Set 4 — 2026 past papers

1. 4.01: Arithmetic progression from equal sums0606/12/F/M/26 — Question 4 · 3 marks
2. 4.02: Geometric progressions0606/11/M/J/26 — Question 9 · 8 marks
3. 4.03: Arithmetic progression interval sum0606/12/M/J/26 — Question 4 · 5 marks
4. 4.04: Geometric progression from three terms0606/12/M/J/26 — Question 10 · 8 marks
5. 4.05: Arithmetic progression conditions0606/13/M/J/26 — Question 2 · 5 marks
6. 4.06: Arithmetic progression and least sum0606/21/M/J/26 — Question 3 · 8 marks
7. 4.07: Geometric progression differences0606/23/M/J/26 — Question 11 · 8 marks

Set 3 — 2021–2025 past papers

1. 3.60: AP sum relation and AP–GP common ratio0606/11/O/N/25 — Question 5 · 7 marks
2. 3.62: GP with $S_{2}=9$ and $S_{\infty}=25$0606/12/O/N/25 — Question 3 · 6 marks
3. 3.63: Log/exponential equations; AP and dual GPs0606/13/O/N/25 — Question 9 · 14 marks
4. 3.65: AP terms forming a geometric progression0606/22/O/N/25 — Question 8 · 7 marks
5. 3.85: Term independent of $x$ in a product of expansions0606/22/O/N/25 — Question 3 · 6 marks
6. 3.29: GP common ratio in terms of $k$0606/12/M/J/25 — Question 7 · 7 marks
7. 3.31: Logarithmic AP inequality and 25th term0606/22/M/J/25 — Question 7 · 9 marks
8. 3.33: AP linked to GP; trig GP infinity sum0606/23/M/J/25 — Question 9 · 12 marks
9. 3.9: Linked geometric and arithmetic progressions0606/12/F/M/25 — Question 8 · 7 marks
10. 3.55: Exponential derivative; GP and trig GP0606/11/O/N/24 — Question 9 · 11 marks
11. 3.56: Shaded area; tan AP and cos GP0606/12/O/N/24 — Question 9 · 19 marks
12. 3.57: Trapezium vectors; log AP and trig GP0606/13/O/N/24 — Question 9 · 17 marks
13. 3.58: Surd rationalisation; marathon GP; AP–GP link0606/23/O/N/24 — Question 9 · 12 marks
14. 3.22: Particle relative motion; trig AP and log GP0606/12/M/J/24 — Question 9 · 16 marks
15. 3.23: Trigonometric motion; AP product; exponential GP0606/13/M/J/24 — Question 9 · 15 marks
16. 3.25: AP partial sums and convergent GP0606/21/M/J/24 — Question 8 · 10 marks
17. 3.79: Binomial expansion of $\left(2 + \dfrac{x}{2}\right)^{n}$0606/22/M/J/24 — Question 11 · 8 marks
18. 3.69: Binomial independent term and surd identity0606/23/M/J/24 — Question 4 · 8 marks
19. 3.7: Logarithmic AP and GP with ratio one third0606/12/F/M/24 — Question 9 · 12 marks
20. 3.73: Binomial expansion beginning $b^{4} + 48b^{3}x$0606/22/F/M/24 — Question 10 · 10 marks
21. 3.51: Trig AP and cosec GP0606/11/O/N/23 — Question 9 · 12 marks
22. 3.83: Descending expansion of $\left(2x - \dfrac{1}{4x^{2}}\right)^{n}$0606/13/O/N/23 — Question 8 · 6 marks
23. 3.84: Product $(2 + ax)^{5}(1 + bx)$: find $a$ and $b$0606/21/O/N/23 — Question 4 · 7 marks
24. 3.52: Derivative of $x\mathrm{sin}\,2x$; AP of twelve terms0606/22/O/N/23 — Question 8 · 10 marks
25. 3.53: AP of twelve terms and GP sum inequality0606/22/O/N/23 — Question 9 · 10 marks
26. 3.54: Exponential calculus; AP and linked GP0606/23/O/N/23 — Question 9 · 17 marks
27. 3.18: Log AP, exponential GP term, trig GP convergence0606/11/M/J/23 — Question 9 · 11 marks
28. 3.19: Shaded area; log AP and GP conditions0606/12/M/J/23 — Question 9 · 13 marks
