Mensuration: past paper questions

Where the questions come from

• Question 7May/June 2026, paper 12Structured3 marksHas a diagram

  The diagram shows a trapezium. All the lengths are in centimetres. The area of the trapezium is $100{\text{ cm}}^2$.

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• Question 10Oct/Nov 2025, paper 11Structured2 marks

  A circle has diameter $12\text{ cm}$. Find the area of the circle.

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• Question 15Oct/Nov 2024, paper 11Structured4 marks

  A sector of a circle with angle ${60}^{\circ }$ has arc length $4\pi \mathrm{c}\mathrm{m}$. Find the area of the sector.

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• Question 8Oct/Nov 2023, paper 11Structured2 marks

  Convert $78\text{ mm}$ to $\text{cm}$.

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• Question 17May/June 2026, paper 12Structured9 marks

  In a right-angled triangle • the base is $x\text{ cm}$ • the height is $7\text{ cm}$ shorter than the base • the hypotenuse (longest side) is $2\text{ cm}$ longer than the base. Use this information to form an equation and show that it simplifies to $x^2-18x+45=0$.

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

  The diagram shows an empty container. The container is a cuboid of width $10\text{ cm}$, length $8\text{ cm}$ and height $9\text{ cm}$. Water drips into the container at a rate of 6 millilitres per second.

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• Question 17Oct/Nov 2024, paper 12Structured4 marksHas a diagram

  The diagram shows a shaded triangle, $ABC$, drawn on a $1\mathrm{c}\mathrm{m}$ square grid. The equation of the line $AC$ is $y=-\frac{3}{2}x+1$. The shaded region inside triangle $ABC$ is defined by three inequalities.

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• Question 21Oct/Nov 2023, paper 12Structured5 marksHas a diagram

  Diagram A shows a sector of a circle, centre D and radius 3/4y cm. The obtuse angle EDF = 6x°. Diagram B shows a sector of a circle, centre P and radius y cm.

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• Question 19May/June 2026, paper 12Structured6 marksHas a diagram

  The diagram shows a solid hemisphere and a solid cylinder. All the lengths are in centimetres. The radius of the hemisphere is $3x$.

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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 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 9Oct/Nov 2023, paper 21Structured14 marksHas a diagram

  The diagram shows a triangular prism. $AB=6\text{ cm}$, angle $BAC={55}^{\circ }$ and the length of the prism is $20\text{ cm}$. The area of triangle $ABC$ is $34.4{\text{ cm}}^2$.

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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 24Oct/Nov 2025, paper 11Structured10 marks

  The diagram shows a rectangle and a triangle. The length of the rectangle is $x\text{ cm}$ and the area of the rectangle is $30{\text{ cm}}^2$. The triangle has sides of length $(x-1)\text{ cm}$, $(x+2)\text{ cm}$ and $(2x-3)\text{ cm}$.

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• Question 3Oct/Nov 2024, paper 22Structured10 marksHas a diagram

  The diagram shows a tank. The tank is a cuboid with length $1.2\text{ m}$, width $0.6\text{ m}$ and height $h\text{ m}$. The volume of the tank is $1.8{\text{ m}}^3$.

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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 20May/June 2026, paper 22Structured3 marks

  The area of a rectangle is $69.5{\text{ m}}^2$, correct to the nearest $0.5{\text{ m}}^2$. The width of the rectangle is $3.8\text{ m}$, correct to the nearest $0.1\text{ m}$. Calculate the upper bound of the length of the rectangle.

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• Question 18Oct/Nov 2025, paper 12Structured5 marksHas a diagram

  The diagram shows a solid cylinder and a solid hemisphere. The radius of the cylinder is equal to the radius of the hemisphere. The volume of the cylinder is equal to the volume of the hemisphere.

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• Question 9Oct/Nov 2024, paper 22Structured10 marksHas a diagram

  $A$, $B$, $C$ and $D$ are points on a circle, centre $O$. $AOD$ and $OCE$ are straight lines. $DE$ is a tangent to the circle at $D$.

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• Question 8Oct/Nov 2023, paper 22Structured9 marksHas a diagram

  The diagram shows a small rectangle inside a large rectangle. The height of the large rectangle is $x\text{ cm}$. The length of the large rectangle is 4 times its height.

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• Question 22May/June 2026, paper 22Structured8 marksHas a diagram

  The diagram shows a triangular garden $ABD$. A path from $A$ meets $BD$ at point $C$. $CD=8\text{ m}$, angle $ADC={18}^{\circ }$, angle $ACB={34}^{\circ }$ and angle $ABC={90}^{\circ }$.

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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 2May/June 2024, paper 11Structured2 marks

  At the start of the day the mass of a bird is $4.628\text{ kg}$. Later in the day the mass of this bird is $4.693\text{ kg}$. Calculate the increase in the mass of the bird.

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• Question 10Oct/Nov 2023, paper 22Structured12 marksHas a diagram

  [Volume of a cone $=\frac{1}{3}\pi r^{2}h$] [Curved surface area of a cone $=\pi rl$] A solid is formed from a large cone with a small cone removed from the centre. The small cone is mathematically similar to the large cone.

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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 3Oct/Nov 2025, paper 22Structured2 marks

  Idris has 5 kg of rice. He cooks rice for 12 people. He uses 75 g of rice for each person.

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• Question 21May/June 2024, paper 11Structured4 marksHas a diagram

  Prism $A$ and prism $B$ are mathematically similar. In the diagram, the cross-sections of the prisms are shaded. The volume of prism $A$ is $5000{\text{ cm}}^3$.

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• Question 24May/June 2026, paper 22Structured8 marksHas a diagram

  The diagram shows a solid cuboid. All the lengths are in centimetres. The volume of the cuboid is $720{\text{ cm}}^3$.

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• Question 23Oct/Nov 2025, paper 22Structured5 marksHas a diagram

  The diagram shows a shaded area in a large circle, centre $O$. The radius of the large circle is $10\text{ cm}$. $OAB$ is a sector of a small circle, centre $O$.

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• Question 4May/June 2024, paper 12Structured2 marks

  Convert 4 kilograms to grams.

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