Cambridge International Mathematics

IfTis the period andlis the length, then T/

p

l.

a

l 25 70

T 1 : 00

lis multiplied by^7025

)

p

l is multiplied by

q

70

25

) T is multiplied by

q

70

25 fasT/

p

lg

) T=1: 00 £

q

70

25

¼ 1 : 67

So, the period would be 1 : 67 seconds.

b l 25

T 1 : 00 2

Tis multiplied by 2

)

p

lis multiplied by 2 fas T/

p

lg

) lis multiplied by 22

) l=25£ 22 = 100

So, the length would be 100 cm.

Example 7 Self Tutor

The volume of a cylinder of fixed height varies in direct proportion to the square of the base radius.

Find the change in volume when the base radius is increased by18%.

Method 1:

Ifris increased by18%then

r 2 = 118%ofr 1

) r 2 =1: 18 r 1

Now V 1 =kr 12 and V 2 =kr 22

) V 2 =k(1: 18 r 1 )^2

) =k£ 1 : 3924 r 12

) V 2 =1: 3924 V 1

) V 2 = 139:24% of V 1

) Vhas increased by 39 :24%.

Method 2:

If the volume isVand the radius isr,

then V/r^2.

When the radius is increased by18%,

ris multiplied by118%or 1 : 18

) r^2 is multiplied by(1:18)^2

) Vis multiplied by (1:18)^2 =1: 3924

) Vis multiplied by 139 :24%

) Vis increased by 39 :24%:

EXERCISE 30A.2

1 By finding values of

y

x^2

for each point in the following tables, establish that y/x^2 and state the

rule connectingyandx. Hence find the value ofa.

a x^2357

y 16 36 100 a

b x^134 a

y 3 27 48 108

2 By finding values of

y

x^3

, establish that y/x^3 and find the value ofb.

a x 1 2 3 4

y 5 40 135 b

b x 2 3 5 b

y 4 13 : 5 62 : 5 108

£Uw_Pt_

£ 2

V 2

610 Variation and power modelling (Chapter 30)

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Y:\HAESE\IGCSE01\IG01_30\610IGCSE01_30.CDR Monday, 27 October 2008 2:57:38 PM PETER