Edexcel International GCSE Maths Speed and Density Past Paper Questions and Solutions (4MA1 Higher)

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Edexcel International GCSE Maths A (4MA1) · Higher · Geometry and Trigonometry

Measures, Speed and Density: Edexcel 4MA1 Past Paper Questions and Worked Solutions

This page collects every measures, speed and density question from the Pearson Edexcel International GCSE Mathematics A (4MA1) Higher tier Paper 1H and Paper 1HR, January 2020 to June 2025: 14 questions worth 50 marks. Questions run from easier to harder. Try each one first, then click “Show solution” for a step-by-step method with the reason for every step. All answers are checked against the official Pearson mark schemes.

13 marksHigherJune 2021 · Paper 1H (4MA1/1H) · Q1

A plane flew from Madrid to Dubai. The distance the plane flew was 5658 km. The flight time was 8 hours 12 minutes. Work out the average speed of the plane.

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  1. Convert the time to hours: 12 minutes = 12⁄60 = 0.2 hours, so the time is 8.2 hours.
  2. Speed = distance ÷ time = 5658 ÷ 8.2

Answer: 690 km/h

Tip: 8 hours 12 minutes is not 8.12 hours. Always divide the minutes by 60.
23 marksHigherJanuary 2021 · Paper 1HR (4MA1/1HR) · Q4

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.

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  1. 24 minutes = 24⁄60 = 0.4 hours, so the time is 3.4 hours.
  2. Speed = 433.5 ÷ 3.4

Answer: 127.5 km/h

33 marksHigherJune 2020 · Paper 1H (4MA1/1H) · Q6

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.

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  1. Time = distance ÷ speed = 100 ÷ 28 440 = 0.003 516… hours
  2. 1 hour = 3600 seconds, so time = 0.003 516… × 3600 = 12.658…

Answer: 13 seconds

44 marksHigherJune 2020 · Paper 1HR (4MA1/1HR) · Q7

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.

Show solution
  1. Pedro’s time in hours: 42 minutes = 42⁄60 = 0.7 hours, so 2.7 hours.
  2. Distance = speed × time = 90 × 2.7 = 243 km
  3. Janine’s speed = 243 ÷ 3

Answer: 81 km/hour

54 marksHigherJanuary 2022 · Paper 1HR (4MA1/1HR) · Q7

Milly went on a car journey 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.

Show solution
  1. Breigh to Clando time = 220 ÷ 80 = 2.75 hours
  2. Clando to Duckbridge: 50 minutes = 50⁄60 hours, distance = 72 × 50⁄60 = 60 km
  3. Total distance = 245 + 220 + 60 = 525 km
  4. Total time = 2.5 + 2.75 + 0.8333… = 6.0833… hours
  5. Average speed = 525 ÷ 6.0833… = 86.30…

Answer: 86.3 km/h

Tip: Do not average the three speeds. Average speed is always total distance ÷ total time.
64 marksHigherJune 2022 · Paper 1H (4MA1/1H) · Q7

A cylinder of height 18 cm is placed on the ground. 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. Using pressure = force⁄area, work out the volume of the cylinder. Give your answer correct to 3 significant figures.

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  1. Rearrange the formula: area = force ÷ pressure = 72 ÷ 1.4 = 51.428… cm2. This is the area of the circular base.
  2. Volume = base area × height = 51.428… × 18 = 925.71…

Answer: 926 cm3

73 marksHigherJune 2022 · Paper 1HR (4MA1/1HR) · Q7

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.

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  1. The radius is half the diameter: 9 cm. Volume = π × 92 × 3.5 = 890.64… cm3
  2. The density must be in g/cm3, so convert the mass to grams: 7.04 kg = 7040 g
  3. Density = mass ÷ volume = 7040 ÷ 890.64… = 7.904…

Answer: 7.9 g/cm3

83 marksHigherJune 2025 · Paper 1HR (4MA1/1HR) · Q7

Change a speed of 50x metres per second to a speed in kilometres per hour.

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  1. In one hour there are 60 × 60 = 3600 seconds, so in one hour the distance is 50x × 3600 = 180 000x metres.
  2. There are 1000 metres in a kilometre: 180 000x ÷ 1000 = 180x km

Answer: 180x km/h

93 marksHigherJune 2024 · Paper 1H (4MA1/1H) · Q8

A cylinder of height 21 cm 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. Using pressure = force⁄area, work out the pressure on the table due to the cylinder.

21 cm
Show solution
  1. The force acts on the circular base, so we need the area of the base.
  2. Volume of a cylinder = area of base × height, so 1575 = area × 21
  3. Area of base = 1575 ÷ 21 = 75 cm2
  4. Pressure = force ÷ area = 84 ÷ 75

Answer: 1.12 newtons/cm2

Tip: You do not need to find the radius. Dividing the volume by the height gives the base area directly.
105 marksHigherJanuary 2020 · Paper 1HR (4MA1/1HR) · Q9

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 measuring 1.5 cm by 2 cm by 8 cm. 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.

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  1. Mass in grams: 5.73 kg = 5730 g
  2. Volume of the statue = mass ÷ density = 5730 ÷ 19.32 = 296.58… cm3
  3. Volume of one block = 1.5 × 2 × 8 = 24 cm3
  4. Blocks needed = 296.58… ÷ 24 = 12.35…
  5. 12 blocks would not be enough, so round up.

Answer: 13 blocks

113 marksHigherJune 2020 · Paper 1HR (4MA1/1HR) · Q9

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. Using pressure = force⁄area, work out the force exerted by the box on the table.

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  1. Area of the square face = 1.5 × 1.5 = 2.25 m2
  2. Rearrange the formula: force = pressure × area = 34.8 × 2.25

Answer: 78.3 newtons

125 marksHigherNovember 2021 · Paper 1H (4MA1/1H) · Q10

A solid aluminium cylinder has radius 10 cm and height h cm. The mass of the cylinder is 5.4 kg. The density of aluminium is 0.0027 kg/cm3. Calculate the value of h. Give your answer correct to one decimal place.

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  1. Volume = mass ÷ density = 5.4 ÷ 0.0027 = 2000 cm3 (the units already match: kg and kg/cm3)
  2. Volume of a cylinder = πr2h = π × 100 × h
  3. 100πh = 2000, so h = 2000 ÷ (100π) = 6.366…

Answer: h = 6.4

133 marksHigherJune 2023 · Paper 1HR (4MA1/1HR) · Q11

The diagram shows a block of iron in the shape of a cuboid. The block has length w cm, 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.

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  1. Volume = mass ÷ density = 1950 ÷ 7.8 = 250 cm3
  2. Volume of the cuboid = w × 5 × 4 = 20w
  3. 20w = 250, so w = 250 ÷ 20

Answer: w = 12.5

144 marksHigherJanuary 2020 · Paper 1H (4MA1/1H) · Q13

The diagram shows a solid cube of side w cm. 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. Using pressure = force⁄area, work out the volume of the cube.

Show solution
  1. Area of the face on the table = force ÷ pressure = 56 ÷ 0.14 = 400 cm2
  2. The face is a square, so w2 = 400 and w = 20 cm
  3. Volume = w3 = 203

Answer: 8000 cm3

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