Pythagoras’ theorem: past paper questions

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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 23Oct/Nov 2025, paper 12Structured4 marksHas a diagram

  The diagram shows a square-based pyramid. $X$ is the centre of the square base. Vertex $E$ is vertically above $X$ and $EX=7\text{ cm}$.

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• Question 8Oct/Nov 2024, paper 21Structured8 marksHas a diagram

  $ABCD$ is a field. $AB=320\text{ m}$, $BC=250\text{ m}$, $CD=132\text{ m}$ and $AD=365\text{ m}$. Angle $BCD={90}^{\circ }$.

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• Question 25Oct/Nov 2025, paper 21Structured6 marks

  The diagram shows a cuboid.

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• Question 10May/June 2024, paper 22Structured7 marksHas a diagram

  The diagram shows a pentagon. Calculate the interior angle $B$.

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