Set 4 — 2026 past papers

1. 4.01: Perpendicular bisector and reflection0606/22/F/M/26 — Question 2 · 6 marks
2. 4.02: Perpendicular bisector and distance ratio0606/12/M/J/26 — Question 2 · 7 marks
3. 4.03: Linearising a power relationship0606/23/M/J/26 — Question 4 · 6 marks

Set 3 — 2021–2025 past papers

1. 3.79: Simultaneous equations (tagged SLG paper)0606/11/O/N/25 — Question 8 · 5 marks
2. 3.87: Exponential model from a straight-line log graph0606/21/O/N/25 — Question 6 · 4 marks
3. 3.83: Line meets curve; area of triangle $POQ$0606/22/O/N/25 — Question 1 · 9 marks
4. 3.91: Linear law: $\mathrm{e}^{y}$ against $x^{3}$0606/22/O/N/25 — Question 4 · 6 marks
5. 3.84: Linear law: $\ln y$ against $\ln x$ for $y=Ax^{b}$0606/23/O/N/25 — Question 9 · 6 marks
6. 3.43: Polynomial factors then exponential equation0606/12/M/J/25 — Question 5 · 10 marks
7. 3.85: Exponential model from a straight-line graph0606/12/M/J/25 — Question 6 · 6 marks
8. 3.46: Permutations of members (tagged SLG paper)0606/21/M/J/25 — Question 3 · 5 marks
9. 3.48: Linear law: $y$ against $x^{3}$0606/23/M/J/25 — Question 3 · 4 marks
10. 3.71: Cubic polynomial with derivative and factor conditions0606/11/O/N/24 — Question 6 · 6 marks
11. 3.72: Linear law: $e^{5y}$ against $x^{3}$0606/11/O/N/24 — Question 7 · 8 marks
12. 3.73: Tangent meets axes; mid-point of $XY$0606/12/O/N/24 — Question 8 · 8 marks
13. 3.74: Linear law: $\ln y$ against $x^{2}$ for $y=Ab^{x^{2}}$0606/13/O/N/24 — Question 6 · 9 marks
14. 3.75: Differentiate $y=x^{3}\ln x$; definite integral0606/13/O/N/24 — Question 7 · 6 marks
15. 3.76: Line meets curve; perpendicular bisector0606/13/O/N/24 — Question 8 · 12 marks
16. 3.77: Normal to $y=x\cos x$; area of triangle $POQ$0606/21/O/N/24 — Question 7 · 7 marks
17. 3.37: Line meets curve; point on perpendicular bisector0606/12/M/J/24 — Question 7 · 11 marks
18. 3.38: Exact integral $\int_0^2 e^{x^{2}/2}\,\mathrm{d}x$ form0606/13/M/J/24 — Question 4 · 5 marks
19. 3.39: Linear law: $e^{2y}$ against $x^{3}$0606/13/M/J/24 — Question 5 · 6 marks
20. 3.40: Linear law: $\ln y$ against $x$ for $y=Ae^{kx}$0606/22/M/J/24 — Question 8 · 9 marks
21. 3.41: Area with curve $y=32x-4x^{2}-48$ and chord0606/22/M/J/24 — Question 9 · 9 marks
22. 3.42: Perpendicular bisector; area of triangle $OCD$0606/23/M/J/24 — Question 1 · 5 marks
23. 3.89: Logarithmic straightening of $y = Ab^x$0606/22/F/M/24 — Question 8 · 10 marks
24. 3.59: Linear law: $\ln y$ against $\ln x$ for $y=Ax^{b}$0606/11/O/N/23 — Question 4 · 9 marks
25. 3.60: Trigonometric function $g$ (adjacent)0606/12/O/N/23 — Question 2 · 5 marks
26. 3.61: Linear law: $\ln(y+2)$ against $x^{2}$0606/12/O/N/23 — Question 3 · 5 marks
27. 3.64: Value of $a$ for a tangent line to a curve0606/21/O/N/23 — Question 6 · 6 marks
28. 3.66: Intersection of two lines; distance from origin0606/22/O/N/23 — Question 1 · 7 marks
29. 3.67: Exact integral $\int_{2}^{3}\dfrac{(x + 2)^{2}}{x}\,\mathrm{d}x$0606/22/O/N/23 — Question 6 · 6 marks
30. 3.69: Cylinder surface area minimum0606/23/O/N/23 — Question 5 · 8 marks
31. 3.27: Point on perpendicular bisector; reflection0606/11/M/J/23 — Question 3 · 7 marks
32. 3.29: Line and curve; point on perpendicular bisector0606/13/M/J/23 — Question 4 · 8 marks
