Geometry: past paper questions

Where the questions come from

• Question 5May/June 2026, paper 12Structured4 marksHas a diagram

  The scale drawing shows the positions of two villages, $A$ and $B$. The scale is $2\text{ cm to }1\text{ km}$. Farm $C$ is $4\text{ km}$ from village $A$ and $2.5\text{ km}$ from village $B$.

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• Question 4Oct/Nov 2025, paper 11Structured4 marksHas a diagram

  The diagram shows five straight lines. The diagram shows three horizontal parallel lines and two sloping parallel lines. Find the value of $p$.

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• Question 4Oct/Nov 2024, paper 11Structured2 marksHas a diagram

  Shade one more small square so the diagram has one line of symmetry.

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• Question 6Oct/Nov 2023, paper 11Structured2 marksHas a diagram

  The diagram shows a straight line crossing two parallel lines. Work out the value of $x$.

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• Question 16May/June 2026, paper 12Structured6 marksHas a diagram

  $ABCD$ is a rhombus. $M$ is a point on $DC$. $AM$ and $BD$ intersect at $X$.

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• Question 16Oct/Nov 2025, paper 11Structured6 marksHas a diagram

  Points $Q$, $R$, $S$ and $T$ lie on a circle, centre $O$. $UV$ is a tangent to the circle at $T$. $SOQV$ is a straight line.

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• Question 10Oct/Nov 2024, paper 12Structured6 marksHas a diagram

  The scale drawing shows a field $ABCDE$. The field contains a stage that is a sector of a circle, centre $C$. The scale is $1\mathrm{c}\mathrm{m}$ to $2.5\mathrm{m}$.

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• Question 10Oct/Nov 2023, paper 11Structured4 marks

  Four exterior angles of a pentagon are ${150}^{\circ }$, ${100}^{\circ }$, ${45}^{\circ }$ and ${35}^{\circ }$. Calculate the size of the remaining exterior angle.

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• Question 3May/June 2026, paper 22Structured2 marksHas a diagram

  The diagram shows the net of a cuboid made from four congruent rectangles and two congruent squares. Find the total length of the edges of the cuboid.

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• Question 17Oct/Nov 2025, paper 11Structured7 marksHas a diagram

  The diagram shows a prism. The cross-section of the prism is an isosceles triangle with sides $13\text{ cm}$, $13\text{ cm}$ and base $10\text{ cm}$. The length of the prism is $3\text{ cm}$.

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• Question 15Oct/Nov 2024, paper 12Structured2 marks

  Each interior angle of a regular polygon is ${160}^{\circ }$. Find the number of sides of the polygon.

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• Question 12Oct/Nov 2023, paper 11Structured5 marksHas a diagram

  The scale drawing shows the positions of two boats $A$ and $B$. The scale is $1:20000$. Find the actual distance of boat $A$ from boat $B$ in kilometres.

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• Question 18May/June 2026, paper 22Structured4 marksHas a diagram

  $A$, $B$ and $C$ lie on a circle, centre $O$. $DE$ is a tangent to the circle at $A$. Angle $BAC={80}^{\circ }$ and angle $BAD={55}^{\circ }$.

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• Question 3Oct/Nov 2025, paper 12Structured4 marksHas a diagram

  ABCD is a parallelogram. $E$ is a point on $AB$ and $EC=BC$. Angle $ECB={40}^{\circ }$ and angle $DEC={60}^{\circ }$.

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• Question 19Oct/Nov 2024, paper 12Structured2 marksHas a diagram

  The diagram shows two mathematically similar mugs. The small mug has width $w\mathrm{c}\mathrm{m}$ and holds $270\mathrm{m}\mathrm{l}$ when full. The large mug has width $8\mathrm{c}\mathrm{m}$ and holds $640\mathrm{m}\mathrm{l}$ when full.

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• Question 15Oct/Nov 2023, paper 11Structured4 marksHas a diagram

  $B$, $C$ and $D$ are points on the circle, centre $O$. $AB$ and $AC$ are tangents to the circle. Angle $BAC={38}^{\circ }$.

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• Question 23May/June 2026, paper 22Structured12 marksHas a diagram

  The diagram shows a sector of a circle with centre $O$ and radius $9.1\text{ cm}$. The length of the major arc $AB$ is $44\text{ cm}$. Find the angle of the major sector $AOB$.

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• Question 14Oct/Nov 2025, paper 12Structured4 marksHas a diagram

  $A$, $B$, $C$ and $D$ are points on a circle, centre $O$. $EF$ is a tangent to the circle at $A$. Angle $BAF={65}^{\circ }$ and angle $AOD={80}^{\circ }$.

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• Question 6Oct/Nov 2024, paper 21Structured10 marksHas a diagram

  [Volume of sphere $=\frac{4}{3}\pi r^3$] The diagram shows a sphere inside a cube. The sphere touches all 6 faces of the cube. The volume of the cube is $343{\text{ cm}}^3$.

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• Question 6Oct/Nov 2023, paper 12Structured2 marksHas a diagram

  AB and CD are parallel lines. EC and FB are parallel lines. Angle ABF = 73°.

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• Question 17Oct/Nov 2025, paper 12Structured4 marksHas a diagram

  Triangle $ABC$ is similar to triangle $PQR$. Calculate $PR$.

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• Question 9Oct/Nov 2024, paper 21Structured10 marksHas a diagram

  $ABD$ is a triangle. $C$ is a point on $BD$ and $E$ is a point on $AD$. $AB$ is parallel to $EC$ and $CD=DE$.

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• Question 14Oct/Nov 2023, paper 12Structured5 marks

  Measure angle ABC.

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• Question 3Oct/Nov 2025, paper 21Structured3 marks

  In this question, all lengths are in centimetres. The diagram shows the net of a cuboid. Find the total surface area of the cuboid.

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• Question 8Oct/Nov 2024, paper 22Structured12 marksHas a diagram

  $ADB$ and $AEC$ are straight lines. $BC$ is parallel to $DE$. $BC=9.8\text{ cm}$, $BD=2.7\text{ cm}$, $DE=5.6\text{ cm}$ and $CE=3.9\text{ cm}$.

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• Question 10Oct/Nov 2023, paper 21Structured8 marksHas a diagram

  The diagram shows a circle, centre $O$, with diameters $AC$ and $BD$. Show that triangle $OAB$ is congruent to triangle $ODC$.

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• Question 5Oct/Nov 2025, paper 21Structured3 marksHas a diagram

  The diagram shows an isosceles triangle. Work out the value of x.

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• Question 2Oct/Nov 2023, paper 22Structured8 marksHas a diagram

  Find the size of one interior angle of a regular 15-sided polygon.

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• Question 7Oct/Nov 2025, paper 21Structured2 marks

  Work out the size of the interior angle of a regular decagon.

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• Question 4May/June 2024, paper 11Structured3 marks

  $ABC$ is a triangle with $AC=5\text{ cm}$ and $BC=10\text{ cm}$. Using a ruler and compasses only, construct triangle $ABC$. $AB$ has been drawn for you.

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