Cambridge International Mathematics

EXERCISE 30C

1 Find the variation model for these data sets:

a x^12345

y 4 32 108 256 500

b x 1 214 4 9

y 3 412 6 9

c x 1 2 3 4

y 16 8 513 4

d x 1 2 4 5

y 100 25 614 4

2 The distance to the horizon (dkm) is proportional to the square

root of the height (hm) of a person above sea level.

The graph ofdagainsthis shown alongside.

Find a model connectingdandh.

3

4

x 0 : 25 0 : 5 1 2

y 80 20 5 1 : 25

5 The table opposite contains data from an experiment.

Show that the model relatingxtoyis of the form y=

k

x^2

and find the value ofk.

l 0 : 25 0 : 36 0 : 49 0 : 64 0 : 81 1 : 00

T 1 1 : 2 1 : 4 1 : 6 1 : 8 2 : 0

6 A student wants to find the relationship between the

length (l m) of a pendulum and the time period

(Tseconds) that it takes for one complete swing. In

an experiment she collected the following results:

a Show that the model relatingTandlis of the form T=k

p

l:

b Find the value ofk.

c If a pendulum has length 2 m, what will its period be?

h

1 2 3 4 5

12

10

8

6

4

2

d

O

Scale models of a car are made in different sizes.

The mass of a car ( kg) is directly proportional to the

cube of its length ( m).

The graph of against is shown.

Find a model connecting and.

m

l

ml

ml

l

1 2 3 4 5 6

60

50

40

30

20

10

m

O

()4 ¡32,

()2 ¡4,

It is suspected that for two variables and ,

varies inversely to.

Find the equation of the model connecting

and using data from the graph.

xy

yx

y

x

10

x

y

O 5

618 Variation and power modelling (Chapter 30)

IGCSE01

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Y:\HAESE\IGCSE01\IG01_30\618IGCSE01_30.CDR Monday, 27 October 2008 2:58:04 PM PETER