GCSE Maths Proportion & rates questions by topic

Speeds and conversions.

1. (a)Convert 45 km/h into m/s.[2]
2. (b)A train travels 330 km in 2.5 hours. Find its average speed in km/h.[2]

Density and pressure.

1. (a)A stone has mass 210 g and volume 30 cm³. Find its density in g/cm³.[2]
2. (b)A box of weight 450 N rests on a base of area 0.09 m². Find the pressure in Pa.[2]

Notebooks in direct proportion.

1. (a)Nine identical notebooks cost £11.25 in total. Find the cost of four notebooks.[2]
2. (b)How many notebooks can be bought for exactly £20?[2]

A jogger keeps a steady pace.

1. (a)She runs 8.4 km in 42 minutes. Find her speed in km/h.[2]
2. (b)At the same speed, how far does she run in 1 hour 15 minutes?[2]

Speeds on a delivery route are converted.

1. (a)The van covers 150 km in 2 hours 30 minutes. Work out its average speed in km/h.[2]
2. (b)Convert your answer to m/s, giving it correct to 1 decimal place.[2]

A scone recipe is scaled.

1. (a)A recipe uses 400 g of flour for 8 scones. Work out the flour needed for 14 scones.[2]
2. (b)Work out how many scones can be made with 1200 g of flour.[2]

A direct proportion equation.

1. (a)y is proportional to x. When x = 4, y = 36. Find the equation connecting y and x.[2]
2. (b)Find y when x = 11.[1]
3. (c)Find x when y = 153.[2]

Pumps drain a reservoir.

1. (a)Six identical pumps drain a reservoir in 18 hours. How long would nine pumps take?[2]
2. (b)How long would four pumps take?[2]
3. (c)State one assumption your answers depend on.[1]

Holiday money and a worse bureau.

1. (a)The exchange rate is £1 = €1.16. Convert £240 to euros.[2]
2. (b)A different tourist receives €348 at this rate. How many pounds did they change?[2]
3. (c)A bureau offers only €1.10 per pound. How many fewer euros would the £240 get there?[1]

Speeds in both units.

1. (a)Convert 90 km/h into m/s.[2]
2. (b)A cheetah sprints at 31 m/s. Convert this to km/h.[2]
3. (c)Explain why the same speed has a smaller number in m/s than in km/h.[1]

Food supplies are stretched over more guests.

1. (a)The hotel kitchen has food for 60 guests for 12 days. Work out how long the same food would last 90 guests.[3]
2. (b)Write down the assumption your calculation makes.[1]
3. (c)Work out how long the food would last 40 guests.[1]

Proportion with squares. (Higher)

1. (a)y is proportional to x². When x = 3, y = 45. Find the equation connecting y and x.[2]
2. (b)Find y when x = 6.[1]
3. (c)p is inversely proportional to q. When q = 3, p = 8. Find the equation connecting p and q.[2]
4. (d)Find p when q = 12.[1]

Toads in a pond. (Higher)

1. (a)Ecologists catch 30 toads, tag them and release them. A week later they catch 45 toads and 9 are tagged. Estimate the pond population.[3]
2. (b)Give two assumptions the estimate depends on.[2]
3. (c)The second catch found one fifth of its toads were tagged. Explain why the estimate is 30 × 5.[1]

Gas pressure and volume. (Higher)

1. (a)The volume V of a gas is inversely proportional to its pressure P. When P = 50 kPa, V = 240 cm³. Find the equation connecting V and P.[2]
2. (b)Find V when P = 75 kPa.[1]
3. (c)Find P when V = 480 cm³.[1]
4. (d)Explain what happens to V when P doubles.[2]

Filling a pool and a density conversion. (Higher)

1. (a)A tap pours 30 litres of water in 4 minutes. Find the filling rate in litres per hour.[2]
2. (b)At this rate, how long does a 1500-litre pool take to fill? Give your answer in hours and minutes.[2]
3. (c)The water has density 0.92 g/cm³. Express this in kg/m³.[2]

Density and base pressure for a statue. (Higher)

1. (a)A statue has mass 5200 g and volume 2000 cm³. Work out its density in g/cm³.[2]
2. (b)The statue weighs 130 N and its base has area 0.05 m². Work out the pressure on the ground, in Pa.[2]
3. (c)Write down the equivalent unit name for N/m².[1]

A square-root proportion is unlocked. (Higher)

1. (a)y is directly proportional to √x. When x = 9, y = 6. Find the equation connecting y and x.[3]
2. (b)Work out y when x = 25.[1]
3. (c)Work out x when y = 14.[2]

Squirrels are tagged in a wood. (Higher)

1. (a)Ecologists tag 30 squirrels and release them. Later they catch 45 squirrels and find 15 are tagged. Estimate the squirrel population of the wood.[3]
2. (b)Give two assumptions the estimate relies on.[2]
3. (c)A second survey catches 200 squirrels and 40 are tagged. Work out the new estimate and say how it compares.[1]