Page 28 - ACE YR IGCSE A TOP APPR' TO ADD MATH

(b) f(x ) = 16x
2
y
kx – h = 16x
2
(–4)x – (–2) – 16x = 0
2
12
–4 – 16x + 2 = 0
2
2x + 8x – 1 = 0
2
10 x = 0.12, –4.12
[4]
= 1 8
2 7 2 Quadratic Functions
= √3 6
1. y = 2x − 1
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= √(7) – 4 3x + (2x − 1) = x(2x − 1) + 15
2
2
2
3x + 4x − 4x + 1 − 2x + x − 15 = 0
2
2
2
5x − 3x − 14 = 0
2
2
2
= 1 8 2 + 3 2 (x − 2)(5x + 7) = 0
= x x = 2 or x = − 7
5
= –2 0 2 7 4 19
3 y = 3 or y = −
Range: 0 < fg(x) < 13 [5] 5
[5]
20. (a) ff(x) = 3(3x – 4) – 4
= 9x – 12 – 4 2. y = 3
= 9x – 16 x
[2] y = 3x
2
(b) gf(x) = 3 [2] y(3x) = 21 − 7x
2
3x – 4 36x + 7x − 21 = 0
2
(c) Let f (x) = y x = –(7) ± √(7) – 4(36)(–21)
–1
f(y) = x 2(36)
x = 3y – 4 x = 0.673 or x = −0.87
x + 4 = 3y y = 2.02 or y = −2.6
x + 4 [5]
y =
3 3. 3ax + 4ax + a + x − 1 = 0
2
2
2
f (x) = x + 4 (3a + 1)x + 4ax + a − 1 = 0
–1
3 [2] b − 4ac = 0
2
2
(d) 3 = 9x – 16 (4a) − 4(3a + 1)(a − 1) = 0
2
2
3x – 4 16a − 12a + 8a + 4 = 0
3 = 27x – 48x – 36x + 64 a + 2a + 1 = 0
2
2
27x – 84x + 61 = 0 (a + 1) = 0
2
2
14 + √13 14 – √13 a = −1
x = or x = [5]
9 9
[3]
4. z − 6x = x(2x + z)
2
21. (a) f (x) = k(kx – h) – h 2x + zx + 6x − z = 0
2
= k x – kh – h 2x + (z + 6)x − z = 0
2
2
k x = 16x b − 4ac , 0
2
2
k = ±4 (z + 6) − 4(2)(−z) , 0
2
–kh – h = 6 z + 12z + 8z + 36 , 0
2
4h + h = 6 z + 20z + 36 , 0
2
5h = 6 (z + 2)(z + 18) , 0
h = 6 −18 , z , −2
5 [5]
4h – h = –6
3h = –6
h = –2
k = –4, h = –2
[4]
Cambridge IGCSE
TM
168 Ace Your Additional Mathematics
Answers Add Math.indd 168 14/03/2022 12:29 PM