Geometrical constructions: past paper questions

Where the questions come from

• Question 6May/June 2026, paper 11Structured2 marks

  Triangle $ABC$ has sides $AC=7.4\text{ cm}$ and $BC=4.6\text{ cm}$. Using a ruler and compasses only, construct triangle $ABC$. Leave in your construction arcs.

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• Question 5Oct/Nov 2025, paper 11Structured2 marks

  In triangle $ABC$, $AB=8\text{ cm}$ and $BC=6.4\text{ cm}$. Using a ruler and compasses only, construct triangle $ABC$. Leave in your construction arcs.

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• Question 6Oct/Nov 2024, paper 12Structured2 marks

  Triangle $ABC$ has sides $AC=4.2\text{ cm}$ and $BC=5.6\text{ cm}$. Using a ruler and compasses only, construct triangle $ABC$. Leave in your construction arcs.

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• Question 7Oct/Nov 2023, paper 13Structured3 marks

  In triangle $LMN$, $LN=7.5\text{ cm}$ and $MN=8\text{ cm}$. Using a ruler and compasses only, construct triangle $LMN$. Leave in your construction arcs.

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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 1Oct/Nov 2025, paper 13Structured2 marks

  Measure the length of line $AB$ in centimetres.

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• Question 4Oct/Nov 2024, paper 31Structured6 marksHas a diagram

  A parallelogram $ABCD$ has sides $8\text{ cm}$ and $6\text{ cm}$. Lines $AB$ and $BC$ have been drawn. By constructing triangle $ACD$, complete the parallelogram.

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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 2May/June 2024, paper 11Structured1 mark

  Measure the length of line $AB$ in millimetres. Measure the length of line $AB$ in millimetres.

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• Question 2May/June 2023, paper 12Structured2 marks

  Draw a line perpendicular to the line $AB$.

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• Question 4May/June 2025, paper 12Structured2 marks

  The diagram shows a line $AB$ and a point $P$. Measure the length of line $AB$ in millimetres.

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• Question 17May/June 2024, paper 11Structured2 marksHas a diagram

  The diagram shows a circle, centre $O$. $P$ lies on the circle. Write down the mathematical name of the line $OP$.

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• Question 6May/June 2025, paper 31Structured2 marks

  In triangle $ABC$, $AC=6.4\text{ cm}$ and $BC=5.3\text{ cm}$. Using a ruler and compasses only, construct triangle $ABC$. Leave in your construction arcs.

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• Question 2May/June 2024, paper 12Structured4 marks

  Measure the size of angle $x$.

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