Page 42 - ACE YR IGCSE A TOP APPR' TO MATHS

(e) Minimum point = (2, –25) [1] (d) $60 × 4 + $70 × 14 = $1220 [3]
(f) x = 2 [1] 5 (a) x > 2y
x > 120
Inequalities y > 80
x + y ≤ 500 [4]
1 (a) 4 ≥ 3x – 4x (b)
2
3x – 4x – 4 ≤ 0
2
(3x + 2)(x − 2) ≤ 0 y
2
– ≤ x ≤ 2 [2]
3 500
(b) 10x + 6 > –6 + 15 x
5x < 12 400
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12
x < [2]
5
(c) –9 ≤ 2x + 1 < 15 300
–10 ≤ 2x < 14
–5 ≤ x < 7 [3]
2. 200
y
25 100
20
x
15 0 100 200 300 400 500
10
[4]
5 (c) 160 × $15 + 80 × $20 = $4000 [2]
x
0 5 10 15 20 25 30 35 40 45 50
Sequences
[4]
3 L , y ≤ x 1 (a) 29 + 5 = 34 [1]
1
L , 10y – 2 ≥ 3 (b) T = a + (n – 1)d
n
2
L , y < 4 [3] = 14 + (n – 1)(5)
3
4 (a) (i) x ≥ 4 [1] = 9 + 5n [2]
(ii) y ≥ 6 [1] (c) 9 + 5n = 324
(iii) x + y ≤ 18 [1] n = 63 [2]
(b) 60x + 70y ≥ 840 2 (a) 20a – 6a = 14a [1]
6x + 7y ≥ 84 [1] (b) T = a + (n – 1)d
n
(c) = 38a + (n – 1)(–6a)
y = 38a – 6an + 6a
= 44a − 6an [2]
20 (c) (i) T = 44(2) – 6(2)n
n
T = 88 – 12n
n
88 – 12n < 0
15 –12n < –88
n > 7 1
3
n = 8 [2]
10 (ii) 88 – 12n = –1172
n = 105 [2]
3 (a) T = a + (n – 1)d
n
5 = 5 + (n – 1)(2)
= 3 + 2n
n
T = [2]
x n 3 + 2n
0 5 10 15 20 118
(b) T =
118
[4] 3 + 2(118)
118
= [1]
239

Cambridge IGCSE
TM
162 Ace Your Mathematics

Answers.indd 162 15/03/2022 11:08 AM