Edexcel IGCSE Maths
Topic questions Ratio, proportion and rates of change Compound measures
55 questions · 195 marks · about 4 hours
Also involves Converting between units
A bus travels a distance of 1262 km from Beijing to Shanghai. The bus takes 17 
hours.
Work out the average speed of the bus. Give your answer, in km/h, correct to the nearest whole number.
Change a speed of 50x metres per second to a speed in kilometres per hour.
Also involves Converting between units
Change a speed of 50 x metres per second to a speed in kilometres per hour.
The mass of a silver coin is 48.3 g The density of silver is 10.5 g/cm3
Work out the volume of the silver coin.
The scale diagram shows the positions of a castle and a tower.
Angela walks from the castle to the tower along a straight path.
She takes 18 minutes to walk each km.
Work out how many minutes Angela takes to walk from the castle to the tower.
Also involves Converting between units
The diagram shows a solid wooden cylinder.
The cylinder has radius 8 cm and height h cm. The volume of the cylinder is 1208 cm3
Work out the value of h Give your answer correct to the nearest whole number.
The density of the wood is 1.25 g/cm³
Work out the mass of the cylinder. Give your answer in kilograms.
A cylinder is placed on a table.
The volume of the cylinder is 1575 cm3 The force exerted by the cylinder on the table is 84 newtons.
Work out the pressure on the table due to the cylinder.
Also involves Rearranging formulae · Converting between units
The diagram shows a solid wooden cylinder.
The cylinder has radius 8 cm and height h cm. The volume of the cylinder is 1208 cm3
Work out the value of h Give your answer correct to the nearest whole number.
The density of the wood is 1.25 g/cm³
Work out the mass of the cylinder. Give your answer in kilograms.
A cylinder is placed on a table.
The volume of the cylinder is 1575 cm3 The force exerted by the cylinder on the table is 84 newtons.
Work out the pressure on the table due to the cylinder.
Also involves Sine and cosine rules
The diagram shows the positions of three villages, A, B and C
The bearing of B from A is 054° The bearing of C from B is 132°
Melur walks from A to B She then walks from B to C and from C to A
Melur walks at an average speed of 6 km/h
Work out the total time Melur takes. Give your answer in hours and minutes.
Also involves Forming and solving equations
The diagram shows a block of iron in the shape of a cuboid.
The block has length wcm, width 5 cm and height 4 cm
The density of iron is 7.8 g / cm3 The mass of the block is 1950 g
Work out the value of w
Also involves Forming and solving equations
The diagram shows a block of iron in the shape of a cuboid.
The block has length wcm, width 5 cm and height 4 cm
The density of iron is 7.8 g / cm3 The mass of the block is 1950 g
Work out the value of w
The scale drawing shows the positions of two airports P and Q
Find, by measuring, the bearing of P from Q
A small plane flies directly from P to Q The plane takes 2 hours to fly from P to Q
Work out the average speed of the plane. Give your answer in km / h
Change a speed of 27 kilometres per hour to a speed in metres per second.
Also involves Converting between units
Change a speed of 27 kilometres per hour to a speed in metres per second.
Also involves Volume and surface area
The diagram shows two solids, A and B, made from two different metals.
Solid A is in the shape of a cylinder with radius 3 cm and height 7 cm Solid A has a mass of 2000 g
Solid B has a mass of 3375 g Solid B has a volume of 450 cm3
All of the metal from Solid A and Solid B is melted down to make a uniform Solid C
Given that there is no change to mass or volume during this process
work out the density of Solid C Give your answer correct to one decimal place.
........ g / cm3
Also involves Converting between units
Change a speed of 90 kilometres per hour to a speed in metres per second. Show your working clearly.
The diagram shows two solids, A and B, made from two different metals.
Solid A is in the shape of a cylinder with radius 3 cm and height 7 cm Solid A has a mass of 2000 g
Solid B has a mass of 3375 g Solid B has a volume of 450 cm3
All of the metal from Solid A and Solid B is melted down to make a uniform Solid C
Given that there is no change to mass or volume during this process
work out the density of Solid C Give your answer correct to one decimal place.
........ g / cm3
Also involves Volume and surface area
A cylinder is placed on the ground.
The height of the cylinder is 18 cm.
The force exerted by the cylinder on the ground is 72 newtons. The pressure on the ground due to the cylinder is 1.4 newtons / cm2
Work out the volume of the cylinder. Give your answer correct to 3 significant figures.
Also involves Converting between units
The diagram shows a solid cylinder made from iron.
The cylinder has diameter 18 cm and height 3.5 cm The mass of the cylinder is 7.04 kg
Work out the density of the iron. Give your answer in g/cm3 correct to 2 significant figures.
Also involves Volume and surface area
A cylinder is placed on the ground.
The height of the cylinder is 18 cm.
