)(6x+ 8)

B = 6×6x²+ 10×6x+ 6×8x+ 10×8 B = 6×6x²+ (10×6 + 6×8)x+ 10×8 B = 36x²+ (60 + 48)x+ 80

B = 36x²+ 108x+ 80

C = (4x+ 9)²

C = (4x+ 9)(4x+ 9)

C = 4×4x²+ 9×4x+ 4×9x+ 9×9 C = 4×4x²+ (9×4 + 4×9)x+ 9×9 C = 16x²+ (36 + 36)x+ 81

C = 16x²+ 72x+ 81

D = (10x−9)²

D = (10x−9)(10x−9)

D = 10×10x²−9×10x+ 10×(−9)x−9×(−9) D = 10×10x²+ (−9×10 + 10×(−9))x−9×(−9) D = 100x²+ (−90−90)x+ 81

D = 100x²−180x+ 81

Solution:

A= 8x²+ 20x= 2x(4x+ 10)

(46)

Solution:

B= 16x²+ 8x=−4x(−4x−2)

C = 12x²−24x=−3x(−4x+ 8)

D = 49x²+ 70x+ 25 = (7x+ 5)²

Exercice 2

1 1x+ 5 = 0

Solution:

1x+ 5 = 0 x+ 5 = 0 x+ 5−5 = 0−5 x+ 5−5 =−5

x=−5

2 ²⁷₁₁x+ 8 = 0

Solution:

27

11x+ 8 = 0 27

11x+ 8−8 = 0−8 27

11x+ 8−8 =−8 27

11x=−8

2711x

2711

= −8

2711 2711

2711

x=−8× 11 27 27

11 × 11

27x= −8×11 1×27 27×11

11×27x= −88 1 27

1×1x= −88 1 27

1x= −88

−2788

(47)

(48)

Solution:

23x+ 44 = 2 23x+ 44−44 = 2−44 23x+ 44−44 =−42

23x=−42 23x

23 = −42 23 23

23x= −42 23 x= −42

23

4 20x+ 15 =−2x−9

Solution:

20x+ 15 =−2x−9 20x+ 15−15 =−2x−9−15

20x=−2x−24

20x−(−2x) =−2x−24−(−2x) 20x+ 2x=−2x−24 + 2x (20 + 2)x=−2x+ 2x−24 22x= (−2 + 2)x−24 22x=−24

22x

22 = −24 22 22

22x= −12×2 11×2 x= −12

11

Exercice 3

13 ≈0.15

13 ≈0.46

≈0.23

(49)

J V V R V B J B B V V B J R

Effectif 4 3 5 2

Solution: Fréquence de boules vertes : ₁₄⁵

Solution: 4.25

Solution: 6

(50)

Devoir maison: 5

Sujet 32

Solution Exercice 1

1 Développer les expressions suivantes a. A=−2(3x−6)

Solution:

A = −2(3x−6)

A = −2×3x−2×(−6) A = −6x+ 12

b. B= (7x+ 8)(5x+ 3)

Solution:

B = (7x+ 8)(5x+ 3)

B = 7×5x²+ 8×5x+ 7×3x+ 8×3 B = 7×5x²+ (8×5 + 7×3)x+ 8×3 B = 35x²+ (40 + 21)x+ 24

B = 35x²+ 61x+ 24

C = (2x+ 3)²

C = (2x+ 3)(2x+ 3)

C = 2×2x²+ 3×2x+ 2×3x+ 3×3 C = 2×2x²+ (3×2 + 2×3)x+ 3×3 C = 4x²+ (6 + 6)x+ 9

C = 4x²+ 12x+ 9

D = (9x−3)²

D = (9x−3)(9x−3)

D = 9×9x²−3×9x+ 9×(−3)x−3×(−3) D = 9×9x²+ (−3×9 + 9×(−3))x−3×(−3) D = 81x²+ (−27−27)x+ 9

D = 81x²−54x+ 9

Solution:

A=−50x²+ 50x= 5x(−10x+ 10)

(51)

Solution:

B=−5x²−45x=−5x(1x+ 9)

C =−8x²+ 8x=−1x(8x−8)

D = 100x²+ 60x+ 9 = (10x+ 3)²

Exercice 2

1 −6x−5 = 0

Solution:

−6x−5 = 0

−6x−5−(−5) = 0−(−5)

−6x−5 + 5 = 0 + 5

−6x−5 + 5 = 5

−6x= 5

−6x

−6 = 5

−6

−6x= −5 6 x= −5

6

2 ²⁷₁₆x+ 9 = 0

Solution:

27

16x+ 9 = 0 27

16x+ 9−9 = 0−9 27

16x+ 9−9 =−9 27

16x=−9

2716x

2716

= −9

2716 2716

2716

x=−9× 16 27 27

16 × 16

27x= 9×(−1)×16 1×9×3 27×16

16×27x= −1×16 1×3 1

1x= −16 3 x= −16

3

(52)

