Page 54 - ACE YR IGCSE A TOP APPR' TO ADD MATH

(c) 8! × 2! × 2 = 161280 T – T = (x + 1)y – xy
2
1
[3] d = xy + y – xy
12. (a) P = 720 d = y
6
6 2
[1] d = d = y
2
1
(b) 3! × 3! = 36 [2]
[2] (b) 24 = xy + 8y
2! × 4! × 3 1
(c) = 24 = (2y)y + 8y
6 P 5 2
6 [3] 2y + 8y − 24 = 0
y = 6 (rejected) or y = 2
5
5
13. ( C × C × C ) × 3 = 1500
5
3 3 4 When y = 2, x = 4
[4] Area of first rectangle = xy = 2x = 8 cm 2
Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
47
14. ( C × C ) + ( C × C ) + C = 2.309 × 10 16 [2]
47
53
47
53
23 2 24 1 25
[4] a 120
2. (a) S = =
5
3
15. ( C ) = 243 ∞ 1 – r 9
2 120(1 – r)
[2] a = …… (1)
9
9
16. C = 126 Second term = ar = a – 5
5
[1] 6
5
6
17. (a) C = 15 a = …… (2)
2 6(1 – r)
[2]
6
(b) C = 6 Equation (1) = Equation (2)
5 120(1 – r) 5
[2] =
9 6(1 – r)
5
12
18. C × P = 95 040
3
5
5 5 r = (accepted) and r = (rejected because it
[2] 4 4
leads to a negative first term)
19. C × C × P = 64800
6
6
4
4 2 6
[2] a = 10 (accepted) and a = –10 (rejected
3
3
20. (a) C × C = 840 because all the terms are positive)
8
6
3 4
[2] [4]
6
8
8
6
(b) 840 + ( C × C ) + ( C × C ) = 1016 (b) S – S
2 5 1 6 7 5
[3] 10 3 7
1 –
(c) C – 1016 + 840 = 3256 3 1 1 2 2 70985
14
4
7 S = =
[3] 7 3 6144
1 –
6
6
12
21. (a) C – C – ( C × C ) = 696 4
6
5 5 4 1 5
3
[4] 10 1 1 2 2
1 –
(b) More pianists than violinists S = 3 4 = 3905
2
2
= ( C × C ) + ( C × C ) + ( C × C × C ) 5 1 – 3 384
4
6
2
4
4
1
1
3
2
2
4
2
= 42 4
Same number of pianists and violinists 70985 – 3905 = 2835 = 1.38
6
4
= ( C × C × C ) + ( C × C × C ) 6144 384 2048
6
2
4
2
2
1
2
3
1
1
= 108 [3]
12 C – 42 – 108 = 642 3. Fourth term
5
[7] = ar n – 1
a
2
= 1 2 (r)
3
11 Series 2 2
= 8a
54
1. (a) T = xy r = 8a 2 × 2
3
1
T = (x + 1)y 54 a 2
2
T = (x + 2)y r = 2
3 3
T – T = (x + 2)y – (x + 1)y a 2
2
3
d = xy + 2y – xy – y S = a = 1 2 = 3a 2
2
d = y ∞ 1 – r 2 2
1 1 –
3 [5]
Cambridge IGCSE
TM
194 Ace Your Additional Mathematics
Answers Add Math.indd 194 14/03/2022 12:29 PM