Similarity: past paper questions

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• Question 23May/June 2026, paper 21Structured3 marksHas a diagram

  The two solids are mathematically similar. The volume of the larger solid is $64{\text{ cm}}^3$ and the volume of the smaller solid is $27{\text{ cm}}^3$. The height of the larger solid is $10\text{ cm}$ and the height of the smaller solid is $h\text{ cm}$.

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• Question 14Oct/Nov 2025, paper 21Structured9 marksHas a diagram

  $A,B,C,D$ and $E$ lie on the circle. $AC$ and $BD$ intersect at $X$. Angle $ACD={55}^{\circ }$ and angle $CXD={88}^{\circ }$.

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• Question 14Oct/Nov 2024, paper 21Structured4 marks

  Two solid steel statues are mathematically similar. The smaller statue has height $12\text{ cm}$ and the larger statue has height $15\text{ cm}$. The larger statue has a mass $2.5\text{ kg}$.

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• Question 11Oct/Nov 2023, paper 22Structured4 marksHas a diagram

  The two shapes are mathematically similar. Find the value of $h$.

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• Question 20May/June 2026, paper 22Structured3 marks

  Two bottles are mathematically similar. The volume of the larger bottle is $216{\text{ cm}}^3$ and the volume of the smaller bottle is $27{\text{ cm}}^3$. The height of the larger bottle is $10\text{ cm}$ and the height of the smaller bottle is $h\text{ cm}$.

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• Question 11Oct/Nov 2025, paper 22Structured7 marksHas a diagram

  In the diagram, $S$ lies on $PQ$ and $T$ lies on $PR$. $ST$ is parallel to $QR$. Explain why triangle $PQR$ is mathematically similar to triangle $PST$.

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• Question 23Oct/Nov 2024, paper 22Structured3 marksHas a diagram

  The small box is mathematically similar to the large box. The volume of the large box is $72.8\mathrm{\%}$ greater than the volume of the small box. The small box has length $3.5\text{ cm}$ and the large box has length $x\text{ cm}$.

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• Question 8Oct/Nov 2023, paper 41Structured14 marksHas a diagram

  The diagram shows a solid formed by joining two hemispheres and a cylinder. The radius of the large hemisphere is $5.4\text{ cm}$. The radius of the small hemisphere and the radius of the cylinder are both $3.6\text{ cm}$.

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• Question 20May/June 2026, paper 23Structured3 marksHas a diagram

  The two cylinders, $A$ and $B$, are mathematically similar. The surface area of $A$ is $80{\text{ cm}}^2$ and the surface area of $B$ is $180{\text{ cm}}^2$. The height of $A$ is $h\text{ cm}$ and the height of $B$ is $12\text{ cm}$.

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• Question 22Oct/Nov 2025, paper 43Structured5 marksHas a diagram

  The diagram shows two mathematically similar triangles. Find the value of $x$.

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• Question 18Oct/Nov 2024, paper 23Structured3 marks

  Two mathematically similar solids have volumes $81{\text{ cm}}^3$ and $24{\text{ cm}}^3$. The height of the smaller solid is $4.8\text{ cm}$. Calculate the height of the larger solid.

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• Question 9May/June 2023, paper 21Structured2 marks

  Triangle $ABC$ is similar to triangle $DEF$. Calculate the value of $h$.

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• Question 8May/June 2026, paper 43Structured5 marksHas a diagram

  $AB$ and $CD$ are parallel lines. $AD$ and $BC$ are straight lines that intersect at $X$. Angle $ABX=y^{\circ }$.

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• Question 17May/June 2025, paper 23Structured3 marksHas a diagram

  Solid $A$ is mathematically similar to solid $B$. The height of solid $A$ is $7\text{ cm}$ and its surface area is $60{\text{ cm}}^2$. The surface area of solid $B$ is $540{\text{ cm}}^2$.

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• Question 20May/June 2024, paper 22Structured3 marks

  Two parcels are mathematically similar. The larger parcel has volume $80{\text{ cm}}^3$ and height $5.2\text{ cm}$. The smaller parcel has volume $33.75{\text{ cm}}^3$.

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• Question 12May/June 2023, paper 21Structured4 marksHas a diagram

  $AO$, $OB$ and $OC$ are all radii of the circle. $AB=BC$. Therefore triangle $AOB$ is congruent to triangle $COB$.

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• Question 13May/June 2025, paper 42Structured4 marksHas a diagram

  Triangle $ABC$ and triangle $PQR$ are mathematically similar. Calculate the length of $PR$.

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• Question 2May/June 2024, paper 41Structured8 marks

  On the grid, draw the image of triangle $T$ after a reflection in the $x$-axis

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• Question 3May/June 2023, paper 42Structured13 marks

  The diagram shows a right-angled triangle $ABC$. The area of the triangle is $60{\text{ cm}}^2$. Show that $2x^2+11x-105=0$.

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• Question 23May/June 2025, paper 43Structured4 marksHas a diagram

  The diagram shows a frustum made by removing a small cone from a large cone. The height of the small cone is $7.5\text{ cm}$. The height of the frustum is $4.5\text{ cm}$.

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• Question 8May/June 2024, paper 43Structured14 marksHas a diagram

  The diagram shows a solid made from a cylinder and a cone. The height of the cylinder is $16\text{ cm}$ and the height of the cone is $1.5\text{ cm}$. The radius of the cylinder and the base radius of the cone are each $0.35\text{ cm}$.

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• Question 3May/June 2023, paper 43Structured10 marks

  The scale drawing shows two sides, $AB$ and $BC$, of a field. The scale is 5 centimetres represents 200 metres. Measure angle $ABC$.

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