(53)

Solution:

9x+ 21 = 2 9x+ 21−21 = 2−21 9x+ 21−21 =−19

9x=−19 9x

9 = −19 9 9

9x= −19 9 x= −19

9

4 −9x−5 =−8x+ 19

Solution:

−9x−5 =−8x+ 19

−9x−5−(−5) =−8x+ 19−(−5)

−9x−5 + 5 =−8x+ 19 + 5

−9x=−8x+ 24

−9x−(−8x) =−8x+ 24−(−8x)

−9x+ 8x=−8x+ 24 + 8x (−9 + 8)x=−8x+ 8x+ 24

−x= (−8 + 8)x+ 24

−x= 24

−x

−1 = 24

−1

−1x=−24 x=−24

Exercice 3

25 ≈0.4

25 ≈0.68

(54)

J J B B J R R B R B J B B B

Effectif 7 4 3

Solution: Fréquence de boules vertes : ₁₄⁰

Solution: 4.25

Solution: 6

(55)

Devoir maison: 5

Sujet 50

Solution Exercice 1

1 Développer les expressions suivantes a. A= 7(7x−1)

Solution:

A = 7(7x−1)

A = 7×7x+ 7×(−1) A = 49x−7

b. B= (10x+ 10)(10x+ 7)

Solution:

B = (10x+ 10)(10x+ 7)

B = 10×10x²+ 10×10x+ 10×7x+ 10×7 B = 10×10x²+ (10×10 + 10×7)x+ 10×7 B = 100x²+ (100 + 70)x+ 70

B = 100x²+ 170x+ 70

C = (5x+ 5)²

C = (5x+ 5)(5x+ 5)

C = 5×5x²+ 5×5x+ 5×5x+ 5×5 C = 5×5x²+ (5×5 + 5×5)x+ 5×5 C = 25x²+ (25 + 25)x+ 25

C = 25x²+ 50x+ 25

D = (3x−2)²

D = (3x−2)(3x−2)

D = 3×3x²−2×3x+ 3×(−2)x−2×(−2) D = 3×3x²+ (−2×3 + 3×(−2))x−2×(−2) D = 9x²+ (−6−6)x+ 4

D = 9x²−12x+ 4

Solution:

A= 16x²+ 8x= 8x(2x+ 1)

(56)

À rendre le Mercredi 18 avril 2016 Devoir maison: 5 b. B= 28x²−63x

Solution:

B= 28x²−63x=−7x(−4x+ 9)

C =−40x²+ 80x= 8x(−5x+ 10)

d. D = 64x²+ 128x+ 64 Solution:

D = 64x²+ 128x+ 64 = (8x+ 8)²

Exercice 2

1 1x+ 1 = 0

Solution:

1x+ 1 = 0 x+ 1 = 0 x+ 1−1 = 0−1 x+ 1−1 =−1

x=−1

2 ²²₃ x+ 24 = 0

Solution:

22

3 x+ 24 = 0 22

3 x+ 24−24 = 0−24 22

3 x+ 24−24 =−24 22

3 x=−24

223 x

223

= −24

223 223

223

x=−24× 3 22 22

3 × 3

22x= 2×(−12)×3 1×2×11 22×3

3×22x= −12×3 1×11 1

1×1x= −36 1 11

1x= −36

−1136

(57)

(58)

Solution:

4x+ 2 = 47 4x+ 2−2 = 47−2 4x+ 2−2 = 45

4x= 45 4x

4 = 45 4 4

4x= 45 4 x= 45

4

4 3x−1 = 10x−8

Solution:

3x−1 = 10x−8

3x−1−(−1) = 10x−8−(−1) 3x−1 + 1 = 10x−8 + 1

3x= 10x−7

3x−10x= 10x−7−10x (3−10)x= 10x−10x−7

−7x= (10−10)x−7

−7x=−7

−7x

−7 = −7

−7

−7x= 1 x= 1

Exercice 3

32 ≈0.31

32 ≈0.5

≈0.19

(59)

J J B J B B V J B R J R B J

Effectif 5 6 1 2

Solution: 4.25

Solution: 6

(60)

Devoir maison: 5

Sujet 15

Solution Exercice 1

1 Développer les expressions suivantes a. A=−9(2x−9)

Solution:

A = −9(2x−9)

A = −9×2x−9×(−9) A = −18x+ 81

b. B= (2x+ 7)(10x+ 4)

Solution:

B = (2x+ 7)(10x+ 4)

B = 2×10x²+ 7×10x+ 2×4x+ 7×4 B = 2×10x²+ (7×10 + 2×4)x+ 7×4 B = 20x²+ (70 + 8)x+ 28

