Indices and surds

39 past-paper questions with KaTeX-typeset statements, diagram crops, and worked solutions.

Set 3 — 2021–2025 past papers

  1. 3.1: Equation reducible to a quadratic in cube roots0606/12/M/J/25 — Question 2 · 4 marks
  2. 3.5: Square and rationalise a surd expression0606/22/F/M/23 — Question 2 · 4 marks
  3. 3.2: Surd quadratic equation0606/11/O/N/22 — Question 4 · 6 marks
  4. 3.3: Quadratic with surd coefficients0606/12/F/M/22 — Question 2 · 6 marks
  5. 3.4: Simplify an index expression0606/12/M/J/21 — Question 1 · 3 marks

Set 2

  1. 2.18: Quadratic equation with √7 coefficients0606/23/O/N/20 — Question 11 · 7 marks
  2. 2.8: Substituting a surd into a curve equation0606/22/M/J/20 — Question 2 · 5 marks
  3. 2.15: Simplifying surd fractions0606/23/M/J/20 — Question 5 · 6 marks
  4. 2.12: Quadratic equation with √5 coefficients0606/22/O/N/19 — Question 11 · 6 marks
  5. 2.3: Rationalising a squared surd numerator0606/21/M/J/19 — Question 4 · 4 marks
  6. 2.6: Expanding and rationalising surd expressions0606/21/O/N/18 — Question 3 · 7 marks
  7. 2.11: Quadratic equation with surd coefficients0606/22/O/N/18 — Question 7 · 6 marks
  8. 2.5: Squaring a surd expression0606/21/O/N/17 — Question 8 · 6 marks
  9. 2.10: Linear expression in a surd variable0606/22/O/N/17 — Question 1 · 5 marks
  10. 2.17: Finding integers in a surd equation0606/23/O/N/17 — Question 3 · 4 marks
  11. 2.2: Simplifying surds and solving a linear equation0606/21/M/J/17 — Question 2 · 6 marks
  12. 2.7: Negative power with surd rationalisation0606/22/M/J/17 — Question 2 · 5 marks
  13. 2.14: Index laws with surds0606/23/M/J/17 — Question 1 · 3 marks
  14. 2.4: Finding constants in a surd identity0606/21/O/N/16 — Question 2 · 5 marks
  15. 2.9: Finding constants in a surd identity0606/22/O/N/16 — Question 2 · 5 marks
  16. 2.16: Rationalising to show a surd identity0606/23/O/N/16 — Question 1 · 3 marks
  17. 2.1: Rationalising and expanding surd squares0606/21/M/J/16 — Question 5 · 6 marks
  18. 2.13: Rationalising and expanding surd squares0606/23/M/J/16 — Question 5 · 6 marks

Set 1

  1. 1.6: Index laws with fractional powers0606/11/O/N/20 — Question 3 · 3 marks
  2. 1.5: Trapezium perimeter and area with surds0606/11/O/N/19 — Question 8 · 6 marks
  3. 1.10: Rewriting a surd and index quotient0606/12/O/N/19 — Question 6 · 3 marks
  4. 1.8: Simplifying a compound index expression0606/12/M/J/19 — Question 4 · 3 marks
  5. 1.14: Index laws with reciprocal form0606/13/M/J/19 — Question 2 · 3 marks
  6. 1.15: Right triangle with surds0606/13/M/J/19 — Question 7 · 8 marks
  7. 1.3: Rationalising, surd simplification and quadratic equation0606/11/M/J/18 — Question 10 · 9 marks
  8. 1.7: Equating indices with mixed bases0606/12/M/J/18 — Question 12 · 3 marks
  9. 1.13: Rationalising, surd simplification and quadratic equation0606/13/M/J/18 — Question 10 · 9 marks
  10. 1.2: Simplifying surds and solving with fractional indices0606/11/M/J/17 — Question 3 · 6 marks
  11. 1.12: Isosceles triangle area and tangent0606/13/M/J/17 — Question 4 · 5 marks
  12. 1.4: Index laws with three variables0606/11/O/N/16 — Question 2 · 3 marks
  13. 1.9: Index laws with three variables0606/12/O/N/16 — Question 2 · 3 marks
  14. 1.16: Simplifying a surd fraction0606/13/O/N/16 — Question 2 · 3 marks
  15. 1.1: Exponential equation and index laws0606/11/M/J/16 — Question 2 · 5 marks
  16. 1.11: Exponential equation and index laws0606/13/M/J/16 — Question 2 · 5 marks