Rates: past paper questions

Where the questions come from

• Question 24May/June 2026, paper 31Structured4 marks

  Ali drives 56km at an average speed of 48km/h. He then drives for 30 minutes at 54km/h. Calculate the average speed for his whole journey.

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• Question 3Oct/Nov 2025, paper 31Structured1 mark

  Total cost of a journey = number of litres of fuel used $\times$ cost of fuel per litre. A journey uses 128 litres of fuel.

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• Question 9Oct/Nov 2024, paper 31Structured6 marks

  Samir leaves home at 2 pm. He jogs 6 km to a café at a constant speed of 8 km per hour. He stops to rest for 1 hour.

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• Question 24Oct/Nov 2023, paper 11Structured3 marks

  Change $1.2{\text{ m}}^2$ into ${\text{mm}}^2$.

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• Question 21May/June 2026, paper 32Structured3 marks

  Sam leaves home at 1430 and drives 106 km to town $A$. His average speed is $40\text{ km/h}$. Calculate the time he arrives at town $A$.

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• Question 16Oct/Nov 2025, paper 31Structured5 marksHas a diagram

  Bob travels from town $A$ to town $B$. The travel graph shows his journey. Between which two times did Bob stop for a rest?

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• Question 6Oct/Nov 2024, paper 33Structured13 marksHas a diagram

  The diagram shows a plan of Zak’s garden. Find the perimeter of the garden.

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• Question 5Oct/Nov 2023, paper 31Structured8 marksHas a diagram

  A railway line has three stations, Town, Port and Cove. Train $A$ leaves Town for Cove and train $B$ leaves Cove for Town. Both trains stop at Port.

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• Question 15May/June 2026, paper 33Structured6 marksHas a diagram

  Tom leaves Alton at 0800 and drives to Newtown. The travel graph shows Tom’s journey. Find how long it takes Tom to reach Newtown.

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• Question 28Oct/Nov 2025, paper 33Structured3 marks

  The travel graph shows Chi’s journey from home to the station. Calculate Chi’s average speed for the whole journey.

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• Question 23May/June 2024, paper 11Structured2 marks

  Change $9.6\text{ km/h}$ into $\text{m/s}$. Change $9.6\text{ km/h}$ into $\text{m/s}$.

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• Question 2Oct/Nov 2023, paper 33Structured10 marks

  Bayside, Millwater and Westbridge are towns beside a lake. The scale drawing shows the positions of Bayside ($B$) and Millwater ($M$). The scale is 1 centimetre represents 2 kilometres.

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• Question 10May/June 2025, paper 11Structured5 marksHas a diagram

  Ky cycles from his office to a meeting and back again. The travel graph shows his time at the meeting and his journey back. How far is the meeting from his office?

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• Question 7May/June 2024, paper 12Structured2 marks

  A gardener charges $6.55 for each hour he works plus a fixed charge of $15.50 . Calculate the total amount he charges when he works for 4 hours.

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• Question 8May/June 2023, paper 31Structured9 marks

  Two friends, Diego and Javier, meet at a swimming pool. The travel graph shows Diego’s journey by bicycle from his home to the swimming pool. Calculate Diego’s speed for his journey from his home to the swimming pool.

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• Question 25May/June 2025, paper 31Structured3 marks

  A bar of gold in the shape of a cuboid has dimensions $2\text{ cm}$ by $4\text{ cm}$ by $6.5\text{ cm}$. The density of gold is $19.32{\text{ g/cm}}^3$. Calculate the mass of this bar of gold.

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• Question 9May/June 2024, paper 32Structured6 marks

  Sara rides her bicycle at a speed of 420 metres per minute. Work out her speed in kilometres per hour.

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• Question 1May/June 2023, paper 32Structured14 marks

  Write the number three hundred thousand and three in figures.

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• Question 18May/June 2025, paper 32Structured4 marks

  A factory produces brass at a rate of 172 kilograms per hour. Convert this rate into grams per second.

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• Question 21May/June 2025, paper 33Structured8 marks

  These are the distances above the surface of the Earth of five satellites, $A$, $B$, $C$, $D$ and $E$. Each distance is in kilometres.

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• Question 22May/June 2025, paper 33Structured4 marksHas a diagram

  The diagram shows a solid cylinder with height 10 cm. The volume of the cylinder is $478{\text{ cm}}^3$. Find the radius of the cylinder.

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