2026 IGCSE Additional Mathematics February/March 0606/22 Q11

2026 IGCSE Additional Mathematics February/March 0606/22 Q11

7 marks
  1. Find, in descending powers of \(x\), the first three terms in the expansion of \(\left(x^2+\dfrac1{2x}\right)^9\).
    Give each term in its simplest form.[3]
  2. The expansion of \(\left(x^2+\dfrac1{2x}\right)^n\), where \(n\) is a positive integer, has a term that is independent of \(x\).
    Show that \(n\) is divisible by \(3\).[4]

Solution:

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Answer:(a) \(x^{18}+\dfrac92x^{15}+9x^{12}\) (b) \(2n=3r\) with integer \(r\), hence \(3\mid n\) (shown).

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