Page 40 - ACE YR IGCSE A TOP APPR' TO ADD MATH

3
2
15. 6x + 8x – 4 = 10 (b) √x y 2
x 2 1
3
2
6x + 8x − 4 = 10x 2 = (x )(y )
2
1
x − 2x + 1 = 0 = (2p) (8 )
2
3
q 2
(x − 1) = 0 p
2
x = 1 = 2 · 2
3
6q
= 1 [4] = 2 p 3 + 6q
2 16. 8 · 5 x − 1 + 2 = 5 x + 1 [3]
x
−1
x
1
= √3 8 · 5 · 5 + 2 = 5 · 5 1
x
Let 5 = y 21. Let e = y
2
x
= √(7) – 8y 13y = 14 + 19y
2
2
log x Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
2
5 + 2 = 5y 13y − 19y − 14 = 0
7
2
2
= 1 8 + 3 17y = 10 y = – 13 or y = 2
10
2
1 y = 17 1 2 x 7 1 2 x
= 2 2 10 e = – 13 (rejected) or e = 2
x
= 5 = 17 1 x = ln2

x = −0.3297 2 x = 2 ln 2
[4] [4]
17. y = 2 , log y = b 22. 2x log e = log √2 − 3x log(2e + 1)
b
2
3
x
2
4
3
log 2 3 4 2x log e + 3x log(2e + 1) = log √2
3
8y
3
4
3
= log x − log 8y x[2 log e + 3 log(2e + 1)] = log √2
2
3
4
2
2
3
= 2 log x − [log 2 + log y] x = log √2
3
2
2
2
= 2a − 3 − b 2 log e + 3 log(2e + 1)
3
4
[3] = 0.0502
2
18. 9e − e x = 27 − 3x [3]
3x
2
3x
e (9 − x ) = 3(9 − x )
2
2
3x
3x
2
e = 3 or 9 − x = 0 23. (a)
x = ln 3 or x = ±3 f(x)
3 [3] 8
19. Let y = log x 7
5
3 log 5
2 log x = 1 + log x 6 f(x) = 2In (4x – 3)
5
5
2y = 1 + 3 5 5
y
2y – y – 3 = 0 4 e + 3
2
x
2
3
–1
y = or y = –1 3 f (x) = 4
2
x = √5 or x = 1 2
3
5 [4] 1
20. (a) log 16y x
x
= log 16 + log y 0 1 2 3 4 5 6 7 8
x
x
4 log 2 log y [2]
= 2 + 2
−1
2
2 log x (b) Let f (x) = y
= 4 + 3q 2 ln (4y − 3) = x
p p x
= 4 + 3q ln (4y − 3) = ln e 2
p x 2
[4] f (x) = e + 3
–1
4
[3]
Cambridge IGCSE
TM
180 Ace Your Additional Mathematics
Answers Add Math.indd 180 14/03/2022 12:29 PM