Cambridge International Mathematics

Challenge #endboxedheading

9 The diameter of a scallop is measured at regular intervals of 3 months. The results were:

Age(nquarters) 1 2 4 5 6 8 9 10 12

Diameter(Dmm) 32 42 56 62 67 75 79 82 89

a Find thepowermodel which best fits the data.

b Use the model fromato estimate the diameter of the scallop when:

i n=3 ii n=7 iii n=11 iv n=14.

c Which of your estimates inbis least likely to be reliable?

1 The square of the velocity of a vehicle varies inversely as the distance travelled from its starting

point. If the distance is increased by20%, find the approximate percentage decrease in the velocity.

2aIfyvaries directly asxn, y=y 1 when x=x 1 and y=y 2 when x=x 2 , show that

y 2

y 1

=

μ

x 2

x 1

¶n

.

b Ifyvaries inversely asxn, show that

y 2

y 1

=

μ

x 1

x 2

¶n

.

3aThe sum of the reciprocals of two variables is constant. Show that the sum of the variables is

directly proportional to their product.

b

4aOne variable is directly proportional to another.

Show that their sum is directly proportional to their difference.

b For different models of a tricycle, the front wheel radius is directly proportional to the back

wheel radius.

Show that the difference between the areas of the front and back wheels is directly proportional

to the square of the difference between their radii.

5 The income made by a train service varies

directly as the excess speed above km/h.

Expenses however, vary directly as the square

of the excess speed above km/h. Given that

a speed of km/h just covers expenses, find

the speed which will maximise the profits.

40

40

60

624 Variation and power modelling (Chapter 30)

Suppose that when the two variables in are equal, each has a value of. If one variable has

a value of , find the value of the other variable.

4

8

a

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Y:\HAESE\IGCSE01\IG01_30\624IGCSE01_30.CDR Wednesday, 29 October 2008 4:05:40 PM PETER