Similarity: past paper questions

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

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

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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 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 21May/June 2025, paper 22Structured11 marksHas a diagram

  The diagram shows a solid formed by joining a cone to a hemisphere. The diameter of the cone is $14\text{ cm}$ and the diameter of the hemisphere is $14\text{ cm}$. The total height of the solid is $24\text{ cm}$.

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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 19May/June 2023, paper 11Structured3 marksHas a diagram

  $A$ and $B$ are points on the circumference of a circle, centre $O$. $TA$ and $TB$ are tangents to the circle. Show that triangles $OBT$ and $OAT$ are congruent.

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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 21May/June 2023, paper 11Structured3 marksHas a diagram

  The diagram shows two rectangles. Rectangle $ABCD$ is mathematically similar to rectangle $PQRS$. $AB=12\text{ cm}$, $BC=9\text{ cm}$ and $PQ=8\text{ cm}$.

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• Question 15May/June 2024, paper 12Structured2 marksHas a diagram

  Triangle $ABC$ is mathematically similar to triangle $CBD$. $AB=5\mathrm{c}\mathrm{m}$, $AC=7\mathrm{c}\mathrm{m}$ and $BC=8\mathrm{c}\mathrm{m}$. Calculate $BD$.

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• Question 8May/June 2023, paper 22Structured11 marksHas a diagram

  The length of the rectangle $R$ is twice its width. Rectangle $R$ has a perimeter of $20.4\text{ cm}$. Find the length and width of the rectangle $R$.

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• Question 3May/June 2024, paper 21Structured5 marksHas a diagram

  Triangle $PQR$ is isosceles with $PQ=QR$. The exterior angle of the triangle at $R$ is ${142}^{\circ }$. Calculate angle $PQR$.

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