Geometry: past paper questions

Where the questions come from

• Question 7May/June 2026, paper 21Structured2 marks

  The diagram shows the positions of three ships $P$, $Q$ and $R$. Ship $Q$ is $40\text{ km}$ due east of ship $R$. Ship $P$ is $40\text{ km}$ due north of ship $Q$.

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• Question 2Oct/Nov 2025, paper 21Structured3 marksHas a diagram

  In the diagram, $AC=BC$. Work out angle $CAB$.

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• Question 6Oct/Nov 2024, paper 21Structured3 marksHas a diagram

  The diagram shows a right-angled triangle $ABC$ and a quadrilateral $AEDC$. Find the value of $x$

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• Question 1Oct/Nov 2023, paper 21Structured2 marksHas a diagram

  The diagram shows an isosceles triangle. Find the value of $x$.

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• Question 23May/June 2026, paper 21Structured3 marksHas a diagram

  The two solids are mathematically similar. The volume of the larger solid is $64{\text{ cm}}^3$ and the volume of the smaller solid is $27{\text{ cm}}^3$. The height of the larger solid is $10\text{ cm}$ and the height of the smaller solid is $h\text{ cm}$.

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• Question 3Oct/Nov 2025, paper 21Structured2 marks

  Find the interior angle of a regular 20-sided polygon.

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• Question 9Oct/Nov 2024, paper 21Structured3 marks

  The diagram shows part of a regular polygon. The interior angle of the polygon is ${132}^{\circ }$ larger than the exterior angle. Calculate the number of sides of this polygon.

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• Question 17Oct/Nov 2023, paper 21Structured3 marksHas a diagram

  $A$, $B$ and $C$ are points on the circumference of a circle, centre $O$. Tangent $DE$ touches the circle at $C$. Angle $BCE={53}^{\circ }$ and angle $ACO={20}^{\circ }$.

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• Question 11May/June 2026, paper 22Structured2 marks

  Find the number of sides of a regular polygon with interior angle ${140}^{\circ }$.

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• Question 14Oct/Nov 2025, paper 21Structured9 marksHas a diagram

  $A,B,C,D$ and $E$ lie on the circle. $AC$ and $BD$ intersect at $X$. Angle $ACD={55}^{\circ }$ and angle $CXD={88}^{\circ }$.

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• Question 14Oct/Nov 2024, paper 21Structured4 marks

  Two solid steel statues are mathematically similar. The smaller statue has height $12\text{ cm}$ and the larger statue has height $15\text{ cm}$. The larger statue has a mass $2.5\text{ kg}$.

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• Question 5Oct/Nov 2023, paper 22Structured2 marksHas a diagram

  The diagram shows two intersecting straight lines crossing two parallel lines. Find the value of $x$.

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• Question 15May/June 2026, paper 22Structured5 marksHas a diagram

  $A$, $B$, $C$ and $D$ are points on a circle. $EF$ is a tangent to the circle at $A$. Angle $ADB={20}^{\circ }$ and angle $BCD={75}^{\circ }$.

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• Question 6Oct/Nov 2025, paper 22Structured4 marksHas a diagram

  ABCD is a quadrilateral. E lies on CD and AE is parallel to BC. EA = ED.

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• Question 7Oct/Nov 2023, paper 22Structured2 marksHas a diagram

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

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• Question 20May/June 2026, paper 22Structured3 marks

  Two bottles are mathematically similar. The volume of the larger bottle is $216{\text{ cm}}^3$ and the volume of the smaller bottle is $27{\text{ cm}}^3$. The height of the larger bottle is $10\text{ cm}$ and the height of the smaller bottle is $h\text{ cm}$.

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• Question 11Oct/Nov 2025, paper 22Structured7 marksHas a diagram

  In the diagram, $S$ lies on $PQ$ and $T$ lies on $PR$. $ST$ is parallel to $QR$. Explain why triangle $PQR$ is mathematically similar to triangle $PST$.

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• Question 8Oct/Nov 2024, paper 22Structured4 marksHas a diagram

  The diagram shows a parallelogram. Work out the size of the smallest interior angle of the parallelogram.

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• Question 11Oct/Nov 2023, paper 22Structured4 marksHas a diagram

  The two shapes are mathematically similar. Find the value of $h$.

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• Question 7May/June 2026, paper 23Structured3 marksHas a diagram

  The diagram shows the position of two towns, $A$ and $B$. The scale is $1\text{ cm}$ represents $2\text{ km}$. Work out the actual distance between $A$ and $B$.

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• Question 16Oct/Nov 2025, paper 22Structured4 marks

  $AB$ and $BD$ are two sides of a regular 15-sided polygon. $AB$ and $BC$ are two sides of a regular $n$-sided polygon. Angle $DBC={14}^{\circ }$.

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• Question 17Oct/Nov 2024, paper 22Structured2 marksHas a diagram

  $A$, $B$ and $C$ are points on the circumference of a circle with centre $O$. $DA$ and $DC$ are tangents to the circle. Angle $ABC={64}^{\circ }$.

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• Question 17Oct/Nov 2023, paper 22Structured4 marksHas a diagram

  $A$, $B$ and $C$ are points on a circle, centre $O$. Angle $OBA={28}^{\circ }$. Find angle $ACB$.

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• Question 11May/June 2026, paper 23Structured2 marks

  The interior angle of a regular polygon is ${135}^{\circ }$. Find the number of sides of this regular polygon.

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• Question 23Oct/Nov 2024, paper 22Structured3 marksHas a diagram

  The small box is mathematically similar to the large box. The volume of the large box is $72.8\mathrm{\%}$ greater than the volume of the small box. The small box has length $3.5\text{ cm}$ and the large box has length $x\text{ cm}$.

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• Question 5Oct/Nov 2023, paper 23Structured3 marksHas a diagram

  The diagram shows triangle $ABC$. $M$ is the midpoint of $AC$. Triangle $ABC$ is rotated ${180}^{\circ }$ about centre $M$.

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• Question 13May/June 2026, paper 23Structured3 marksHas a diagram

  $A$, $B$ and $C$ are points on a circle with centre $O$. $AOC$ is a straight line and $M$ is the midpoint of $AB$. $AB=6\text{ cm}$ and $OM=4\text{ cm}$.

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• Question 3Oct/Nov 2025, paper 23Structured1 markHas a diagram

  The diagram shows a net for a dice. The dice has six faces numbered 1 to 6. The sum of each pair of opposite faces on the dice is 7.

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• Question 4Oct/Nov 2024, paper 23Structured3 marksHas a diagram

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

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• Question 5Oct/Nov 2023, paper 41Structured14 marksHas a diagram

  $ACD$ is a right-angled triangle. $B$ is on $AC$ and $BC=54.5\text{ m}$. $AD=83.2\text{ m}$ and angle $ABD={38}^{\circ }$.

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