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 · Non-calculator · 15 questions

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1.A straight-line graph shows the distance travelled, d kilometres, against the time taken, t hours, for a cyclist. The line passes through the origin and has a gradient of 18. Write down what the gradient of this line represents.
(a)The distance the cyclist travels in 18 hours
(b)The total distance the cyclist travels, in kilometres
(c)The time the cyclist takes, in hours
(d)The cyclist's speed, in kilometres per hour
2.Two cars leave the same point at the same time and travel in opposite directions. One travels at 80 km/h and the other at 60 km/h. Work out how long it takes until the cars are 350 km apart.
(a)5 hours
(b)2.5 hours
(c)17.5 hours
(d)4.375 hours
3.Ffion is paid £11.20 per hour. She works 6 hours on Monday and 4.5 hours on Tuesday. Work out her total pay for the two days.
(a)£67.20
(b)£50.40
(c)£106.40
(d)£117.60
4.The angles of a triangle are in the ratio 2:3:4. Work out the size of the smallest angle.
(a)80°
(b)60°
(c)40°
(d)20°
5.A gardener mixes 300 ml of plant feed concentrate with 1.2 litres of water to make a spray. Write the ratio of concentrate to water in its simplest form.
(a)4 : 1
(b)3 : 12
(c)1 : 4
(d)1 : 1.2
6.5 tins of soup cost £8 in total. Work out the multiplier that changes the number of tins into the total cost in pounds.
(a)0.625
(b)40
(c)1.6
(d)3
7.A dog walker's charge, C pounds, for walking a dog for m minutes is shown on a straight-line graph. The line passes through the points (20, 14) and (50, 26). Work out the charge for a 65-minute walk.
(a)£33.80
(b)£40
(c)£32
(d)£26
8.A car travels 90 km using 6 litres of petrol. Work out how far the car can travel, at the same rate, using 9 litres of petrol.
(a)135 km
(b)60 km
(c)99 km
(d)45 km
9.A plan is drawn to a scale of 1 : 25. A real fence is 10 m long. Work out the length of the fence on the plan, in centimetres.
(a)0.4 cm
(b)4 cm
(c)25000 cm
(d)40 cm
10.A blue ribbon is 45 cm long. A red ribbon is 30 cm long. Write the length of the blue ribbon as a fraction of the length of the red ribbon. Give your answer in its simplest form.
(a)3/5
(b)2/3
(c)1/2
(d)3/2
11.The amount of fuel left in a car's tank, F litres, is plotted against the distance travelled, d miles, and the points lie on a straight line. The line passes through (0, 45) and (150, 15). Work out the gradient of the line and say what it tells you.
(a)−5, the car uses 5 litres of fuel for each mile
(b)−30, the car uses 30 litres of fuel for each mile
(c)−0.2, the car uses 0.2 litres of fuel for each mile
(d)0.2, the car gains 0.2 litres of fuel for each mile
12.A plan is drawn to a scale of 1 : 500. Work out how many metres are represented by 1 cm on the plan.
(a)500 m
(b)5 m
(c)50 m
(d)0.5 m
13.A scale drawing states '1 cm represents 25 m'. Which of these is the correct way to write this scale in the form 1 : n?
(a)1 : 25
(b)1 : 2.5
(c)1 : 250
(d)1 : 2500
14.A jug of squash is made by mixing water and syrup in the ratio 6:1. Nia wants to make 8.4 litres of squash. Work out how much syrup she needs, in litres.
(a)0.84
(b)1.4
(c)1.2
(d)7.2
15.y is inversely proportional to x, so y = k ÷ x. When x = 5, the value of y is 8. Work out the value of k.
(a)3
(b)1.6
(c)13
(d)40

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