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0606/11 May/Jun 2025, Question 4: Hidden Quadratics and Harder Simultaneous Equations

Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 9 marks

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The question, in short

Solve a fractional-index equation in x, then solve simultaneous equations involving a logarithm and a quadratic in x and y.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 4 marks

Solve x^(1/3) − x^(1/6) = 2 for x.

  1. 1Let u = x^(1/6): u² − u − 2 = 0
  2. 2(u − 2)(u + 1) = 0
  3. 3u = 2 (u = −1 has no solution)
  4. 4x = 2⁶ = 64

Answerx = 64

Part (b) · 5 marks

Solve lg(x + 2y) = 0 together with x² + 4xy + y = 1 for x and y.

  1. 1lg(x + 2y) = 0 gives x + 2y = 1, so x = 1 − 2y
  2. 2(1 − 2y)² + 4y(1 − 2y) + y = 1
  3. 31 − 4y + 4y² + 4y − 8y² + y = 1
  4. 4y − 4y² = 0, so y(1 − 4y) = 0
  5. 5y = 0, x = 1 or y = 1/4, x = 1/2

Answerx = 1, y = 0 and x = 1/2, y = 1/4

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Also searched as: 0606/11/M/J/25 · 0606_s25_qp_11 · 0606 s25 11 · question 4.
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