29. 3.66: Binomial expansion in descending powers0606/13/M/J/23 — Question 5 · 6 marks
30. 3.77: Binomial expansion: independent term and coefficient of $x^{6}$0606/21/M/J/23 — Question 10 · 7 marks
31. 3.78: Binomial expansions of $(1 + 7x)^{5}$ and $(2 - kx)^{8}$0606/22/M/J/23 — Question 6 · 9 marks
32. 3.21: AP terms forming a convergent GP0606/23/M/J/23 — Question 10 · 15 marks
33. 3.72: Coefficient of $x^{8}$ in a binomial product0606/12/F/M/23 — Question 3 · 5 marks
34. 3.5: Geometric progression terms and arithmetic sum0606/22/F/M/23 — Question 6 · 11 marks
35. 3.41: AP fourth and ninth terms0606/11/O/N/22 — Question 5 · 6 marks
36. 3.81: Product of binomial expansions: coefficients $a$ and $b$0606/11/O/N/22 — Question 6 · 7 marks
37. 3.43: Logarithmic AP sum0606/12/O/N/22 — Question 10 · 8 marks
38. 3.82: Descending binomial product: find $a$, $b$, $c$0606/12/O/N/22 — Question 12 · 9 marks
39. 3.45: GP fifteenth term and sum near infinity0606/13/O/N/22 — Question 5 · 7 marks
40. 3.47: GP with $S_3=17.5$ and $S_\infty=20$0606/21/O/N/22 — Question 7 · 6 marks
41. 3.48: Triangle with surds; GP terms0606/22/O/N/22 — Question 9 · 15 marks
42. 3.49: Exponential curve calculus; AP sums0606/23/O/N/22 — Question 9 · 14 marks
43. 3.70: Binomial expansion coefficients0606/23/O/N/22 — Question 6 · 6 marks
44. 3.15: Logarithmic AP and GP sum to infinity0606/11/M/J/22 — Question 7 · 9 marks
45. 3.67: Binomial expansion in descending powers0606/13/M/J/22 — Question 1 · 6 marks
46. 3.76: Binomial expansions and a term independent of $x$0606/21/M/J/22 — Question 5 · 7 marks
47. 3.16: Shaded cubic region; AP 12th term; GP equation0606/23/M/J/22 — Question 10 · 23 marks
48. 3.3: Trigonometric AP sum and convergent GP0606/12/F/M/22 — Question 9 · 12 marks
49. 3.68: Binomial expansion of $(1+3x)^7$ and independent term0606/22/F/M/22 — Question 6 · 6 marks
50. 3.34: Curve sketch; Jess AP and Kyle GP running0606/11/O/N/21 — Question 9 · 17 marks
51. 3.80: Binomial expansion $(2 + ax)^{n}$ with $64 + bx + cx^{2}$0606/11/O/N/21 — Question 7 · 7 marks
52. 3.35: Binomial expansion in powers of $x^{2}$0606/13/O/N/21 — Question 4 · 6 marks
53. 3.36: GP with $S_4=17S_2$0606/13/O/N/21 — Question 5 · 6 marks
54. 3.37: Normal to a curve; AP and GP with shared form0606/22/O/N/21 — Question 9 · 15 marks
55. 3.39: AP first term, common difference and $S_n$ identity0606/23/O/N/21 — Question 9 · 12 marks
56. 3.74: Product of binomial expansions: find $a$, $b$, $c$0606/11/M/J/21 — Question 4 · 8 marks
57. 3.11: AP sum inequality and geometric progression0606/12/M/J/21 — Question 9 · 10 marks
58. 3.12: AP terms forming a geometric progression0606/21/M/J/21 — Question 11 · 10 marks
59. 3.75: Binomial expansion of $(1 + e^{2x})^{4}$0606/22/M/J/21 — Question 1 · 2 marks
60. 3.13: Cone surface-area minimum; AP and GP0606/23/M/J/21 — Question 10 · 15 marks
61. 3.2: GP sum to infinity and AP of logarithms0606/12/F/M/21 — Question 6 · 11 marks
62. 3.71: Binomial expansion: coefficient and product of expansions0606/22/F/M/21 — Question 9 · 8 marks