Set 4 — 2026 past papers

1. 4.01: Modulus equation and inequality0606/12/F/M/26 — Question 6 · 7 marks
2. 4.02: Cubic graph inequality0606/22/F/M/26 — Question 3 · 4 marks
3. 4.03: Modulus equation0606/11/M/J/26 — Question 1 · 3 marks
4. 4.04: Logarithmic, exponential and modulus equations0606/13/M/J/26 — Question 3 · 12 marks
5. 4.05: Cubic graph and inequality0606/21/M/J/26 — Question 1 · 5 marks
6. 4.06: Modulus graph and function0606/22/M/J/26 — Question 4 · 7 marks
7. 4.07: Modulus graph and inequality0606/23/M/J/26 — Question 1 · 5 marks
8. 4.08: Cubic graphs and roots0606/23/M/J/26 — Question 7 · 2 marks

Set 3 — 2021–2025 past papers

1. 3.92: Solve $|x^{2} - 5| = 6 - x$0606/11/O/N/25 — Question 6 · 5 marks
2. 3.93: Sketch $(x - 1)(5 - x)(2x - 5)$ and inequality0606/12/O/N/25 — Question 1 · 5 marks
3. 3.94: Solve $|x^{2} - 10| = 5 - 2x$0606/12/O/N/25 — Question 6 · 5 marks
4. 3.95: Area between $y = 12 - x^{2}$ and $y = x^{4} - 4x^{2} + 8$0606/13/O/N/25 — Question 8 · 7 marks
5. 3.96: Graphical inequality with $y = |x| + 3$0606/21/O/N/25 — Question 2 · 3 marks
6. 3.98: Reflection of a graph and inverse/composition of functions0606/23/O/N/25 — Question 2 · 8 marks
7. 3.101: Completing the square, sketch and inequality0606/23/O/N/25 — Question 3 · 9 marks
8. 3.57: Solve a rational inequality0606/11/M/J/25 — Question 2 · 4 marks
9. 3.58: Differentiate $\left(\dfrac{x^{2} - 1}{x^{2} + 1}\right)^{4}$0606/11/M/J/25 — Question 6 · 8 marks
10. 3.59: Cubic graph coefficients and $y \geqslant 2$0606/13/M/J/25 — Question 1 · 5 marks
11. 3.60: Values of $k$ for equal roots0606/13/M/J/25 — Question 2 · 4 marks
12. 3.61: Set of $k$ for distinct real roots0606/21/M/J/25 — Question 2 · 5 marks
13. 3.62: Solve a modulus inequality0606/22/M/J/25 — Question 1 · 4 marks
14. 3.63: Solve $(x + 2)(4 - x) \geqslant 0$0606/23/M/J/25 — Question 1 · 2 marks
15. 3.64: Differentiate and factorise0606/23/M/J/25 — Question 2 · 3 marks
16. 3.105: Square of a linear function: sketch and inequality0606/23/M/J/25 — Question 4 · 8 marks
17. 3.14: Sketch graphs and solve a linear–modulus inequality0606/12/F/M/25 — Question 1 · 7 marks
18. 3.15: Stationary points, sketch and number of roots0606/22/F/M/25 — Question 2 · 9 marks
19. 3.16: Solve an equation with reciprocal terms0606/22/F/M/25 — Question 3 · 4 marks
20. 3.86: Find $f$ from $f''$ and two conditions0606/11/O/N/24 — Question 8 · 8 marks
21. 3.103: Stationary points and sketch of a cubic factorisation0606/12/O/N/24 — Question 2 · 9 marks
22. 3.87: Exponential equation and integer $a,b$0606/21/O/N/24 — Question 3 · 10 marks
23. 3.88: Cubic with given roots0606/22/O/N/24 — Question 3 · 5 marks
24. 3.89: Graphical solution of $|2x - 8| > 4$0606/22/O/N/24 — Question 4 · 5 marks
25. 3.90: Simplify $(5 - \sqrt{3})(\sqrt{6} + \sqrt{2})^{-2}$ to $a + b\sqrt{3}$0606/22/O/N/24 — Question 6 · 5 marks
