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Tangents and normals past paper questions

Mathematics 9709 · Differentiation. Gradient at a point; equations of tangents and normals to curves

In Cambridge A Level Mathematics 9709, Tangents and normals came up in 55 of the 69 papers on Paperstreak, for about 5 marks a paper when it does. It last came up in October/November 2025.

Often set with Area, Finding a curve from its gradient, Stationary points, Volume of revolution.

60 questions, newest first

1. 9709/11/O/N/25 Question 11 part (a) · 3 marks
2. 9709/12/O/N/25 Question 4 part (a) · 1 mark
3. 9709/13/O/N/25 Question 11 part (a) · 6 marks
4. 9709/11/M/J/25 Question 2 part (a) · 2 marks
5. 9709/12/M/J/25 Question 9 part (d) · 4 marks
6. 9709/13/M/J/25 Question 1 · 4 marks
7. 9709/12/F/M/25 Question 2 part (a) · 2 marks
8. 9709/11/O/N/24 Question 7 part (a) · 4 marks
9. 9709/11/O/N/24 Question 9 part (b) · 4 marks
10. 9709/12/O/N/24 Question 10 part (a) · 3 marks
11. 9709/13/O/N/24 Question 11 part (c) · 6 marks
12. 9709/11/M/J/24 Question 11 part (b) · 8 marks
13. 9709/13/M/J/24 Question 9 part (a) · 5 marks
14. 9709/12/F/M/24 Question 5 · 6 marks
15. 9709/11/O/N/23 Question 10 part (d) · 2 marks
16. 9709/12/O/N/23 Question 3 part (a) · 2 marks
17. 9709/13/O/N/23 Question 9 part (a) · 3 marks
18. 9709/11/M/J/23 Question 10 part (b) · 6 marks
19. 9709/12/M/J/23 Question 11 part (c) · 4 marks
20. 9709/13/M/J/23 Question 9 part (b) · 4 marks
21. 9709/13/M/J/23 Question 10 part (b) · 3 marks
22. 9709/12/F/M/23 Question 10 part (a) · 1 mark
23. 9709/11/O/N/22 Question 2 part (a) · 2 marks
24. 9709/11/O/N/22 Question 10 part (b) · 5 marks
25. 9709/13/O/N/22 Question 7 part (a) · 4 marks
26. 9709/12/M/J/22 Question 10 part (e) · 6 marks
27. 9709/13/M/J/22 Question 8 part (a) · 4 marks
28. 9709/13/M/J/22 Question 11 · 10 marks
29. 9709/11/O/N/21 Question 10 part (c) · 4 marks
30. 9709/12/O/N/21 Question 11 part (a) · 5 marks
31. 9709/13/O/N/21 Question 8 part (b) · 4 marks
32. 9709/11/M/J/21 Question 11 part (a) · 5 marks
33. 9709/13/M/J/21 Question 11 part (b) · 4 marks
34. 9709/12/F/M/21 Question 11 part (b) · 4 marks
35. 9709/11/O/N/20 Question 6 · 5 marks
36. 9709/11/M/J/20 Question 11 part (a) · 6 marks
37. 9709/12/M/J/20 Question 8 part (b) · 3 marks
38. 9709/11/O/N/19 Question 3 · 5 marks
39. 9709/12/O/N/19 Question 10 part (ii) · 4 marks
40. 9709/13/O/N/19 Question 11 part (i) · 3 marks
41. 9709/11/M/J/19 Question 11 part (i) · 5 marks
42. 9709/13/M/J/19 Question 10 part (i) · 5 marks
43. 9709/12/F/M/19 Question 9 part (ii) · 6 marks
44. 9709/12/F/M/19 Question 10 parts (ii) (iii) · 6 marks
45. 9709/11/O/N/18 Question 10 part (i) · 8 marks
46. 9709/13/O/N/18 Question 10 part (ii) · 5 marks
47. 9709/12/M/J/18 Question 11 part (i) · 6 marks
48. 9709/13/M/J/18 Question 8 part (i) · 6 marks
49. 9709/11/O/N/17 Question 1 · 4 marks
50. 9709/12/O/N/17 Question 10 part (i) · 4 marks
51. 9709/13/O/N/17 Question 11 part (ii) · 5 marks
52. 9709/11/M/J/17 Question 10 part (i) · 5 marks
53. 9709/12/M/J/17 Question 5 part (i) · 5 marks
54. 9709/13/M/J/17 Question 6 · 6 marks
55. 9709/12/F/M/17 Question 9 parts (i) (iii) · 7 marks
56. 9709/11/O/N/16 Question 11 part (i) · 5 marks
57. 9709/12/O/N/16 Question 7 part (iii) · 4 marks
58. 9709/13/O/N/16 Question 10 part (i) · 3 marks
59. 9709/13/M/J/16 Question 3 part (i) · 1 mark
60. 9709/12/F/M/16 Question 10 part (ii) · 5 marks

More in Differentiation: Differentiation techniques, Increasing and decreasing functions, Rates of change, Stationary points, Gradient as a limit.

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