Cambridge International Mathematics

b What features of the graph suggest that D=

k

p

p

is an appropriate model for the data?

c Determinek.

d FindD, correct to 1 decimal place, when p=13:

d 0 : 5 1 : 0 1 : 4 1 : 7 2 : 0 2 : 5

R 0 : 7 4 : 0 9 : 3 15 : 0 22 : 6 39 : 7

9 Water flows into a channel at a rate ofRm^3 /s. The

depth of the channel isdmetres. The following

table gives corresponding values ofRandd.

a Find the power model which best fits the data.

b Explain whether the power model is appropriate.

c Use the model fromato estimate the rate of flow when the depth is 2 : 2 m.

d How much water flows into the channel each minute when the depth is 2 : 2 m?

Review set 30B

1 The variablespandqin the table alongside

are directly proportional. Findaandb.

p 2 4 7 a

q 6 12 b 42

2 Ifyis inversely proportional tox, what happens to:

a yifxis trebled b xifyis increased by50%?

3 Ifxis inversely proportional toy, andy=65whenx=10, find:

a the law connectingxandy b ywhen x=12

c xwhen y= 150.

4 If 5 bags of fertiliser are required to fertilise a lawn 26 mby 40 m, how many bags would be

required to fertilise a lawn 39 mby 100 m?

5 The resistance,Rohms, to the flow of electricity in a wire varies inversely to the area of the

cross-section of the wire. When the area is 0 : 15 cm^2 , the resistance is 0 : 24 ohms. Find:

a the resistance when the area is 0 : 07 cm^2

b the area when the resistance is 0 : 45 ohms.

6 The intensity of light on a screen varies inversely to the square of the distance between the screen

and the light source. If the screen has 24 units of illumination when the source is 4 m away,

determine the illumination when the screen is 6 m away.

7 The surface area of a sphere is directly proportonal to the square of its radius. Find:

a the change in surface area if the radius is decreased by19%

b the change in radius if the surface area is trebled.

h 2 4 6

V 3 : 2 25 : 6 86 : 4

8 Kelly makes small glass pyramids of heighthcm. She suspects that

the volume of glassV cm^3 is directly proportional to a power ofh,

so V_hn. The following table of volumes for various heights was

obtained:

a Use thefirst twopieces of data to findkandnfor which V=khn.

b Check that the model you found inais satisfied by the final data point.

c Can you suggest why this value ofncould be expected?

d Find: i Vwhen h=8 ii hwhen V=50.

Variation and power modelling (Chapter 30) 623

IGCSE01

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Y:\HAESE\IGCSE01\IG01_30\623IGCSE01_30.CDR Monday, 27 October 2008 2:58:19 PM PETER