Cambridge International Mathematics

Method 2: V/

1

t

t 280

V 40 50

V is multiplied by^5040 =^54

)

1

t

is multiplied by^54 fas V/

1

t

g

) tis multiplied by^45

) t= 280£^45 = 224

) the time taken is 224 seconds.

EXERCISE 30B

1 Calculate the value ofxyfor each point in the following tables. Hence determine for each table whether

xandyare inversely proportional. If an inverse proportionality exists, determine the law connecting

the variables and draw the graph ofyagainstx.

a x^1236

y 12 6 4 2

b x^2369

y 12 8 4 3

c x^76121

y 12 14 7 84

2 Which of the following graphs could indicate thatyis inversely proportional tox?

Ifyis inversely

proportional tox

thenyis directly

proportional to^1 x.

ab

cd

3 Ifyis inversely proportional tox, and y=20 when x=2, find:

a the value ofywhen x=5 b the value ofxwhen y= 100.

4 Ifyis inversely proportional tox, and y=24 when x=6, find:

a the value ofywhen x=8 b the value ofxwhen y=12.

5 The formula connecting average speeds, distance travelledd, and time takent,is s=

d

t

. Complete
the following statements by inserting ‘directly’ or ‘inversely’:
a Ifdis fixed,sis ...... proportional tot.
b Iftis fixed,sis ...... proportional tod.
c Ifsis fixed,dis ...... proportional tot.

6 Mvaries inversely tot^2 where t> 0. When t=2, M=10.

a FindMwhen t=5. b Findtwhen M= 250.

7 Pvaries inversely to the square root ofg. When g=9, P=20:

a FindPwhen g=4. b Findgwhen P=50.

£Tr_Pp_

x

y

O

y x O y 1 x O

x

y

O

614 Variation and power modelling (Chapter 30)

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Y:\HAESE\IGCSE01\IG01_30\614IGCSE01_30.CDR Monday, 27 October 2008 2:57:50 PM PETER