B = 20x²+ 78x+ 28

C = (3x+ 5)²

C = (3x+ 5)(3x+ 5)

C = 3×3x²+ 5×3x+ 3×5x+ 5×5 C = 3×3x²+ (5×3 + 3×5)x+ 5×5 C = 9x²+ (15 + 15)x+ 25

C = 9x²+ 30x+ 25

D = (3x−6)²

D = (3x−6)(3x−6)

D = 3×3x²−6×3x+ 3×(−6)x−6×(−6) D = 3×3x²+ (−6×3 + 3×(−6))x−6×(−6) D = 9x²+ (−18−18)x+ 36

D = 9x²−36x+ 36

2 Factoriser les expressions suivantes a. A= 21x²−6x

Solution:

A= 21x²−6x= 3x(7x−2)

(61)

Solution:

B= 24x²+ 12x=−4x(−6x−3)

C =−60x²−48x= 6x(−10x−8)

D = 9x²+ 24x+ 16 = (3x+ 4)²

Exercice 2

1 −10x+ 7 = 0

Solution:

−10x+ 7 = 0

−10x+ 7−7 = 0−7

−10x+ 7−7 =−7

−10x=−7

−10x

−10 = −7

−10

−10x= 7 10 x= 7

10

2 ²³₈ x+ 2 = 0

Solution:

23

8 x+ 2 = 0 23

8 x+ 2−2 = 0−2 23

8 x+ 2−2 =−2 23

8 x=−2

238 x

238

= −2

238 238

238

x=−2× 8 23 23

8 × 8

23x= −2×8 1×23 23×8

8×23x= −16 1 23

1×1x= −16 1 23

1x= −16 23 x= −16

23

(62)

(63)

Solution:

7x+ 23 = 19 7x+ 23−23 = 19−23 7x+ 23−23 =−4

7x=−4 7x

7 = −4 7 7

7x= −4 7 x= −4

7

4 16x−10 = 5x+ 9

Solution:

16x−10 = 5x+ 9

16x−10−(−10) = 5x+ 9−(−10) 16x−10 + 10 = 5x+ 9 + 10

16x= 5x+ 19 16x−5x= 5x+ 19−5x (16−5)x= 5x−5x+ 19 11x= (5−5)x+ 19 11x= 19

11x

11 = 19 11 11

11x= 19 11 x= 19 11

Exercice 3

25 ≈0.28

25 ≈0.68

(64)

J B B J R J V R J B J R V V

Effectif 3 5 3 3

Solution: Fréquence de boules vertes : ₁₄³

Solution: 4.25

Solution: 6

(65)

Devoir maison: 5

Sujet 37

Solution Exercice 1

Solution:

A = −5(−5x+ 9)

A = −5×(−5)x−5×9 A = 25x−45

b. B= (9x+ 7)(6x+ 4)

Solution:

B = (9x+ 7)(6x+ 4)

B = 9×6x²+ 7×6x+ 9×4x+ 7×4 B = 9×6x²+ (7×6 + 9×4)x+ 7×4 B = 54x²+ (42 + 36)x+ 28

B = 54x²+ 78x+ 28

C = (3x+ 7)²

C = (3x+ 7)(3x+ 7)

C = 3×3x²+ 7×3x+ 3×7x+ 7×7 C = 3×3x²+ (7×3 + 3×7)x+ 7×7 C = 9x²+ (21 + 21)x+ 49

C = 9x²+ 42x+ 49

D = (2x−10)²

D = (2x−10)(2x−10)

D = 2×2x²−10×2x+ 2×(−10)x−10×(−10) D = 2×2x²+ (−10×2 + 2×(−10))x−10×(−10) D = 4x²+ (−20−20)x+ 100

D = 4x²−40x+ 100

Solution:

A= 6x²+ 30x= 6x(1x+ 5)

(66)

Solution:

B=−28x²+ 36x=−4x(7x−9)

C =−63x²−49x=−7x(9x+ 7)

d. D = 81x²+ 108x+ 36 Solution:

D = 81x²+ 108x+ 36 = (9x+ 6)²

Exercice 2

1 3x−4 = 0

Solution:

3x−4 = 0

3x−4−(−4) = 0−(−4) 3x−4 + 4 = 0 + 4 3x−4 + 4 = 4

3x= 4 3x

3 = 4 3 3

3x= 4 3 x= 4 3

13

Solution:

13

29x+ 20 = 0 13

29x+ 20−20 = 0−20 13

29x+ 20−20 =−20 13

29x=−20

1329x

1329

= −20

1329 1329

1329

x=−20× 29 13 13

29 × 29

13x= −20×29 1×13 13×29

29×13x= −580 1 13

1×1x= −580 1 13

1x= −580

−13580

(67)