Page 33 - ACE YR IGCSE A TOP APPR' TO ADD MATH

3
1
Gradient of straight line = – ÷ 3 Let x = y
2
2 5 5y + 32y – 21 = 0
2
5
3
= – 6 y = or y = –7
e = – 5 3 5 3
3
6 x = or x = –7 (rejected)
2
2
f = – 1 5
2 [4] x = 0.711 [7]
15. (a) x . 1 20. Let √x = y
[1] 20
(b) (x – 1)(x + 3) . –6 6y – y = 7
2
2 Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
–4.1 , x , –1.4, x . 0.5 6y – 7y – 20 = 0
2
[3] (3y + 4)(2y – 5) = 0
16. (a) –1.6 < x < 0.6, x > 3 y = – 4 or y = 5
[2] 3 2
4
(b) –1.5 till –1.6 , x , 1 √x = – (rejected) or √x = 5
x . 2.5 till 2.6 3 2
[4] = 6.25
[5]
17. (a) a = –1
b = 2
c = –1 4 Indices and Surds
d = 1
[2] 1. 3 3 + 3 ÷ 3 – 3 = k(3 )
n
n
n
n
(b) –1.1 < x < –0.9 till –0.8 ˙
1
2
1
0 < x < 0.8 till 0.9 3 3 + – 1 = k(3 )
n
n
[2] 3
1
k = 3 + – 1
18. Let x = y 7 3
2
–2y + 9y – y – 12 = 0 = 3
2
3
Let y = –1 [2]
–2(–1) + 9(–1) – (–1) – 12 = 0 2. 4 4 – 4 = 24
2
3
x
x
˙
x
2
–2y + 11y – 12 4 (4 – 1) = 24
x
2
3
y + 1 –2y + 9y – y – 12 4 = 8
2x
3
–2y – 2y 2 = 2
3
2
11y – y x = 1.5
2
11y + 11y [2]
2
– 12y – 12 3. 3(27 3 ) + 4(4 2) = 4
x
x
–2
x
˙
˙
x
x
–1
x
– 12y – 12 27 3 = 4 + (4 8)
˙
˙
x
–1
x
˙
(y + 1)(–2y + 11y – 12) = 0 27 3 = 4 (1 + 8)
2
(y + 1)(2y – 3)(4 – y) = 0 4 x = 3 –1
3 27 x 9
y = –1 or y = or y = 4
4
2 1 2 x = 1
x = –1 (rejected) or x = ± 3 or x = ±2 27 27
2
2 [7] p = 1, q = 27
[3]
1 3
2
2
19. x (5x + 32x – 21) = 0 4. (√5x + 1) = (5 – √x – 2)
2
3
1 5x + 1 = 25 – 10√x – 2 + x – 2
2
x = 0 (4x – 22) = (–10√x – 2)
2
2
x = 0 16x – 276x + 684 = 0
2
3 x = 14.25 (rejected) or x = 3
2
5x + 32x – 21 = 0
3
[4]
Answers 173
Answers Add Math.indd 173 14/03/2022 12:29 PM