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(b) S = a 18. (a) C (1) n − 1 (−3x) = n! (1) n − 1 (−3x)
n
∞ 1 – r 1 (n – 1)!1!
176 = –3nx
=
3
1 – 1 2 n C (1) n − 2 (−3x) = n! (1) n − 2 (−3x)
2
2
4
1
(n – 2)!2!
= 704 cm 9n(n – 1)x 2
[2] = 2
2 9801
(c) Area = 1936 cm , 1089 cm , cm 2 9n(n – 1)
2
16 –3n + 2 = 228
Second term = ar = 1936r = 1089 9n − 15n − 456 = 0
2
r = 1089 = 9
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1936 16 n = –19 (rejected) and n = 8
Sum of the area of the first 10 squares 3 [6]
1 1 2 2
1936 1 – 9 10 (b) C (1) (−3x) = 5670x
4
8
4
4
= 16 4 [2]
1 – 9
16 3
= 4411 cm 19. S = 2(1 – r ) = 42
2
1 – r
3
[3]
2r − 42r + 40 = 0
3
16. (2) C (2) n − 4 (x) = (3) C (2) n − 5 (x) r = −5, 1, 4
n
n
4
5
4 5
n!
n!
(2) 1 (n – 4)!4! 2 (2) n – 4 = (3) 1 (n – 5)!5! 2 (2) n – 5 r = 4 only
4
S = 2(1 – 4 )
n – 4
2
1 – 4
4
1 n – 52 1 n(n – 1)(n – 2)(n – 3) 2 = 170
(2)
24
2
= (3) 1 n(n – 1)(n – 2)(n – 3)(n – 4) 2 2 [3]
120
2 3 –3
2 4 –3
5
5
2 5
5
3
2
x
x
0
1
2
=
(2) 1 2 1 120 2 (n – 4) 20. (a) C (x ) + C (x ) 1 2 + C (x ) 1 2 +
2 2 –3
1 2
3
24
C (x )

5
n = 32 3 x [3]
3 [6] (b) (−270x)(x) + (90x ) 1 2
1
4
2
17. (a) S − S = 13.5 = −270x + 30x 2 3x 2
5 4 = −240x
2
4
5
a(1 – r ) – a(1 – r ) = 13.5 [2]
1 – r 1 – r
a = 13.5 …… (1) 1 1 + T 22
r 4 21. 1 , T , 2
S − S = –20.25 2 2 2
1
6 5 T = ar = r
6
5
a(1 – r ) – a(1 – r ) = –20.25 2 2
1 – r 1 – r T = ar = r
1
2
2
a = –20.25 …… (2) 3 2
r 5 1 1
2
Equation (1) = Equation (2) 1 r = 2 + r
2
13.5 = –20.25 2 2
2
r 4 r 5 2r − r − 1 = 0
–3 8 r = 1 (rejected) and r = − 1
r = and a = 2
2 3
[5]
5
1 1 1 1 2 2
1 – –
8
1 2 S = 2 2
(b) S = 3 5 1
1
∞ –3 1 – – 2
1 – 1 2 11 2
2
= 16 = 32
15 [2] [5]
Cambridge IGCSE
TM
196 Ace Your Additional Mathematics
Answers Add Math.indd 196 14/03/2022 12:29 PM