Cambridge International Mathematics

748 ANSWERS

biun=9¡ 2 n iiun=n^3 iii un=

n

n+1

iv un=(n+1)^2 v un=3n¡^1

vi un=(n+1)^2 ¡ 3 n¡^1

c u 393 du 11

6b i¼ 147 o ii ¼ 33 o ciq+p ii q¡p

dp+3q e^12 p+^52 q fip=

¡ 0

24

¢

ii

¡ 7

¡ 24

¢

g 50 units

7ay=k

x^2

k=5^2 £ 4 :8 = 120

) x^2 y= 120

by=30

c x=2

p

3 fasx> 0 g d x¼ 4 : 93 e yis quartered

f xis increased by25% gx=

r

120

y

fasx> 0 g

8a b ip=25

iiq=40

iii x=n^2 , y=(n+1)^2 ,

z=2n(n+1)

c Diagram 12 3 4 5

Total lines 4164080140

i e=^23 , f=2,g=^43 ii 880 one cm lines

9aE 1216 b E 1 : 47 c ¼ 15 :2% dE 621 eE 4830

fi¼ 723 km/h ii¼ 201 m/s

10 a 12 cm b 192 cm^3 c ¼ 67 : 4 o d ¼ 36 : 9 o

ei¼ 76 : 7 o ii¼ 6 : 40 cm

11 a imode=1 iik=3 iii m=4 iv 9

bix¼ 38 : 2 ii 3307

cip=20,q=72

ii

12 a 64 : 8 m^3 b 864 m^3 ,¼1230%increase

c 22 : 1 m d 150 m

13 a ia rhombus iia kite

b(2x)o and(180¡ 2 x)o c 120 cm^2 d 13 cm

14 a ic¡d iid¡^12 c iii^32 c¡d

bi 120 o ii 16

p

3 cm^2 iii 8

p

3 cm iv 96

p

3 cm^2

15 a¼553 000cm^3 (or¼ 0 : 553 m^3 )

b¼ 6 : 86 hours (¼ 6 hours 51 min) c ¼ 8 mm

16 a iBbAC=36: 9550 ::::¼ 37 o ii 014 : 0 o

iii ¼ 842 m^2

bip= 70 cos 39o¼ 54 : 4 iiq= 70 sin 39o¼ 44 : 1

c BD¼ 36 : 5 m

17 a ¼ 6 : 54 cm^3

biw=4: 2 , x=1: 4 ii¼ 106 cm^3 iii ¼ 74 :2%

cil=

p

(1:5)^2 +(0:35)^2 ¼ 1 : 54 cm ii¼ 38 : 4 cm^2

18 a i

PQ= (12¡ 2 x)cm

) x^2 +x^2 = (12¡ 2 x)^2 fPythagorasg

i.e., 2 x^2 = (12¡ 2 x)^2

iii x¼ 3 : 51

bi¼ 56 : 2 cm ii¼ 169 cm^2

19 a i¼ 528 cm^3

ii OC=

p

R^2 ¡r^2 =

p

102 ¡ 62 =8cm

OS=R=10cm

) SC=OC+OS=18cm

iii ¼ 4070 cm^3 iv ¼ 87 :0%

bi SC=CT+TS

=2r+1

) OC=SC¡OS

=(2r+1)¡ 3

=(2r¡2)cm

ii OC^2 =9¡r^2

iii simplify (2r¡2)^2 =9¡r^2 iv r¼ 2 : 08

v CT=h¼ 4 : 16 cm

20 a iBX=^12 BD

=^12 (7: 5 ¡ 2 £3 cos 70o)

¼ 2 : 724 cm

iiBbCX¼ 76 : 6 o

bi¼ 1 : 77 cm^2 ii¼ 18 : 3 cm^2 iii ¼ 14 : 1 cm^2

iv ¼ 41 : 2 cm^2

21 a ¼ 18 : 8 cm^2 b¼ 7 : 85 cm c 140 o fangle at centreg

d r=

1

2 (QR)

sin 70o¼^4 :^18 cm e ¼^10 :^2 cm f^220

o

22 a iV=^16 abhcm^3 ii 40 cm^3

biV=4x(x+3)cm^3

iisimplify 4 x(x+ 3) = 2(2x+3)

iii x¼ 0 : 58 fasx> 0 g iv RS¼ 3 : 58 cm

v PMOb ¼ 81 : 5 o

23 aa=90,b=90,c= 138,d=69,e=45

b ‘...... GAC arecongruent.’

ciGA¼ 141 cm iiGX=GA+AX

¼141 + 54

iii ¼ 262 cm iv ¼ 121 cm

24 a iOC=xcm, OF=(x¡10)cm

iix^2 =20^2 +(x¡10)^2

iii Equation iniisimplifies to 20 x= 500 etc.

c ¼ 3480 cm^2 d ¼ 4 : 52 kg

25 a 14 hours 31 min biMbCB¼ 123 o ii 247 o

ci 7 hours 38 min iiarrives at 20 : 18 , after sunset

26 a i¼ 0 : 770 m^2 ii=2:704 592::::::¼ 2 : 705 m

iii ¼ 1 : 83 m^2 iv ¼ 2 : 60 m^2

x

xx

x

ABPQ

A'

12 cm

(^020406080)
1
2
3
4
freq. density
0.667 t
2.4
P Q
IB MYP_3 ANS
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\748IB_IGC1_an.CDR Friday, 21 November 2008 9:54:33 AM PETER