The force exerted by the cylinder on the ground is 72 newtons. The pressure on the ground due to the cylinder is 1.4 newtons / cm2
Work out the volume of the cylinder. Give your answer correct to 3 significant figures.
Milly went on a car journey. She travelled from Anesey to Breigh to Clando and then to Duckbridge.
For Anesey to Breigh, Milly drove the 245 km in 2.5 hours. For Breigh to Clando, Milly drove the 220 km at an average speed of 80 km/h For Clando to Duckbridge, Milly drove at an average speed of 72 km/h in 50 minutes.
Work out Milly’s average speed, in km/h, for the journey from Anesey to Duckbridge. Give your answer correct to one decimal place.
Also involves Forming and solving equations
The diagram shows a solid made from a cylinder and a hemisphere. The cylinder and the hemisphere are both made from the same metal.
The plane face of the hemisphere coincides with the upper plane face of the cylinder.
The radius of the cylinder and the radius of the hemisphere are both xcm. The height of the cylinder is 3 x cm.
The total surface area of the solid is 81πcm2 The mass of the solid is 840 grams.
The following table gives the density of each of four metals.
| Metal | Density (g/cm3) |
| Aluminium | 2.7 |
| Nickel | 8.9 |
| Gold | 19.3 |
| Silver | 10.5 |
The metal used to make the solid is one of the metals in the table.
Determine the metal used to make the solid. Show your working clearly.
Also involves Converting between units
A train journey from Paris to Amsterdam took 3 hours 24 minutes. The total distance the train travelled was 433.5 km.
Work out the average speed of the train. Give your answer in kilometres per hour.
Also involves Converting between units
A train journey from Paris to Amsterdam took 3 hours 24 minutes. The total distance the train travelled was 433.5 km.
Work out the average speed of the train. Give your answer in kilometres per hour.
Also involves Converting between units
A train takes 6 hours 39 minutes to travel from New Delhi to Kanpur. The train travels a distance of 429 km.
Work out the average speed of the train. Give your answer in km/h correct to one decimal place.
Also involves Converting between units
A rocket travelled 100 km at an average speed of 28 440 km/h.
Work out how long it took the rocket to travel the 100 km. Give your answer in seconds, correct to the nearest second.
Pedro drove from Toulouse to Montpellier in 2 hours 42 minutes. He drove at an average speed of 90 km/hour.
Janine drove from Toulouse to Montpellier along the same route as Pedro. The journey took her 3 hours.
Work out Janine’s average speed for the journey.
A box is put on a horizontal table.
The face of the box in contact with the table is a square of side 1.5 metres. The pressure on the table due to the box is 34.8 newtons/m2
A rocket travelled 100 km at an average speed of 28 440 km/h.
Work out how long it took the rocket to travel the 100 km. Give your answer in seconds, correct to the nearest second.
Also involves Converting between units
Pedro drove from Toulouse to Montpellier in 2 hours 42 minutes. He drove at an average speed of 90 km/hour.
Janine drove from Toulouse to Montpellier along the same route as Pedro. The journey took her 3 hours.
Work out Janine’s average speed for the journey.
Also involves Rearranging formulae
A box is put on a horizontal table.
The face of the box in contact with the table is a square of side 1.5 metres. The pressure on the table due to the box is 34.8 newtons/m2
Also involves Standard units and compound measures
Freda is playing a car racing game on her computer.
She sets up her computer so that her car completes each lap in the same number of seconds. Her car completes 3 laps in 72 seconds.
To win the game, Freda has to complete 68 laps in less than half an hour.
Does Freda win the game? Give a reason for your answer.
Also involves Rounding
The scale drawing shows the positions of a ship, S, and a port, P.
Find the bearing of S from P.
The ship S now sails directly towards port P. The ship sails at an average speed of 24 km/h.
Work out how long it takes the ship to get to P. Give your answer correct to the nearest hour.
Also involves Rounding · Converting between units
Pablo made a solid gold statue.
He melted down some gold blocks and used the gold to make the statue. Each block of gold was a cuboid, as shown below.
The mass of the statue is 5.73 kg. The density of gold is 19.32 g/cm3
Work out the least number of gold blocks Pablo melted down in order to make the statue. Show your working clearly.
Also involves Rounding
Pablo made a solid gold statue.
He melted down some gold blocks and used the gold to make the statue. Each block of gold was a cuboid, as shown below.
The mass of the statue is 5.73 kg. The density of gold is 19.32 g/cm3
Work out the least number of gold blocks Pablo melted down in order to make the statue. Show your working clearly.
Also involves Rearranging formulae
The diagram shows a solid cube. The cube is placed on a table so that the whole of one face of the cube is in contact with the table.
The cube exerts a force of 56 newtons on the table. The pressure on the table due to the cube is 0.14 newtons/cm2
Work out the volume of the cube.
Also involves Converting between units
A plane takes 3 hours 36 minutes to fly from the Cayman Islands to New York. The plane flies a distance of 2470 km.