26. 3.91: Use a cubic graph to solve an inequality0606/23/O/N/24 — Question 1 · 3 marks
27. 3.45: Quartic from linear factors: sketch and inequality0606/11/M/J/24 — Question 1 · 5 marks
28. 3.46: Exact value of a definite integral0606/11/M/J/24 — Question 6 · 4 marks
29. 3.47: Selecting a mixed team0606/12/M/J/24 — Question 4 · 6 marks
30. 3.48: Solve a quadratic in $3^{x}$0606/13/M/J/24 — Question 2 · 4 marks
31. 3.49: Stationary points, sketch and values of $k$0606/13/M/J/24 — Question 3 · 9 marks
32. 3.50: Sketch $y = |4x - 6|$ and solve an equation0606/21/M/J/24 — Question 1 · 5 marks
33. 3.51: Completing the square and range0606/21/M/J/24 — Question 2 · 4 marks
34. 3.52: Show an equation has no real solutions0606/21/M/J/24 — Question 3 · 3 marks
35. 3.53: Distance between axis intercepts; curve intersections0606/21/M/J/24 — Question 4 · 10 marks
36. 3.54: Cubic factors: sketch, inequality, modulus graph0606/22/M/J/24 — Question 1 · 6 marks
37. 3.55: Values of $k$ for no real roots0606/23/M/J/24 — Question 2 · 4 marks
38. 3.56: Draw graphs and solve a modulus inequality0606/23/M/J/24 — Question 3 · 6 marks
39. 3.10: Modulus equation and quadratic inequality0606/22/F/M/24 — Question 1 · 7 marks
40. 3.11: Similar triangles with surd heights0606/22/F/M/24 — Question 2 · 4 marks
41. 3.12: Intersection of a hyperbola and a line; length PQ0606/22/F/M/24 — Question 7 · 7 marks
42. 3.83: Cubic $f(x) = (2x + 1)(3x - 2)^{2}$: calculus and sketch0606/11/O/N/23 — Question 7 · 10 marks
43. 3.104: Irrational equation solved numerically0606/12/O/N/23 — Question 9 · 4 marks
44. 3.84: Linear and modulus graphs; inequality0606/13/O/N/23 — Question 1 · 6 marks
45. 3.108: Solve a cubic reciprocal equation0606/13/O/N/23 — Question 7 · 4 marks
46. 3.85: Solve an equation with $\sqrt{10}$0606/21/O/N/23 — Question 8 · 7 marks
47. 3.37: Solve an equation with surds0606/12/M/J/23 — Question 2 · 5 marks
48. 3.38: Completing the square and a quadratic inequality0606/13/M/J/23 — Question 2 · 7 marks
49. 3.39: Quadratic graph: coefficients and inequality0606/21/M/J/23 — Question 3 · 5 marks
50. 3.41: Quadratic inequality and tangent at a minimum0606/22/M/J/23 — Question 1 · 7 marks
51. 3.42: Stationary points of $y = x^{2} + 32/x^{2}$0606/22/M/J/23 — Question 2 · 8 marks
52. 3.43: Modulus equation and graphical inequality0606/23/M/J/23 — Question 1 · 5 marks
53. 3.44: Express $\sqrt{98 + 12x}$ in surd form0606/23/M/J/23 — Question 2 · 4 marks
54. 3.109: Stationary points and sketch of a cubic product0606/12/F/M/23 — Question 2 · 10 marks
55. 3.9: Solve a modulus inequality by squaring0606/22/F/M/23 — Question 3 · 4 marks
56. 3.73: Sketch a quadratic and values of $k$0606/12/O/N/22 — Question 2 · 8 marks
57. 3.74: Simplify a product of powers0606/12/O/N/22 — Question 3 · 4 marks
58. 3.76: Line cutting a cubic curve0606/21/O/N/22 — Question 2 · 5 marks
