Rates: past paper questions

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• Question 9May/June 2026, paper 22Structured3 marks

  Amira walks from her home to her friend's house. She leaves home at 0935. She walks a total of $8\text{ km}$ at an average speed of $5\text{ km/h}$.

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• Question 12Oct/Nov 2025, paper 11Structured3 marksHas a diagram

  The diagram shows an empty container. The container is a cuboid of width $10\text{ cm}$, length $8\text{ cm}$ and height $9\text{ cm}$. Water drips into the container at a rate of 6 millilitres per second.

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• Question 8Oct/Nov 2024, paper 12Structured2 marks

  Sophia walks at an average speed of $4\mathrm{k}\mathrm{m}\mathrm{/}\mathrm{h}$. Work out the time Sophia takes to walk $13\mathrm{k}\mathrm{m}$.

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• Question 9Oct/Nov 2023, paper 22Structured11 marksHas a diagram

  $ABCD$ is a rectangular field. $C$ is due south of $A$. $AB=450\text{ m}$ and $BC=210\text{ m}$.

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• Question 22Oct/Nov 2025, paper 22Structured10 marksHas a diagram

  $ABCD$ is a field. A straight path crosses the field from $B$ to $D$. Calculate $AB$.

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• Question 8Oct/Nov 2024, paper 21Structured8 marksHas a diagram

  $ABCD$ is a field. $AB=320\text{ m}$, $BC=250\text{ m}$, $CD=132\text{ m}$ and $AD=365\text{ m}$. Angle $BCD={90}^{\circ }$.

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• Question 6May/June 2023, paper 22Structured8 marks

  Sophia takes part in the Trio Challenge. She walks, then cycles and then swims. Trio Challenge Walk 6.3 km Cycle 3000 m Swim 1800 m Write these distances $\text{walk}:\text{cycle}:\text{swim}$ as a ratio in its simplest form.

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• Question 16May/June 2025, paper 22Structured2 marks

  The population of Kenya is $5.71\times {10}^7$ people. The area of Kenya is $6\times {10}^5{\text{ km}}^2$. The population density is the number of people per ${\text{km}}^2$.

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• Question 9May/June 2024, paper 11Structured3 marksHas a diagram

  The diagram shows the distance–time graph of a cyclist for the first two stages of a race, $AB$ and $BC$. Work out the average speed of the cyclist for the second stage, $BC$.

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• Question 10May/June 2024, paper 11Structured3 marksHas a diagram

  The diagram shows the fuel gauge of a car. This car has 40 litres of fuel in the tank. Calculate the amount of fuel that the tank contains when it is full.

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• Question 8May/June 2024, paper 12Structured4 marks

  A train leaves station $A$ at 07 43. The train arrives at station $B$ at 10 27. Work out the time the train takes to travel from station $A$ to station $B$.

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• Question 9May/June 2024, paper 21Structured10 marksHas a diagram

  The diagram shows the positions of three ports $A$, $B$ and $C$. The bearing of port $B$ from port $A$ is ${107}^{\circ }$. The bearing of port $C$ from port $A$ is ${192}^{\circ }$.

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