IGCSE Mathematics 0580, topic E6.6

Pythagoras’ theorem and trigonometry: past paper questions

9 Cambridge IGCSE Mathematics 0580 questions on Pythagoras’ theorem and trigonometry (E6.6) from 9 papers, 2025 to 2026. Open the paper or try a question free.

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Questions: 9
Papers: 9
Years: 2025 to 2026
Total marks: 55
Average per question: 6.1 marks
Largest question: 9 marks

By type: Structured 9

How hard the questions are

Recall0
Apply9
Analyse0
Not banded0

Derived from the command word Cambridge prints in each question, banded by a fixed table beside the syllabus's own definitions. A question printing no command word is unbanded: unknown, not middling.

Command words

calculateApply8 questions
work out from given facts, figures or information
findApply1 question
show thatApply1 question
write downRecall1 question
give an answer without significant working

Where the questions come from

By year

20263
20256

By session

May/June6
Oct/Nov3

By paper

Paper 22
Paper 47

Questions on this topic

Showing 9 of 9, spread across the years. Open one to write your answer and have it marked.

Question 21May/June 2026, paper 21Structured9 marksHas a diagram
The diagram shows a solid cuboid $A B C D E F G H$ . $B F = 2 cm$ , $B C = 6 cm$ and $C D = 9 cm$ . Calculate the volume of the cuboid.
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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 $10 cm$ . Show that this rod does not fit completely inside the box.
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Question 16May/June 2026, paper 42Structured9 marksHas a diagram
$A B C D E$ is a square-based pyramid. $E C$ and $B D$ intersect at $F$ . $A F$ is perpendicular to the base $B C D E$ .
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Question 27Oct/Nov 2025, paper 41Structured4 marksHas a diagram
The diagram shows a prism of length $15 cm$ . The cross-section of the prism is a trapezium. Angle $D A B = 90^{\circ}$ and angle $A D C = 90^{\circ}$ .
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Question 17May/June 2026, paper 43Structured3 marks
The diagram shows a cuboid, $A B C D E F G H$ . $A B = 18 cm$ , $B C = 14 cm$ and $A E = 16 cm$ . Calculate the length of the diagonal $A G$ .
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Question 24Oct/Nov 2025, paper 43Structured6 marksHas a diagram
The diagram shows a cuboid $A B C D E F G H$ . $A E = 6.4 cm$ , $E H = 5.1 cm$ and $A G = 13 cm$ . Calculate $E F$ .
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Question 20May/June 2025, paper 41Structured9 marksHas a diagram
The diagram shows a pyramid $O A B C D$ . The pyramid has a square base, $A B C D$ , with sides $10.5 cm$ . The vertex $O$ is vertically above the centre of the base, $M$ .
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Question 27May/June 2025, paper 42Structured4 marksHas a diagram
The diagram shows a cube. Calculate the angle between the diagonal $A P$ and the base $A B C D$ .
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Question 18May/June 2025, paper 43Structured8 marksHas a diagram
The diagram shows a solid cuboid with sides of length $4.5 cm$ , $8 cm$ and $13.2 cm$ . Calculate the volume of the cuboid.
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