Cambridge International Mathematics

ANSWERS 743

2bandc3ay=8 b x=0: 4

4ay=18 bx=12

5ainversely bdirectly cdirectly

6aM=1: 6 bt=0: 4 7aP=30 b g=1: 44

8a 20 units b 4 cm^398 days

10 a 0 : 115 seconds b 400 units

11 heat is increased by525% 12 ¼ 8 : 94 m away

EXERCISE 30C

1ay=4x^3 by=3

p

x cy=

16

x

dy=

100

x^2

2 d=4

p

h 3 m=l

3

2

4 y=^10

x

5 Hint: Show thatx^2 y is a constant for all data points

y=

5

x^2

) k=5

6aShow that pT

l

is always constant bk=2

c¼ 2 : 83 seconds

7a

bR=kv^3 fas 3 rd graph is linearg

Show

R

v^3

is a constant to getR=0: 0005 x^3

EXERCISE 30D

1 Notice that(0,0)should not be entered.

2ay¼ 26 : 3 x¡^3 :^02 b M¼ 49 : 8 x¡^0 :^497

3ah¼ 265 m^0 :^624 joules

bIt seems appropriate for the given data asr^2 is very close to

1.

c¼53 900Joules. This could be unreliable as m= 5000

lies well outside the poles (0: 026 m 6 500).

4aR¼ 1 : 00 T^0 :^6667

bThe model seems very appropriate asr^2 is very close to 1.

cR^3 ¼T^2

5aV¼140 000P¡^0 :^714 (r^2 ¼1)

bi¼ 542 ml ii ¼ 252 ml

REVIEW SET 30A

1aa=^25 , b=4 2 229 km 36 : 75 days

4ak=4

by= 144

c x=4

5aP=4

p

Q bP=44 c Q¼ 10 : 6

61 : 60 seconds

7aVis multiplied by 4 b 26 :5%increase inr

8a

pp 1 2 3 4 5

D 36 18 12 9 7: 2

bThe graph seems to be asymptotic to the axes.

ck=36 d D¼ 10 : 0

9aR¼ 3 : 99 £d^2 :^51

br^2 is very close to 1 ,

) the power model seems appropriate

cR¼ 28 : 8 m^3 /s d ¼ 1730 m^3 each minute

REVIEW SET 30B

1 a=14, b=21

2ayis divided by 3 b xis decreased by 3313 %

3axy= 650 b y¼ 54 : 2 cx¼ 4 : 33

418 : 75 bags 5a 0 : 514 ohms b 0 : 08 cm^2

610 : 7 units 7areduced by 34 :4% b increased by 73 :2%

8ak=0: 4 ,n=3) V=0: 4 h^3

bwhen h=6, V=86: 4 X

cVolumes in general depend on 3 lengths multiplied together

di¼ 205 cm^3 iih=5cm

9aD¼ 31 : 8 n^0 :^413 mm

bi¼ 50 : 1 mm ii¼ 71 : 0 mm iii¼ 85 : 6 mm

iv ¼ 94 : 6 mm

cbivis least likely to be reliable.

CHALLENGE

1 velocity is decreased by ¼ 8 :71%

2ay=kxn ) y 1 =kx 1 n and y 2 =kx 2 n etc.

bsimilar argument

3b 223 550 km/h

EXERCISE 31A

1alog 2 4=2 blog 4 16 = 2

clog 3 9=2 dlog 5 125 = 3

elog 10 10 000 = 4 flog 7 (^17 )=¡ 1

glog 3 ( 271 )=¡ 3 hlog 27 (3) =^13

i log 5 ( 251 )=¡ 2 j log 2

³

p^1

2

́

=¡^12

klog 2 (4

p

2) = 2: 5 l log 10 (0:001) =¡ 3

2a 23 =8 b 20 =1 c 2 ¡^1 =^12

d 212 =

p

2 e 2 ¡^12 =p^12 f (

p

2)^2 =2

g(

p

3)^4 =9 h 9

(^12)
=3
3a 2 b 3 c 1 d 0 e 3
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Y:\HAESE\IGCSE01\IG01_an\743IB_IGC1_an.CDR Thursday, 20 November 2008 1:54:38 PM PETER