Set 4 — 2026 past papers

  1. 4.01: Minimum sailing cost0606/22/F/M/26 — Question 7 · 8 marks
  2. 4.02: Stationary point of an exponential quotient0606/11/M/J/26 — Question 7 · 9 marks
  3. 4.03: Related rates in a cone0606/13/M/J/26 — Question 6 · 6 marks
  4. 4.04: Related rates for a sphere0606/22/M/J/26 — Question 12 · 4 marks
  5. 4.05: Surface-area optimisation0606/23/M/J/26 — Question 9 · 12 marks

Set 3 — 2021–2025 past papers

  1. 3.63: Differentiate a product x e^{3x}0606/13/O/N/25 — Question 1 · 3 marks
  2. 3.64: Differentiate x e^{3x}0606/13/O/N/25 — Question 2 · 3 marks
  3. 3.67: Exactly one stationary point on a ln curve0606/21/O/N/25 — Question 7 · 6 marks
  4. 3.70: Derivative of xcos 2xx\mathrm{cos}\,2x; integrate xsin 2xx\mathrm{sin}\,2x0606/22/O/N/25 — Question 7 · 6 marks
  5. 3.72: Related rates for a sphere0606/22/M/J/25 — Question 6 · 6 marks
  6. 3.71: Small increments and integrating a sine derivative0606/23/M/J/25 — Question 8 · 9 marks
  7. 3.12: Quotient of ln and linear: rates of change0606/22/F/M/25 — Question 6 · 8 marks
  8. 3.57: Connected rates for a ln function0606/12/O/N/24 — Question 7 · 6 marks
  9. 3.36: Ln quotient: derivative and rates0606/13/M/J/24 — Question 6 · 7 marks
  10. 3.37: Small change for a product of cos and sin0606/21/M/J/24 — Question 5 · 5 marks
  11. 3.38: Small change for cos x sin 2x0606/21/M/J/24 — Question 6 · 5 marks
  12. 3.99: Tangent to exponential curve0606/22/M/J/24 — Question 5 · 6 marks
  13. 3.10: Small change for a logarithmic product0606/22/F/M/24 — Question 5 · 4 marks
  14. 3.121: Related rates for a cylinder's curved surface0606/22/F/M/24 — Question 11 · 5 marks
  15. 3.95: Quotient rule to a given derivative form0606/13/O/N/23 — Question 9 · 5 marks
  16. 3.73: Product rule derivative and stationary point0606/11/M/J/23 — Question 8 · 7 marks
  17. 3.97: Related rates for a sphere0606/21/M/J/23 — Question 5 · 4 marks
  18. 3.31: Derivative of a quotient, small change, and ln integral0606/22/M/J/23 — Question 7 · 12 marks
  19. 3.96: Related rates with a tangent function0606/22/M/J/23 — Question 4 · 6 marks
  20. 3.33: Tangent from exponential curve to axes0606/23/M/J/23 — Question 6 · 6 marks
  21. 3.34: Small change for a mixed trig–algebraic function0606/23/M/J/23 — Question 7 · 6 marks
  22. 3.8: Trigonometric small change and second derivative0606/22/F/M/23 — Question 7 · 9 marks
  23. 3.49: Product rule for x sin x, tangent and integral0606/21/O/N/22 — Question 8 · 10 marks
  24. 3.23: Small change for a power of sine0606/21/M/J/22 — Question 6 · 4 marks
  25. 3.26: Differentiate a product of ln, tan and exponential0606/22/M/J/22 — Question 6 · 4 marks
  26. 3.27: Differentiate ln(tan x) e^{4x}0606/22/M/J/22 — Question 7 · 4 marks
  27. 3.28: Differentiate a product with exponential0606/23/M/J/22 — Question 7 · 2 marks
  28. 3.98: Product rule and related integral0606/23/M/J/22 — Question 8 · 6 marks
  29. 3.46: Derivative of a sine product and normal0606/21/O/N/21 — Question 3 · 9 marks
  30. 3.18: Small change for a product involving e and cos0606/21/M/J/21 — Question 6 · 6 marks
  31. 3.21: Small change for cot x0606/23/M/J/21 — Question 4 · 4 marks

