Pythagoras’ theorem: past paper questions

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• Question 26May/June 2026, paper 31Structured2 marks

  The diagram shows a right-angled triangle. Calculate the value of $x$.

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• Question 24Oct/Nov 2025, paper 31Structured3 marks

  $ABC$ is a right-angled triangle. Calculate $BC$.

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• Question 21Oct/Nov 2023, paper 12Structured3 marksHas a diagram

  $ABC$ is a right-angled triangle. Calculate $AC$.

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• Question 23Oct/Nov 2025, paper 32Structured4 marksHas a diagram

  Calculate the perimeter of this trapezium.

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• Question 4Oct/Nov 2024, paper 32Structured13 marksHas a diagram

  Calculate the volume of a cylinder with radius $7.8\text{ cm}$ and height $15\text{ cm}$.

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• Question 10Oct/Nov 2023, paper 31Structured9 marks

  Triangle $PQR$ is mathematically similar to triangle $UVW$. Calculate $VW$.

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• Question 17May/June 2026, paper 32Structured7 marksHas a diagram

  The diagram shows a compound shape made from two rectangles. Work out the perimeter of the shape.

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• Question 16Oct/Nov 2025, paper 33Structured5 marks

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

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• Question 7Oct/Nov 2024, paper 33Structured12 marksHas a diagram

  Write down the mathematical name for this solid.

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• Question 9Oct/Nov 2023, paper 33Structured10 marksHas a diagram

  The diagram shows a semicircle with diameter $AB$. $O$ is the midpoint of $AB$ and $C$ is a point on the circumference. Calculate the area of triangle $ABC$.

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• Question 25May/June 2026, paper 33Structured5 marksHas a diagram

  The diagram shows a circle, centre $O$ and diameter $AC$. $B$ is a point on the circumference of the circle. Give the geometrical reason why angle $ABC={90}^{\circ }$.

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• Question 29Oct/Nov 2025, paper 33Structured4 marks

  The diagram shows two similar triangles, $A$ and $B$. Calculate the value of $x$.

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• Question 25May/June 2024, paper 11Structured7 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 22May/June 2023, paper 11Structured2 marksHas a diagram

  The diagram shows a right-angled triangle. Calculate the value of $y$.

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• Question 21May/June 2025, paper 31Structured3 marksHas a diagram

  The diagram shows a right-angled triangle $ABC$. Calculate $BC$.

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• Question 22May/June 2023, paper 12Structured6 marksHas a diagram

  The diagram shows a right-angled triangle $ABC$. Calculate $AB$.

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• Question 24May/June 2025, paper 32Structured5 marksHas a diagram

  The diagram shows two right-angled triangles. Calculate the value of $d$.

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• Question 25May/June 2024, paper 12Structured6 marksHas a diagram

  The diagram shows a flagpole, $BD$, held by two ropes, $AD$ and $CD$. $ABC$ is a straight line and angle $ABD={90}^{\circ }$. $AD=21.2\text{ m}$, $AB=16.5\text{ m}$ and angle $BCD={48}^{\circ }$.

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• Question 10May/June 2023, paper 31Structured7 marksHas a diagram

  The diagram shows a right-angled triangle, $ABC$, and a semicircle. The radius of the semicircle is $4.5\text{ cm}$. $AC=8.9\text{ cm}$ and $BC=13.2\text{ cm}$.

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• Question 23May/June 2025, paper 33Structured2 marks

  The diagram shows a right-angled triangle. Calculate the value of $h$.

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• Question 17May/June 2024, paper 13Structured2 marksHas a diagram

  The diagram shows a right-angled triangle. Calculate $AB$.

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• Question 7May/June 2023, paper 33Structured15 marksHas a diagram

  The diagram shows a triangle $ABC$ and a straight line $BCD$. Angle $ACB={108}^{\circ }$. Write down the mathematical name for this type of angle.

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