Page 26 - ACE YR IGCSE A TOP APPR' TO ADD MATH

–1
2
2
7. 1 8 x + 3 + 3 = 52 11. (a) Let f (x) = y
3y
= x
2
2
1 8 x + 3 = 49 y + 1
3y = xy + x
x
= 1 8 + 3 = 7 3y – xy = x
y(3 – x) = x
2 x = 2 x
= √3 [3] y = 3 – x
x
2
2
–1
= 1 8 x + 3 8. a(ax + b) + b = 49x – 40 f (x) = 3 – x [3]
a x + ab + b = 49x – 40
2
2
= a x = 49x (b) x = 3
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= a = 7 or a = −7 (rejected) [1]
ab + b = –40 12. (a) Let f (x) = y
–1
8b = –40 f(y) = x
b = –5 5 – 2y = x
[3] 2y = 5 – x
9. Let y = f(x) y = 5 – x
Let f (x) = z 2
–1
f(z) = x f (x) = 5 – x
–1
x = 3 – z 2
2
z = 3 – x f (–3) = 5 – (–3)
2
–1
z = √3 – x 2
f (x) = √3 – x f (–3) = 4
–1
–1
[2]
y (b) gf(x) = 5(5 – 2x)
3 = 25 – 10x
y = f(x) [gf(x)] = 25 – x
–1
10
(gf) (–5) = 25 – (–5)
–1
10
= 3
–1
y = f (x) [3]
13. a(1 – 3x) + b = a(1 – 6x + 9x ) + b
2
2
x = a – 6ax + 9ax + b
2
3
9a = 1
[5] a = 1
9
10. (a) 2k – 1 = 0 a + b = 6
2k = 1 b = 6 – 1
k = 1 9
2 [1] = 53
(b) (i) gf(x) = x + 3 – 1 9 [4]
2(x + 3) – 1 14. (a)
= x + 2 y
2x + 6 – 1
= x + 2
2x + 5 [2]
(ii) fg(x) = x – 1 + 3 2
2x – 1
= x – 1 + 3(2x – 1)
2x – 1
= x – 1 + 6x – 3 0 2 2 x
2x – 1 3
7x – 4
=
2x – 1
[2]

[3]
Cambridge IGCSE
TM
166 Ace Your Additional Mathematics

= 1
Answers Add Math.indd 166 2 14/03/2022 12:29 PM
= √3
2
2
= 1 8 + 3
x
=
=