59. 3.100: Completing the square and related equation0606/21/O/N/22 — Question 6 · 9 marks
60. 3.77: Solve an equation in $\mathrm{e}^{x}$0606/22/O/N/22 — Question 2 · 4 marks
61. 3.78: Intersection of two polynomial curves0606/22/O/N/22 — Question 5 · 5 marks
62. 3.79: Cylinder with hemisphere: max volume0606/22/O/N/22 — Question 8 · 10 marks
63. 3.80: Solve a fractional inequality0606/23/O/N/22 — Question 1 · 5 marks
64. 3.81: Solve an equation with logarithms0606/23/O/N/22 — Question 3 · 5 marks
65. 3.106: Cubic graph and modulus equations0606/11/M/J/22 — Question 4 · 10 marks
66. 3.31: Logarithmic and substituted cubic equations0606/21/M/J/22 — Question 1 · 5 marks
67. 3.32: Inequality from graphs of two straight lines0606/22/M/J/22 — Question 2 · 5 marks
68. 3.33: Discriminant condition for real roots0606/22/M/J/22 — Question 3 · 5 marks
69. 3.34: Solve $|4x - 7| = 9 - 5x$0606/23/M/J/22 — Question 1 · 3 marks
70. 3.35: Inequality and distinct real roots0606/23/M/J/22 — Question 4 · 5 marks
71. 3.4: Combine fractions and integrate0606/12/F/M/22 — Question 4 · 6 marks
72. 3.6: Intersection of an ellipse and $y = 3/(2x)$0606/22/F/M/22 — Question 4 · 5 marks
73. 3.7: Triangular prism inside a similar pyramid0606/22/F/M/22 — Question 12 · 7 marks
74. 3.66: Sketch $y = (4 - x)(x + 1)(2 - x)\bigl(x + \tfrac{3}{4}\bigr)$0606/13/O/N/21 — Question 1 · 3 marks
75. 3.67: Solve a quadratic inequality0606/21/O/N/21 — Question 1 · 3 marks
76. 3.70: Cone volume maximisation with fixed curved surface0606/21/O/N/21 — Question 11 · 11 marks
77. 3.71: Draw $y = -x^{2} + 5x + 3$ and $y = 11 - x$0606/22/O/N/21 — Question 1 · 6 marks
78. 3.18: Cubic sketch and inequality0606/11/M/J/21 — Question 1 · 5 marks
79. 3.21: Modulus graph and inequality0606/12/M/J/21 — Question 2 · 5 marks
80. 3.22: Parameter $k$ for two distinct real roots0606/13/M/J/21 — Question 1 · 4 marks
81. 3.23: Rational squared curve: stationary points and $k$0606/13/M/J/21 — Question 9 · 10 marks
82. 3.25: Complete the square and minimum point0606/21/M/J/21 — Question 1 · 3 marks
83. 3.107: Modulus inequality and quadratic0606/21/M/J/21 — Question 3 · 6 marks
84. 3.26: Sketch $y = (3 - x)(x - 1)(x + 2)$0606/22/M/J/21 — Question 2 · 3 marks
85. 3.27: Rationalise a surd denominator0606/23/M/J/21 — Question 1 · 3 marks
86. 3.28: Solve for $x$ in a given exponential expression0606/23/M/J/21 — Question 2 · 4 marks
87. 3.29: Quadratic inequality and enclosed area0606/23/M/J/21 — Question 5 · 6 marks
88. 3.102: Absolute-value quadratic: stationary point and sketch0606/12/F/M/21 — Question 4 · 9 marks
89. 3.1: Modulus equation with linear expressions0606/22/F/M/21 — Question 1 · 3 marks
90. 3.2: Equal roots condition for a quadratic in $k$0606/22/F/M/21 — Question 2 · 4 marks
91. 3.3: Cubic graph: find coefficients and solve inequality0606/22/F/M/21 — Question 3 · 5 marks