Set 2

  1. 2.28: Logarithm of a trigonometric expression0606/21/O/N/20 — Question 4 · 6 marks
  2. 2.78: Logarithmic trigonometric differentiation0606/23/O/N/20 — Question 4 · 9 marks
  3. 2.44: Small change using differentiation0606/22/M/J/20 — Question 1 · 4 marks
  4. 2.45: Tangent to a trigonometric curve and intercept distance0606/22/M/J/20 — Question 6 · 7 marks
  5. 2.27: Exponential product: stationary point, tangent and integral0606/21/O/N/19 — Question 8 · 10 marks
  6. 2.54: Second derivative identity with a sine combination0606/22/O/N/19 — Question 2 · 5 marks
  7. 2.10: Quotient rule and small change for a logarithmic ratio0606/21/M/J/19 — Question 2 · 5 marks
  8. 2.40: Quotient rule with logarithmic denominator0606/22/M/J/19 — Question 1 · 4 marks
  9. 2.61: Product rule with tangent and cosine0606/23/M/J/19 — Question 2 · 4 marks
  10. 2.52: Quotient rule with sine in the denominator0606/22/O/N/18 — Question 3 · 6 marks
  11. 2.6: Logarithmic function and approximate change in x0606/21/M/J/18 — Question 2 · 5 marks
  12. 2.23: Differentiation with secant and solving a trig equation0606/21/O/N/17 — Question 12 · 10 marks
  13. 2.50: Cubic factorisation linked to a trigonometric derivative0606/22/O/N/17 — Question 10 · 11 marks
  14. 2.4: Logarithmic differentiation and small increments0606/21/M/J/17 — Question 3 · 4 marks
  15. 2.59: Product and quotient differentiation0606/23/M/J/17 — Question 7 · 8 marks
  16. 2.16: Bacterial growth model with exponential decay term0606/21/O/N/16 — Question 4 · 7 marks
  17. 2.69: Tangent to 7+tan⁡x7 + \tan x and a derivative equation0606/23/O/N/16 — Question 6 · 8 marks

Set 1

  1. 1.24: Quotient rule with trigonometric functions and rates of change0606/11/O/N/20 — Question 4 · 7 marks
  2. 1.55: Normal to a logarithmic quotient0606/12/O/N/20 — Question 7 · 7 marks
  3. 1.11: Equation of a tangent to a logarithmic rational curve0606/11/M/J/20 — Question 5 · 6 marks
  4. 1.37: Cosine curve intersecting a horizontal line0606/12/M/J/19 — Question 9 · 9 marks
  5. 1.17: Quotient rule and tangent to a logarithmic rational curve0606/11/O/N/18 — Question 6 · 6 marks
  6. 1.19: Exponential function and small changes0606/11/O/N/18 — Question 9 · 8 marks
  7. 1.77: Chain rule and related rates0606/13/O/N/18 — Question 4 · 6 marks
  8. 1.79: Normal to a logarithmic quotient0606/13/O/N/18 — Question 9 · 8 marks
  9. 1.16: Logarithmic curve: derivative and stationary point0606/11/O/N/17 — Question 7 · 9 marks
  10. 1.47: Quotient rule with a logarithm0606/12/O/N/17 — Question 4 · 6 marks
  11. 1.1: Normal to a logarithmic curve at the positive x-intercept0606/11/M/J/16 — Question 3 · 5 marks
  12. 1.26: Differentiating a product with an exponential and a square root0606/12/M/J/16 — Question 6 · 5 marks
  13. 1.58: Normal to a logarithmic curve at the positive x-intercept0606/13/M/J/16 — Question 3 · 5 marks