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0606/23 May/Jun 2025, Question 7: The Binomial Expansion

Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 5 marks

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The question, in short

Two-part binomial question: locate the constant term in a power of a two-term expression, then use a ratio of coefficients to determine a positive constant a.

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Part (a) · 2 marks

Find the term with no x in the expansion of (x² − 3/x⁴)¹⁵.

  1. 1General term: ¹⁵Cᵣ (x²)¹⁵⁻ʳ (−3/x⁴)ʳ
  2. 2Power of x: 30 − 2r − 4r = 0, so r = 5
  3. 3¹⁵C₅ × (−3)⁵ = 3003 × (−243)
  4. 4= −729 729

Answer−729 729

Part (b) · 3 marks

In (1 + ax)⁹ the x³ coefficient is 7 times the x² coefficient; find positive a.

  1. 1Coefficient of x³ = ⁹C₃a³ = 84a³
  2. 2Coefficient of x² = ⁹C₂a² = 36a²
  3. 384a³ = 7 × 36a² = 252a²
  4. 4a = 3 (a > 0)

Answera = 3

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Also searched as: 0606/23/M/J/25 · 0606_s25_qp_23 · 0606 s25 23 · question 7.
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