Geometry: past paper questions

Where the questions come from

• Question 3May/June 2026, paper 11Structured2 marks

  Measure angle $a$.

  Try this question
• Question 2Oct/Nov 2025, paper 11Structured2 marksHas a diagram

  The diagram shows a circle, centre $O$. On the diagram draw a diameter

  Try this question
• Question 3Oct/Nov 2024, paper 11Structured2 marks

  Measure angle $x$.

  Try this question
• Question 1Oct/Nov 2023, paper 11Structured1 mark

  Write down the mathematical name for this type of angle.

  Try this question
• Question 4May/June 2026, paper 11Structured2 marksHas a diagram

  Points $A$ and $B$ lie on a circle, centre $O$, as shown in the diagram. Write down the mathematical name for line $AB$.

  Try this question
• Question 3Oct/Nov 2025, paper 11Structured1 markHas a diagram

  Write down the mathematical name of this polygon.

  Try this question
• Question 8Oct/Nov 2024, paper 11Structured2 marksHas a diagram

  The diagram shows a quadrilateral. Find the value of $y$.

  Try this question
• Question 8Oct/Nov 2023, paper 11Structured2 marksHas a diagram

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

  Try this question
• 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.

  Try this question
• 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.

  Try this question
• Question 12Oct/Nov 2024, paper 11Structured2 marksHas a diagram

  The grid shows half of a shape which has a line of symmetry, $L$. Complete the shape.

  Try this question
• Question 10Oct/Nov 2023, paper 11Structured2 marks

  $AB$ and $CD$ are parallel lines. Find the value of $x$.

  Try this question
• Question 10May/June 2026, paper 11Structured2 marksHas a diagram

  The diagram shows two straight lines intersecting two parallel lines. Complete each of these statements with the correct geometrical reason.

  Try this question
• Question 6Oct/Nov 2025, paper 11Structured1 markHas a diagram

  Shade one square so that the diagram has rotational symmetry of order 4. Shade one square so that the diagram has rotational symmetry of order 4.

  Try this question
• Question 24Oct/Nov 2024, paper 11Structured3 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.

  Try this question
• Question 11Oct/Nov 2023, paper 12Structured2 marksHas a diagram

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

  Try this question
• Question 11May/June 2026, paper 11Structured3 marksHas a diagram

  On the $1{\text{ cm}}^2$ grid, complete a net of this cuboid.

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

  Complete the net of this cuboid on the $1{\text{ cm}}^2$ grid.

  Try this question
• Question 4Oct/Nov 2024, paper 12Structured4 marks

  The diagram shows a regular polygon. Write down the mathematical name for this polygon.

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

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

  Try this question
• Question 12May/June 2026, paper 12Structured3 marksHas a diagram

  To make a solid, a net is drawn on the $1{\text{ cm}}^2$ grid. Write down the mathematical name for the solid.

  Try this question
• 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 $B$.

  Try this question
• 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.

  Try this question
• Question 15Oct/Nov 2023, paper 12Structured2 marks

  Calculate the interior angle of a regular 9-sided polygon.

  Try this question
• Question 13May/June 2026, paper 12Structured3 marks

  A trapezium, $T$, is drawn on the $1{\text{ cm}}^2$ grid. On the grid, draw a different trapezium that is mathematically similar to trapezium $T$

  Try this question
• Question 15Oct/Nov 2025, paper 11Structured3 marksHas a diagram

  $ABC$ is a straight line and $ABD$ is an isosceles triangle. Work out the value of $x$.

  Try this question
• Question 17Oct/Nov 2023, paper 12Structured4 marksHas a diagram

  $A$, $B$ and $C$ are points on a circle, centre $O$. Draw a tangent to the circle at point $A$.

  Try this question
• Question 15May/June 2026, paper 12Structured2 marks

  Write down two geometrical properties of a parallelogram.

  Try this question
• Question 5Oct/Nov 2025, paper 12Structured3 marksHas a diagram

  The diagram is made from equilateral triangles. On the diagram, draw all the lines of symmetry.

  Try this question
• 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 $A$.

  Try this question