Page 30 - ACE YR IGCSE A TOP APPR' TO ADD MATH

2
1
k = – 3 2 2 2 – 2 20. (a) 2x + 3x − 7
3
2
1
2
1 = 2 x + x – 7
= 2
4 2
31
[4] = 2 x + 3 2 – 9 4 – 7
(b) x = 0 + 3 = 1.5 [1] 4 2 16
1
2 = 2 x + 3 2 – 65
,
(c) Maximum point 1 3 1 2 [1] k = – 3 4 8
2 4
4
14. a = 1, b = 3 3 65 [3]
1
4
= 1 [2] (b) Minimum point – , – 8 2
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2 15. 3x − 5x + p = 0 [1]
2
= √3 b – 4ac , 0 (c)
2
(−5) − 4(3)(p) , 0 y
2
= √(7) – 25 − 12p , 0
2
12p . 25 – 3 , 65
4 8
2
2
= 1 8 2 + 3 p . 25 [3]
12
= –(–7) ± (−7) − 4(2√6 )(√6 )
2
= 16. x = 2(2√6) 7
x = 2 or x = 3
√6 2√6 x

3

a = 2 or a = (rejected) – 3 – 65 – 3 + 65
4
4
b = 6 2
[3] [3]
17. x – kx + 2k – 3 = 0 21. (a) y
2
b − 4ac . 0
2
(−k) − 4(1)(2k − 3) . 0 x
2
k − 8k + 12 . 0 –1 7
2
(k − 6)(k − 2) . 0
k , 2, k . 6
[5]
18. mx − 8 = x − 3x − 4 –7
2
x − (3 + m)x + 4 = 0
2
b − 4ac . 0
2
[−(3 + m)] − 4(1)(4) . 0 2 [3]
2
9 + 6m + m − 16 . 0 (b) x − 6x − 7
2
2
m + 6m − 7 . 0 = (x − 3) − 16
2
(m + 7)(m − 1) . 0 m > 16
m , −7, m . 1 [2]
[5] 22. (a) y = –2(x – 4x) – 2
2
2
19. (a) 9 + 4x − 2x = −2[(x − 2) − 4] − 2
2
2
= −2x + 4x + 9 = −2(x − 2) + 6
2
= −2[(x − 1) − 1] + 9 y
2
= −2(x − 1) + 11 (2, 6)
2
= 11 − 2(x − 1)
2
[2]
a = 11, b = 2, c = −1
(b) Maximum point (1, 11) [1] x

–2 2 – 3 2 + 3
(c) −21 > f(x) > 11 [1]
(d) No, it does not have an inverse because it is not
a one-to-one function. [1]
[5]
Cambridge IGCSE
TM
170 Ace Your Additional Mathematics
Answers Add Math.indd 170 14/03/2022 12:29 PM