Pythagoras’ theorem: past paper questions

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• Question 13May/June 2026, paper 23Structured3 marksHas a diagram

  $A$, $B$ and $C$ are points on a circle with centre $O$. $AOC$ is a straight line and $M$ is the midpoint of $AB$. $AB=6\text{ cm}$ and $OM=4\text{ cm}$.

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• Question 19Oct/Nov 2025, paper 22Structured3 marksHas a diagram

  The diagram shows a box in the shape of a cuboid. Mala has a straight rod of length $10\text{ cm}$. Show that this rod does not fit completely inside the box.

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• Question 20Oct/Nov 2024, paper 21Structured5 marksHas a diagram

  The diagram shows two right-angled triangles $PQS$ and $RQT$. $PQR$ and $QTS$ are straight lines. Calculate angle $QTR$.

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

  The diagram shows a cuboid $ABCDEFGH$. $AB=15.1\text{ cm}$, $BC=4.5\text{ cm}$ and $CG=9.2\text{ cm}$. Calculate the angle that the diagonal $BH$ makes with the face $ADHE$.

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• Question 19May/June 2026, paper 23Structured4 marks

  Find the exact value of $x$.

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• Question 10Oct/Nov 2025, paper 23Structured4 marksHas a diagram

  The diagram shows a right-angled triangle $ABC$. Work out the exact length of $AC$.

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• Question 9Oct/Nov 2024, paper 22Structured3 marks

  Points $A$, $B$, $C$ and $D$ lie on a circle. $ABCD$ is a square with area $72{\text{ cm}}^2$. Calculate the area of the circle.

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• Question 21Oct/Nov 2023, paper 23Structured6 marks

  The diagram shows a cuboid $ABCDEFGH$. $AB=14\text{ cm}$, $BC=5\text{ cm}$ and $CG=8\text{ cm}$. $M$ is the midpoint of $HG$.

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• Question 11May/June 2026, paper 42Structured2 marks

  Calculate $XY$.

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• Question 18Oct/Nov 2025, paper 43Structured6 marksHas a diagram

  Calculate the value of $x$.

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• Question 16Oct/Nov 2024, paper 23Structured3 marks

  Calculate the shortest distance from $C$ to $AB$.

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• Question 6Oct/Nov 2023, paper 42Structured7 marks

  The diagram shows a right-angled triangle. Find the value of $w$.

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• Question 7May/June 2026, paper 43Structured5 marks

  The point $A$ is on the top of a vertical building. The horizontal distance from the base of the building to $B$ is $22\text{ m}$. $AB=25\text{ m}$ and the height of the building is $h\text{ m}$.

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• Question 13May/June 2025, paper 21Structured8 marksHas a diagram

  The diagram shows solid $A$ and solid $B$. Solid $A$ is made from a hemisphere and a cone each with radius $6\text{ cm}$. The cone has sloping edge $10\text{ cm}$.

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• Question 22Oct/Nov 2024, paper 23Structured4 marksHas a diagram

  The diagram shows a cuboid with a diagonal $PB$. Calculate the angle between the diagonal $PB$ and the base $ABCD$.

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• Question 10May/June 2023, paper 42Structured8 marksHas a diagram

  $ABCDEFGH$ is a cuboid with a square base of side $x\text{ cm}$. $CG=20\text{ cm}$ and $AG=28\text{ cm}$. Calculate the value of $x$.

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• Question 17May/June 2026, paper 43Structured3 marks

  The diagram shows a cuboid, $ABCDEFGH$. $AB=18\text{ cm}$, $BC=14\text{ cm}$ and $AE=16\text{ cm}$. Calculate the length of the diagonal $AG$.

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• Question 23May/June 2025, paper 23Structured6 marksHas a diagram

  Write down the value of $\cos {90}^{\circ }$.

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• Question 9Oct/Nov 2024, paper 41Structured12 marksHas a diagram

  $ABCDEFGH$ is a solid cuboid. $AB=10\text{ cm}$, $BC=8\text{ cm}$ and $CG=17\text{ cm}$. Work out the volume of the cuboid.

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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 21May/June 2024, paper 21Structured4 marksHas a diagram

  The diagram shows a cuboid. $HD=4\text{ cm}$, $EH=6.5\text{ cm}$ and $EF=9.1\text{ cm}$. Calculate the angle between $CE$ and the base $CDHG$.

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• Question 12May/June 2024, paper 22Structured2 marksHas a diagram

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

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• Question 9May/June 2024, paper 23Structured2 marksHas a diagram

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

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• Question 24May/June 2024, paper 23Structured4 marksHas a diagram

  The diagram shows a triangular prism with cross-section triangle $BCV$. Angle $BCV={90}^{\circ }$, $BC=5\text{ cm}$, $CV=4\text{ cm}$ and $AB=15\text{ cm}$. Calculate the angle between $AV$ and the base $ABCD$.

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• Question 6May/June 2024, paper 43Structured15 marksHas a diagram

  The diagram shows a ladder, $GH$, on horizontal ground, leaning against a vertical wall, $HF$. $GF=1.5\text{ m}$ and $HF=4\text{ m}$. Calculate the length of the ladder, $GH$.

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