Cambridge International Mathematics

Example 8 Self Tutor

Consider the table: x^12345

y 24 12 8 6 4 : 8

Explain why the variablesxandyare inversely proportional.

xandyare inversely proportional ifxyis constant for each ordered pair.

For all 5 ordered pairs in this table, xy=24

) y=

24

x

) yis inversely proportional tox.

Example 9 Self Tutor

IfMis inversely proportional totand M= 200 when t=3, find:

a Mwhen t=5 b twhen M= 746 (to 2 d.p.)

M/

1

t

a

t 3 5

M 200

tis multiplied by^53

)

1

t

is multiplied by^35

) Mis multiplied by^35

) M= 200£^35 = 120

b t 3

M 200 746

Mis multiplied by^746200

)

1

t

is multiplied by^746200

) tis multiplied by^200746

) t=3£^200746 ¼ 0 : 80

Example 10 Self Tutor

The velocityVof a body travelling a fixed distance is inversely proportional to the time takentto

complete the journey. When the velocity is 40 cm/s, the time taken is 280 seconds. Find the time

when the velocity is 50 cm/s.

Method 1: V/

1

t

) V=k

μ

1

t

¶

When V=40, t= 280

) 40 =k

¡ 1

280

¢

) k=40£ 280

) k= 11 200

So, V=

11 200

t

Now when V=50

50 =

11 200

t

) 50 t= 11 200

) t=

11 200

50

= 224

) the time taken is 224 seconds.

£Te_

£Uw_Rp_Yp_

Variation and power modelling (Chapter 30) 613

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Y:\HAESE\IGCSE01\IG01_30\613IGCSE01_30.CDR Monday, 27 October 2008 2:57:47 PM PETER