Set 4 — 2026 past papers

  1. 4.01: Polynomial factor and roots0606/12/F/M/26 — Question 1 · 4 marks
  2. 4.02: Polynomial parameter and roots0606/11/M/J/26 — Question 5 · 8 marks
  3. 4.03: Polynomial factorisation and substitution0606/12/M/J/26 — Question 3 · 7 marks
  4. 4.04: Polynomial factorisation and substitution0606/13/M/J/26 — Question 4 · 6 marks

Set 3 — 2021–2025 past papers

  1. 3.25: Cubic with factor and remainder0606/12/O/N/25 — Question 2 · 7 marks
  2. 3.24: Factor and remainder determine two coefficients0606/21/O/N/25 — Question 1 · 5 marks
  3. 3.31: Find coefficients from factor and remainder0606/23/O/N/25 — Question 1 · 5 marks
  4. 3.11: Two cubics from an absolute-value graph0606/12/M/J/25 — Question 1 · 3 marks
  5. 3.1: Parameter from a linear factor, then unique real root0606/12/F/M/25 — Question 4 · 6 marks
  6. 3.21: Two cubics from an absolute-value graph0606/11/O/N/24 — Question 1 · 3 marks
  7. 3.22: Binomial coefficient and term independent of yy0606/11/O/N/24 — Question 5 · 4 marks
  8. 3.23: Show a linear relation, then find aa, bb, cc0606/13/O/N/24 — Question 5 · 6 marks
  9. 3.9: Division form, then factorise p(x)−5p(x) - 50606/11/M/J/24 — Question 2 · 6 marks
  10. 3.10: Nature of roots of a rational equation; linear fractional equation0606/22/M/J/24 — Question 3 · 8 marks
  11. 3.29: Polynomial coefficients from remainder data0606/11/O/N/23 — Question 2 · 8 marks
  12. 3.16: Factorised cubic from a graph; sign values0606/12/O/N/23 — Question 1 · 5 marks
  13. 3.17: Three conditions on a cubic; unique real root0606/12/O/N/23 — Question 6 · 10 marks
  14. 3.18: Factor and remainder; unique real root0606/13/O/N/23 — Question 4 · 8 marks
  15. 3.19: Password counting and team selection0606/13/O/N/23 — Question 5 · 10 marks
  16. 3.20: Stationary points, sketch and unique kk-level0606/13/O/N/23 — Question 6 · 10 marks
  17. 3.7: Cubic from an absolute-value graph; modulus inequality0606/12/M/J/23 — Question 3 · 7 marks
  18. 3.28: Cubic factor and midpoint of intersection points0606/22/M/J/23 — Question 3 · 8 marks
  19. 3.8: Verify a root and show no other real roots0606/23/M/J/23 — Question 4 · 5 marks
  20. 3.27: Cubic factor and exponential equation0606/22/F/M/23 — Question 5 · 6 marks
  21. 3.26: Polynomial factor and remainder0606/13/O/N/22 — Question 4 · 7 marks
  22. 3.3: Binomial product: coefficients of xx and x2x^{2}0606/12/M/J/22 — Question 5 · 8 marks
  23. 3.4: Factor and remainder on a cubic; p′′(0)p''(0)0606/12/M/J/22 — Question 6 · 7 marks
  24. 3.5: Find a remainder after determining unknown coefficients0606/21/M/J/22 — Question 4 · 6 marks
  25. 3.6: Factor and derivative conditions; full factorisation0606/23/M/J/22 — Question 6 · 8 marks
  26. 3.12: Index form of a product; equation in x5/4x^{5/4}0606/11/O/N/21 — Question 4 · 7 marks
  27. 3.13: Coefficients from pp and p′p'; remainder of p′′p''0606/11/O/N/21 — Question 5 · 7 marks
  28. 3.14: Sign set and expression for a cubic graph0606/12/O/N/21 — Question 1 · 4 marks
  29. 3.15: Factor and remainder; three linear factors0606/12/O/N/21 — Question 6 · 9 marks
  30. 3.2: Factor and remainder conditions imply another factor0606/22/M/J/21 — Question 4 · 6 marks
  31. 3.30: Polynomial factor and remainder0606/22/M/J/21 — Question 4 · 6 marks

Set 2

  1. 2.4: Evaluation and linear factorisation0606/21/O/N/20 — Question 7 · 6 marks
  2. 2.2: Remainder and complete factorisation0606/21/M/J/20 — Question 3 · 6 marks
  3. 2.9: Polynomial from given roots0606/22/M/J/20 — Question 4 · 5 marks
  4. 2.3: Factor theorem and factorisation0606/21/O/N/19 — Question 7 · 3 marks
  5. 2.10: Integer roots of cubics0606/22/O/N/19 — Question 7 · 8 marks
  6. 2.14: Roots and coefficients of a cubic0606/23/O/N/19 — Question 8 · 5 marks
  7. 2.8: Factor theorem and solving a cubic0606/22/M/J/19 — Question 3 · 6 marks
  8. 2.1: Factor and remainder on a cubic0606/21/M/J/18 — Question 4 · 6 marks
  9. 2.7: Factor and remainder to find another remainder0606/22/M/J/18 — Question 3 · 6 marks
  10. 2.11: Factor and remainder on a cubic (Paper 23)0606/23/M/J/18 — Question 4 · 6 marks
  11. 2.13: Repeated positive integer root0606/23/O/N/17 — Question 11 · 8 marks
  12. 2.6: Factorisation without a calculator0606/22/M/J/17 — Question 3 · 5 marks
  13. 2.12: Factor and remainder on a cubic0606/23/O/N/16 — Question 4 · 8 marks
  14. 2.5: Unknown coefficient from a factor0606/22/M/J/16 — Question 4 · 5 marks

Set 1

  1. 1.11: Factor and value conditions on a cubic0606/12/O/N/20 — Question 10 · 8 marks
  2. 1.16: Factor and value condition on a cubic0606/13/O/N/20 — Question 7 · 8 marks
  3. 1.14: Remainders and factorisation of a cubic0606/13/M/J/20 — Question 5 · 8 marks
  4. 1.3: Polynomial with a constant and no real solutions0606/11/M/J/19 — Question 3 · 6 marks
  5. 1.7: Intersection of a cubic curve and a line0606/12/M/J/19 — Question 2 · 5 marks
  6. 1.6: Constants from remainders and divisibility0606/11/O/N/18 — Question 2 · 6 marks
  7. 1.10: Constants from divisibility and derivative conditions0606/12/O/N/18 — Question 9 · 8 marks
  8. 1.15: Polynomial divisible by a linear factor with trig application0606/13/O/N/18 — Question 11 · 10 marks
  9. 1.5: Common factor of a cubic and its derivative0606/11/O/N/17 — Question 2 · 7 marks
  10. 1.9: Coefficients from a factor and a remainder0606/12/O/N/17 — Question 7 · 7 marks
  11. 1.2: Coefficients from a remainder and a derivative condition0606/11/M/J/17 — Question 2 · 5 marks
  12. 1.13: Factor and remainder on a cubic0606/13/M/J/17 — Question 8 · 9 marks
  13. 1.4: Cubic with a repeated factor found without a calculator0606/11/O/N/16 — Question 9 · 9 marks
  14. 1.8: Cubic with a repeated factor found without a calculator0606/12/O/N/16 — Question 9 · 9 marks
  15. 1.1: Divisibility conditions on a cubic and its derivative0606/11/M/J/16 — Question 10 · 8 marks
  16. 1.12: Divisibility conditions on a cubic and its derivative0606/13/M/J/16 — Question 10 · 8 marks