Work out the average speed of the plane in km/h. Give your answer correct to the nearest whole number.
Also involves Rearranging formulae
The diagram shows a box in the shape of a cuboid.
The box is put on a table. The face of the box in contact with the table has length 1.2 metres and width x metres.
The force exerted by the box on the table is 27 newtons. The pressure on the table due to the box is 30 newtons/m2
Work out the value of x.
Also involves Converting between units
Change a speed of 50 metres per second to a speed in kilometres per hour.
........ kilometres per hour
Also involves Converting between units
A plane takes 3 hours 36 minutes to fly from the Cayman Islands to New York. The plane flies a distance of 2470 km.
Work out the average speed of the plane in km/h. Give your answer correct to the nearest whole number.
Also involves Rearranging formulae · Forming and solving equations
The diagram shows a box in the shape of a cuboid.
The box is put on a table. The face of the box in contact with the table has length 1.2 metres and width x metres.
The force exerted by the box on the table is 27 newtons. The pressure on the table due to the box is 30 newtons/m2
Work out the value of x.
Also involves Motion graphs
Jalina left her home at 10 00 to cycle to a park. On her way to the park, she stopped at a friend’s house and then continued her journey to the park. Here is the distance-time graph for her journey to the park.
On her journey to the park, did Jalina cycle at a faster speed before or after she stopped at her friend’s house? Give a reason for your answer.
Jalina stayed at the park for 45 minutes. She then cycled, without stopping, at a constant speed of 16 km/h from the park back to her home.
Show all this information on the distance-time graph.
Work out Jalina’s average cycling speed, in kilometres per hour, for the complete journey to the park and back. Do not include the times when she was not cycling in your calculation. Give your answer correct to 1 decimal place.
The diagram shows a solid cuboid made from wood.
The wood has density 0.7 g/cm3
Work out the mass of the cuboid.
Also involves Motion graphs
Jalina left her home at 10 00 to cycle to a park. On her way to the park, she stopped at a friend’s house and then continued her journey to the park. Here is the distance-time graph for her journey to the park.
On her journey to the park, did Jalina cycle at a faster speed before or after she stopped at her friend’s house? Give a reason for your answer.
Jalina stayed at the park for 45 minutes. She then cycled, without stopping, at a constant speed of 16 km/h from the park back to her home.
Show all this information on the distance-time graph.
Work out Jalina’s average cycling speed, in kilometres per hour, for the complete journey to the park and back. Do not include the times when she was not cycling in your calculation. Give your answer correct to 1 decimal place.
Also involves Volume and surface area
The diagram shows a solid cuboid made from wood.
The wood has density 0.7 g/cm3
Work out the mass of the cuboid.
Also involves Converting between units
Change 22 metres per second to a speed in kilometres per hour. Show your working clearly.
12
A box, in the shape of a cuboid, is going to be put on a table.
The whole of one face of the box will be in contact with the table. The force exerted by the box on the table is always 105 newtons.
The box is 5 m by 4 m by 3 m.
The greatest pressure exerted by the box on the table is P newtons/m2 The least pressure exerted by the box on the table is Q newtons/m2
Work out the value of P
Q
Also involves Converting between units
Change a speed of 72 kilometres per hour to a speed in metres per second.
........ metres per second
Also involves Real-life graphs
Tenzin walks in the mountains. She has a rule to estimate the temperature at different heights on a mountain.
The temperature at a height of 800 metres on a mountain is 6 
C.
Use Tenzin’s rule to work out an estimate of the temperature at a height of 2000 metres on the mountain.
Tenzin also has a rule to estimate the time it will take her to complete a walk in the mountains.
She uses an average speed of 5 km / h for the distance she will walk and then adds on 1 minute for every increase of 10 metres in height.
Tenzin plans to walk 12 km in the mountains with an increase of 800 metres in height.
Use Tenzin’s rule to work out an estimate for the time it will take her to complete this walk. Give your answer in hours and minutes.
A box is put on a table.
The face of the box in contact with the table is in the shape of a rectangle, 2 m by 1.25 m. The pressure on the table due to the box is 42 newtons/m2
Work out the force exerted by the box on the table.
Abelie flew by plane from Dubai to Rome.
The flight time was 6 hours 42 minutes. The average speed of the plane was 650 kilometres per hour.
Work out the distance the plane flew.
A box is put on a table.
The face of the box in contact with the table is in the shape of a rectangle, 2 m by 1.25 m. The pressure on the table due to the box is 42 newtons/m2
Work out the force exerted by the box on the table.
Abelie flew by plane from Dubai to Rome.
The flight time was 6 hours 42 minutes. The average speed of the plane was 650 kilometres per hour.
Work out the distance the plane flew.
Also involves Volume and surface area
A solid metal sphere has radius 1.5 cm. The mass of the sphere is 109.6 grams.
Work out the density of the sphere. Give your answer correct to 3 significant figures.
........ g / cm3
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