Compound shapes and parts of shapes: past paper questions

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• Question 29Oct/Nov 2025, paper 23Structured5 marksHas a diagram

  In this question all measurements are in centimetres. Solid $A$ is made from a cylinder and a hemisphere, both of radius $2R$. The cylinder has height $5R$.

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• Question 7May/June 2024, paper 21Structured7 marksHas a diagram

  The diagram shows a shape made from a triangle $JKL$ and a semicircle with diameter $JL$. $JKL$ is an isosceles right-angled triangle with $JK=JL=12.8\text{ cm}$. Calculate the area of this shape.

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• Question 22Oct/Nov 2023, paper 21Structured4 marksHas a diagram

  $ABCD$ is a rhombus with side length $13.6\text{ cm}$. Angle $ABC={41}^{\circ }$. $BAC$ is a sector of a circle with centre $B$.

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• Question 14Oct/Nov 2025, paper 41Structured10 marks

  A cube contains a solid metal sphere. The sphere touches all the faces of the cube. The side length of the cube is $8\text{ cm}$.

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• Question 9May/June 2024, paper 42Structured10 marksHas a diagram

  $OAB$ is a sector of a circle, centre $O$, radius 17 cm. $OCD$ is a sector of a circle, centre $O$, radius 10 cm. $OCA$ and $ODB$ are straight lines and angle $AOB={60}^{\circ }$.

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• Question 11May/June 2023, paper 22Structured3 marks

  The diagram shows a shape, $ABCD$, formed by the sectors of two circles with the same centre $O$. Both sector angles are ${140}^{\circ }$, $OC=3.2\mathrm{c}\mathrm{m}$ and $CB=2.6\mathrm{c}\mathrm{m}$. The area of the shape is $k\pi {\mathrm{c}\mathrm{m}}^2$.

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• Question 16May/June 2025, paper 22Structured4 marksHas a diagram

  The diagram shows a solid made by joining a hemisphere to a cylinder. The radius of both the hemisphere and the cylinder is $6\text{ cm}$. The height of the cylinder is $5\text{ cm}$.

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• Question 9May/June 2023, paper 43Structured10 marksHas a diagram

  The diagram shows a shape made from a square $ABCD$ and two equal sectors of a circle. The square has side $11\text{ cm}$. $MAB$ and $DCN$ are straight lines.

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• Question 21May/June 2025, paper 43Structured4 marks

  The diagram shows an equilateral triangle $ABC$ with all sides of length $12\text{ cm}$. $ANP$ is a sector of a circle, centre $A$. $N$ lies on $AC$ such that $AN:NC=2:1$.

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