33. 3.30: Linear law: $\ln y$ against $\ln x$ for $y=Ax^{b}$0606/13/M/J/23 — Question 7 · 10 marks
34. 3.33: Linear law: $\lg y$ against $x$0606/21/M/J/23 — Question 1 · 4 marks
35. 3.34: Linear law: $\lg P$ against $T$ for $P=Ab^{T}$0606/22/M/J/23 — Question 5 · 9 marks
36. 3.5: Exact $k$ for a line tangent to a curve0606/12/F/M/23 — Question 1 · 4 marks
37. 3.6: Linear law: $\ln y$ against $x^{2}$ for $y=Ab^{x^{2}}$0606/12/F/M/23 — Question 5 · 11 marks
38. 3.7: Area of shaded region $ABC$0606/12/F/M/23 — Question 8 · 11 marks
39. 3.54: Sine graph sketch (adjacent on paper)0606/11/O/N/22 — Question 2 · 5 marks
40. 3.55: Linear law: $y^{3}$ against $\ln x$0606/11/O/N/22 — Question 3 · 4 marks
41. 3.57: Differentiate $y=(3x^{2}-2)^{2/3}/(x-1)$0606/13/O/N/22 — Question 12 · 7 marks
42. 3.58: Perpendicular bisector of $PQ$; points $R,S$0606/13/O/N/22 — Question 13 · 7 marks
43. 3.16: Express a surd expression in the form $a+b\sqrt{c}$0606/11/M/J/22 — Question 1 · 3 marks
44. 3.17: Particle with $s=\sqrt{t+\tfrac{1}{3}}-\tfrac{1}{2}$0606/11/M/J/22 — Question 2 · 5 marks
45. 3.18: Trigonometric relation $y$ in terms of $x$0606/12/M/J/22 — Question 2 · 4 marks
46. 3.19: Normal to $\ln$ curve; gradient of $BC$0606/12/M/J/22 — Question 9 · 9 marks
47. 3.90: Straight-line log graph for lg(2y+1)0606/12/M/J/22 — Question 3 · 7 marks
48. 3.20: Exponential equation and simultaneous equations0606/13/M/J/22 — Question 3 · 8 marks
49. 3.21: Linear law: $e^{4y}$ against $x$0606/13/M/J/22 — Question 4 · 6 marks
50. 3.23: Logarithm equation (adjacent) then linear law0606/21/M/J/22 — Question 2 · 6 marks
51. 3.24: Linear law: $y^{3}$ against $x^{2}$0606/21/M/J/22 — Question 3 · 4 marks
52. 3.25: Find $k$ in $y=kx^{2}$ with surd data0606/23/M/J/22 — Question 2 · 4 marks
53. 3.26: Mid-point and perpendicular through $C$0606/23/M/J/22 — Question 3 · 5 marks
54. 3.2: Values of $k$ so a line does not meet a curve0606/12/F/M/22 — Question 1 · 5 marks
55. 3.3: Line parallel to $L$ through mid-point of $AB$0606/22/F/M/22 — Question 1 · 3 marks
56. 3.4: Shaded area with $y=6+e^{4x-5}$ and $x=2$0606/22/F/M/22 — Question 11 · 7 marks
57. 3.49: Area between chord and $\ln$ curve; $v$–$t$ graph0606/12/O/N/21 — Question 10 · 17 marks
58. 3.50: Curves meet; perpendicular bisector of $AB$0606/13/O/N/21 — Question 8 · 12 marks
59. 3.51: Linear law: $e^{2y}$ against $x^{2}$0606/13/O/N/21 — Question 9 · 10 marks
60. 3.52: Differential equations from $\dfrac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}}$0606/22/O/N/21 — Question 7 · 6 marks
61. 3.53: Linear law: $y$ against $\log(x+\tfrac{1}{2})$0606/22/O/N/21 — Question 8 · 8 marks
62. 3.86: Straight-line graph for $y=Ax^{b}$0606/12/M/J/21 — Question 8 · 9 marks
63. 3.11: Binomial expansion (adjacent on paper)0606/13/M/J/21 — Question 4 · 6 marks
64. 3.12: Linear law: $e^{y}$ against $x^{2}$0606/13/M/J/21 — Question 5 · 5 marks
65. 3.13: Intersection with $x+y=\pm 2$; perpendicular bisector0606/13/M/J/21 — Question 11 · 12 marks
66. 3.14: Linear law: $\ln y$ against $\ln x$0606/21/M/J/21 — Question 2 · 4 marks
67. 3.88: Perpendicular bisector of OA0606/21/M/J/21 — Question 5 · 8 marks
68. 3.1: Perpendicular bisector of $AB$; point $D$0606/12/F/M/21 — Question 3 · 6 marks