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Circle theorems I past paper questions

O Level Mathematics 4024 · Geometry. Calculate unknown angles and give explanations using the following geometrical properties of circles: angle in a semicircle = 90° angle between tangent and radius = 90° angle at the centre is twice the angle at the circumference angles in the same segment are equal opposite angles of a cyclic quadrilateral sum to 180° (supplementary) alternate segment theorem. Candidates are expected to use the geometrical properties listed in the syllabus when giving reasons for answers.

In Cambridge O Level Mathematics 4024, Circle theorems I came up in 23 of the 46 papers on Paperstreak, for about 4 marks a paper when it does. It last came up in October/November 2025.

Often set with Angles, Circles, arcs and sectors, Circle theorems II, Compound shapes and parts of shapes.

23 questions, newest first

  1. 4024/11/O/N/25 Question 16 · 6 marks
  2. 4024/12/O/N/25 Question 14 · 4 marks
  3. 4024/22/M/J/25 Question 14 · 3 marks
  4. 4024/22/O/N/24 Question 9 part (a) · 5 marks
  5. 4024/11/M/J/24 Question 16 parts (a) (b(i)) · 3 marks
  6. 4024/12/M/J/24 Question 17 · 4 marks
  7. 4024/11/O/N/23 Question 15 parts (b) (c) · 3 marks
  8. 4024/22/O/N/23 Question 2 part (b) · 4 marks
  9. 4024/21/M/J/23 Question 3 part (b) · 4 marks
  10. 4024/22/M/J/23 Question 3 part (b(i)) · 3 marks
  11. 4024/11/O/N/22 Question 14 · 5 marks
  12. 4024/22/O/N/22 Question 10 part (a(ii)) · 2 marks
  13. 4024/11/M/J/22 Question 19 · 4 marks
  14. 4024/12/M/J/22 Question 20 · 3 marks
  15. 4024/12/O/N/21 Question 19 · 2 marks
  16. 4024/21/O/N/21 Question 3 part (a(ii)) · 3 marks
  17. 4024/21/M/J/21 Question 8 part (a) · 4 marks
  18. 4024/22/M/J/21 Question 10 part (a) · 3 marks
  19. 4024/11/O/N/20 Question 17 part (a) · 1 mark
  20. 4024/12/O/N/20 Question 22 · 4 marks
  21. 4024/21/O/N/20 Question 7 part (a) · 3 marks
  22. 4024/21/M/J/20 Question 7 part (b(i)) · 3 marks
  23. 4024/22/M/J/20 Question 9 parts (b(i)) (b(ii)) (b(iii)) (b(iv)) · 5 marks

More in Geometry: Geometrical terms, Geometrical constructions, Scale drawings, Similarity, Symmetry, Angles, Circle theorems II.

Questions and mark schemes from Cambridge International past papers. Paperstreak isn't affiliated with Cambridge.