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Scalar product past paper questions

Pure Maths 3 9709 · Vectors. Scalar product to find angles between lines and the foot of a perpendicular from a point to a line.

In Cambridge A Level Pure Maths 3 9709, Scalar product came up in 38 of the 42 papers on Paperstreak, for about 5 marks a paper when it does. It last came up in October/November 2025.

Often set with Intersecting, parallel and skew lines, Vector operations and magnitude, Equation of a line.

38 questions, newest first

1. 9709/31/O/N/25 Question 11 part (c) · 4 marks
2. 9709/32/O/N/25 Question 11 parts (b) (c) · 7 marks
3. 9709/33/O/N/25 Question 9 part (b) · 3 marks
4. 9709/31/M/J/25 Question 8 part (c) · 3 marks
5. 9709/32/M/J/25 Question 9 parts (b) (c) · 7 marks
6. 9709/33/M/J/25 Question 9 parts (b) (c) · 6 marks
7. 9709/32/F/M/25 Question 8 part (b) · 3 marks
8. 9709/31/O/N/24 Question 9 part (c) · 5 marks
9. 9709/32/O/N/24 Question 9 part (c) · 4 marks
10. 9709/33/O/N/24 Question 6 part (b) · 3 marks
11. 9709/31/M/J/24 Question 9 part (a) · 1 mark
12. 9709/33/M/J/24 Question 10 part (a) · 6 marks
13. 9709/32/F/M/24 Question 9 part (b) · 4 marks
14. 9709/31/O/N/23 Question 11 parts (b) (c) · 9 marks
15. 9709/32/O/N/23 Question 10 · 9 marks
16. 9709/31/M/J/23 Question 6 parts (b) (c) · 7 marks
17. 9709/32/M/J/23 Question 11 part (b) · 4 marks
18. 9709/33/M/J/23 Question 9 · 10 marks
19. 9709/32/F/M/23 Question 10 part (a) · 3 marks
20. 9709/31/O/N/22 Question 11 parts (b) (c) · 7 marks
21. 9709/32/O/N/22 Question 6 · 8 marks
22. 9709/31/M/J/22 Question 9 part (c) · 4 marks
23. 9709/32/M/J/22 Question 9 part (b) · 4 marks
24. 9709/33/M/J/22 Question 9 · 9 marks
25. 9709/32/F/M/22 Question 10 part (b) · 3 marks
26. 9709/31/O/N/21 Question 9 parts (a) (c) · 6 marks
27. 9709/33/O/N/21 Question 8 part (b) · 4 marks
28. 9709/31/M/J/21 Question 8 part (a) · 4 marks
29. 9709/32/M/J/21 Question 11 part (a) · 4 marks
30. 9709/33/M/J/21 Question 9 part (c) · 5 marks
31. 9709/32/F/M/21 Question 7 part (b) · 3 marks
32. 9709/31/O/N/20 Question 11 part (b) · 6 marks
33. 9709/32/O/N/20 Question 8 part (b) · 3 marks
34. 9709/33/O/N/20 Question 11 part (b) · 6 marks
35. 9709/31/M/J/20 Question 9 parts (a) (c) · 7 marks
36. 9709/32/M/J/20 Question 10 part (c) · 3 marks
37. 9709/33/M/J/20 Question 8 part (b) · 3 marks
38. 9709/32/F/M/20 Question 8 part (c) · 4 marks

More in Vectors: Vector operations and magnitude, Equation of a line, Intersecting, parallel and skew lines.

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