Scale drawings: past paper questions

Where the questions come from

• Question 11May/June 2026, paper 31Structured3 marksHas a diagram

  The scale diagram shows the positions of town $A$ and town $B$. The scale is $1\text{ cm}$ represents $15\text{ km}$. Measure the bearing of town $B$ from town $A$.

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• Question 13Oct/Nov 2025, paper 11Structured5 marks

  The scale drawing shows the positions of town $A$ and town $B$. The scale is 1 centimetre represents 10 kilometres. Work out the actual distance from town $A$ to town $B$.

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• Question 12Oct/Nov 2024, paper 12Structured3 marksHas a diagram

  The scale drawing shows the positions of two ships, $A$ and $B$. The scale is $1\text{ cm}$ represents $6\text{ km}$. Measure the bearing of ship $B$ from ship $A$.

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• Question 13Oct/Nov 2023, paper 12Structured2 marksHas a diagram

  Find the bearing of $Q$ from $P$.

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• Question 8May/June 2026, paper 32Structured2 marks

  The scale drawing shows the position of a town, $T$. The scale is 1 centimetre represents 20 kilometres. A village, $V$, is 94 km from $T$ on a bearing of ${112}^{\circ }$.

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• Question 24Oct/Nov 2025, paper 13Structured3 marks

  The scale on a map is 1cm represents 12km. Write this in the ratio $1:n$.

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• Question 9Oct/Nov 2024, paper 13Structured5 marksHas a diagram

  The scale drawing shows the positions of town $K$ and town $L$. The scale is 1 cm represents 10 km. Find the actual distance between town $K$ and town $L$.

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• Question 2Oct/Nov 2023, paper 31Structured10 marksHas a diagram

  The diagram shows a circle. The diameter of this circle is $168\text{ mm}$. Write down the radius of this circle.

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• Question 9May/June 2026, paper 33Structured5 marksHas a diagram

  The scale drawing shows the positions of three towns, $A$, $B$ and $C$. Town $B$ is directly south of town $A$. The scale is $1\text{ cm}$ represents $40\text{ km}$.

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• Question 15Oct/Nov 2025, paper 32Structured2 marks

  The scale drawing shows the position of ship A. The scale is 1 centimetre represents 40 kilometres. Ship B is 220 km from ship A on a bearing of 140°.

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• Question 14May/June 2024, paper 13Structured2 marks

  The scale of a map is $1:40000$. On the map the distance between two villages is $37\text{ cm}$. Calculate the actual distance between the two villages.

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• Question 8Oct/Nov 2023, paper 32Structured10 marksHas a diagram

  In triangle $RST$, $RT=7\text{ cm}$ and $ST=4\text{ cm}$. Using a ruler and compasses only, construct triangle $RST$. Leave in your construction arcs.

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• Question 13May/June 2025, paper 31Structured2 marks

  The scale drawing shows the position of ship $A$. The scale is 1 centimetre represents 50 kilometres. Ship $B$ is $300\text{ km}$ from ship $A$ on a bearing of ${105}^{\circ }$.

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• Question 7May/June 2024, paper 31Structured14 marks

  The scale drawing shows the position of a castle, $C$. The scale is 1 centimetre represents 2 kilometres. Micah walks at $4.8\text{ km/h}$ for 3 hours on a bearing of ${236}^{\circ }$ from $C$, to his house, $H$.

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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 11May/June 2025, paper 32Structured2 marks

  The scale drawing shows the position of a hospital, $H$. The scale is 1 centimetre represents 6 kilometres. Scale: 1 cm to 6 km A school, $S$, is 33 km from $H$ on a bearing of ${155}^{\circ }$.

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• Question 9May/June 2023, paper 12Structured1 markHas a diagram

  The scale drawing shows the positions of town $A$ and town $B$. Measure the bearing of town $B$ from town $A$. The scale drawing shows the positions of town $A$ and town $B$.

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• Question 16May/June 2025, paper 33Structured5 marksHas a diagram

  The scale drawing shows a path from $S$ to $P$. The scale is 1 cm represents 2.5 km. Work out the actual distance between $S$ and $P$.

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• Question 11May/June 2023, paper 12Structured2 marks

  The distance from town $A$ to town $B$ on a map is $3.5\text{ cm}$. The scale on the map is $1:250000$. Find the actual distance, in kilometres, from town $A$ to town $B$.

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• Question 4May/June 2023, paper 33Structured12 marksHas a diagram

  A boat sails from $A$ to $B$. The travel graph shows this journey. Write down the time that the boat leaves $A$.

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