Printable · GCSE Foundation · ages 14-16

Ratio, proportion and rates of change worksheet — GCSE Foundation

Fifteen questions across the ratio, proportion and rates of change statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Ratio, proportion and rates of change worksheet — GCSE Foundation

Maths · GCSE Foundation · Ratio, proportion and rates of change · 15 questions

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1.y is directly proportional to x. If the value of x is trebled (multiplied by 3), what happens to the value of y?
(a)y stays the same
(b)y is divided by 3
(c)y is trebled
(d)y increases by 3
2.A water tank is a cuboid measuring 30 cm × 20 cm × 10 cm. The tank is full of water. Work out how many litres of water it holds.
(a)600 litres
(b)6 litres
(c)0.6 litres
(d)60 litres
3.A garden plan is enlarged by a scale factor of 3. A flower bed on the original plan is 5 cm long. Work out the length of the flower bed on the enlarged plan, in centimetres.
(a)45 cm
(b)8 cm
(c)1.7 cm
(d)15 cm
4.An Ordnance Survey map has a scale of 1 : 50 000. A cycle route measures 9.4 cm on the map. Work out the real length of the route, in kilometres.
(a)4700 km
(b)0.47 km
(c)47 km
(d)4.7 km
5.A plumber's charge, C pounds, for a job lasting h hours is shown on a straight-line graph. The line passes through the points (1, 45) and (3, 85). Work out what the gradient of this line represents, in context.
(a)The plumber charges £20 for each extra hour worked
(b)The plumber charges £20 in total, however long the job takes
(c)The plumber charges £45 for each extra hour worked
(d)The plumber charges £40 for each extra hour worked
6.A ribbon of length 90 cm is cut into two pieces in the ratio 4:5. Work out the length of the shorter piece.
(a)50 cm
(b)10 cm
(c)40 cm
(d)45 cm
7.Two mathematically similar tins have heights 8 cm and 12 cm. Jayden says that the volume of the larger tin is 1.5 times the volume of the smaller tin. Give a reason why Jayden is incorrect, and work out the correct volume scale factor.
(a)3.375
(b)2.25
(c)4.5
(d)1.5
8.Freya buys three items whose prices are in the ratio 2:3:5. Altogether she pays £400. Work out the price of the most expensive item.
(a)£120
(b)£80
(c)£40
(d)£200
9.Tap A fills a swimming pool in 6 hours. Tap B pours water twice as fast as tap A. The time taken to fill the pool is inversely proportional to the rate of flow. Work out how long tap B takes to fill the pool.
(a)3 hours
(b)12 hours
(c)4 hours
(d)1.5 hours
10.Simplify the ratio 12 : 18 : 30 to its simplest form.
(a)3:2:5
(b)4:6:10
(c)6:9:15
(d)2:3:5
11.Line P passes through the origin and the point (3, 21). Line Q passes through the origin and the point (5, 45). Both lines represent the distance, in metres, run by an athlete against the time, in seconds. Work out the gradient of the steeper line.
(a)16 m/s
(b)9 m/s
(c)7 m/s
(d)12 m/s
12.Maya is paid £105.30 for working 9 hours. Work out her rate of pay, in £ per hour.
(a)£11.70
(b)£117.00
(c)£947.70
(d)£96.30
13.A map has a scale of 1 : 40 000. A cycle path measures 7.5 cm on the map. Work out the real length of the cycle path, in kilometres.
(a)30 km
(b)3 km
(c)0.3 km
(d)3000 km
14.Triangle ABC has a right angle at C. AC = 3 cm and BC = 4 cm. Triangle ABC is mathematically similar to triangle PQR, with angle B corresponding to angle Q. Work out the value of tan(angle Q).
(a)3/4
(b)4/3
(c)3/7
(d)4/7
15.Two quantities y and z are each in direct proportion to x, and are given by y = 3x and z = 7x. Work out the difference between the value of y and the value of z when x = 4.
y = 3x
(a)40
(b)16
(c)28
(d)4

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