Cambridge International Mathematics

What to do:

1 Which of the following ideas have merit when finding the period of the pendulum for a particular

length?

² Several students should time one period using their stopwatches.

² Timing 8 complete swings and averaging is better than timing one complete swing.

² If several students do the timing, the highest and lowest scores should be removed and the

remaining scores should be averaged.

2 List possible factors which could lead to inaccurate results.

length (lcm) period (Ts)

20

30

40

..

.

3 After deciding on a method for determining the period, measure

the period for pendulum lengths of 20 cm, 30 cm, 40 cm, ...., 100

cm and record your results in a table like the one alongside.

4 Use technology to determine the law connectingTandl.

Review set 30A

1 The variablesxandyin the table alongside

are inversely proportional. Findaandb.

x 1 3 6 a

y 24 8 b 60

2 If 7 litres of petrol are needed to drive 100 km, how far could you travel on 16 litres of petrol?

3 If 3 men could paint a grain silo in 18 days, how long would it take 8 men to paint the silo working

at the same rate?

x 1 2 3

y 4 16 36

4 Draw the graph ofyagainstx^2 for the points in the table alongside. From

your graph, verify that a law of the form y=kx^2 applies. Hence find:

a the value ofk b ywhen x=6 c xwhen y=64.

5 P is directly proportional to the square root ofQ, and P =12when Q=9. Find:

a the law connectingPandQ b the value ofPwhen Q= 121

c the value ofQwhen P=13.

6 The period of a pendulum varies in direct proportion to the square root of its length. If a 45 cm

pendulum has period 1 : 34 seconds, find the period of a 64 cm pendulum.

7 The volume of a cylinder is directly proportional to the square of its radius. Find:

a the change in volume produced by doubling the radius

b the change in radius needed to produce a60%increase in volume.

p 1 4 9 16 25

D 36 18 12 9 7 : 2

8 It is suspected that two variablesDandpare related by a law

of the formD=

k

p

p

wherekis a constant. An experiment to

a GraphDagainst

p

pfor these data values.

find for various values of was conducted and the results

alongside were obtained.

Dp

622 Variation and power modelling (Chapter 30)

IGCSE01

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Y:\HAESE\IGCSE01\IG01_30\622IGCSE01_30.CDR Wednesday, 29 October 2008 4:04:24 PM PETER