PROPORTION EXAM QUESTIONS
1.
2.
The illumination, L, provided by a torch is inversely proportional to the square of
the distance, d, from the torch.
When L = 2, d = 10.
(a) Find an equation expressing L in terms of d.
(b) Find the value of L when d = 2.
(c) Find the value of d when L = 8.
(3)
(1)
(2)
W and P are both positive quantities.
W is directly proportional to the square root of P.
When W = 12, P = 16.
(a)
(b)
(c)
Express W in terms of P.
What is the value of W when P = 25?
What is the value of P when W = 21?
(3)
(1)
(2)
3.In an experiment measurements of t and h were taken.
These are the results.
t
2
5
6
h
10
62.5
90
Which of these rules fits the results?
You must show all your working.
4.
5.
6.
(A) h  t
(B) h  t2
(C) h  t3
(4)
y is inversely proportional to the square of x.
When y = 3, x = 2
Find the value of y when x = 4
(3)
M and G are positive quantities.
M is inversely proportional to G.
When M = 90, G = 40.
Find the value of M when G = M.
(4)
In an experiment measurements of t and m were taken.
The results were as follows:
t
2
2.4
3
m
36
25
16
The results are connected by one of these rules.
A
7.
8.
tα√m
B tα
1
m
C
tα
1
m
Which rule is the correct one? State your answer clearly. You must show your
working.
(4)
y is inversely proportional to the square root of x.
When x = 16, y = 2
What is the value of y when x = 0.25?
(3)
Salt is sold in different sized blocks.
The weight of each block, B kilograms, is directly proportional to the cube of its
height, h metres.
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1
A block of weight 54 kg has height 3m.
(a) Find an equation connecting h and B.
(b) Find the weight of a block with a height of 1m.
(c) Another block has a weight of 128 kg. Find its height.
9.
(3)
(1)
(3)
The number of days, D, to complete a project is inversely proportional to the
number of people, P, who work on the project.
(a)
(b)
The project takes 18 days to complete if 150 people work on it.
(i) Find an equation connecting D and P.
(ii) How many people are needed to complete the project in 10 days?
Sketch a graph which shows that D is inversely proportional to P.
(3)
(2)
(2)
D
0
P
10. Cheese is sold in different sizes. The weight of each cheese, W kilograms, is
proportional to the cube of its height, h centimetres. A cheese of weight 10 kg
has a height of 12 cm.
(a) Find an equation connecting W and h.
(b) Another cheese has a height of 6 cm. Find its weight.
(c) Find the height of a cheese that has a weight of 20 kg.
(3)
(1)
(3)
11. The area of the screen of a television set is A square inches.
The length of the diagonal of the screen is d inches.
A is directly proportional to the square of d.
A television set with an area of 90 square inches has a diagonal of length 15
inches.
(a) Find an equation connecting A and d.
(b) Find the area of the screen of a television set with a diagonal of length 20
inches.
(c) Another television set has a screen with an area of 250 square inches.
Find the length of its diagonal.
(3)
(1)
(3)
12. The volume, v litres, which a fixed mass of gas occupies, is inversely
proportional to its pressure, p pascals.
When the pressure is 150 000 pascals, its volume is 5 litres.
(a) Find an equation connecting v and p.
(b) Find the volume of the gas when the pressure is 250 000 pascals.
(c) Find the pressure of the gas when its volume is 300 litres.
(3)
(1)
(2)
13. The volume, V cubic metres, of a hot-air balloon is proportional to the cube of its
height,
h metres. A balloon with a height of 10 metres has a volume of 500 cubic
metres.
(a) Find an equation connecting V and h.
(b) Find the volume of a hot-air balloon which has a height of 30 metres.
(c) Another hot-air balloon has a volume of 5000 cubic metres.
(d) Find its height.
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(3)
(1)
(3)
2