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O-LevelAdditional MathematicsSeries4037/22 · May/June 2025 · Q109 Marks

The first three terms, in descending powers of x, in the expansion of (3x²-a)ⁿ (1+2/x²)² can be written as 729x¹² - 972x¹⁰ + bx⁸, where a, b and n are constants. Find the values of a, b and n.

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

  1. [B2] n = 6 stated; nfww (B1 for first term: (3x²)ⁿ or (3x²)⁶ soi)
  2. [B3] -6(3x²)⁵a + 2(729x¹⁰) = -972x¹⁰ oe (B2 for one correct equation)
  3. [B2] a = 1/3
  4. [B2] b = -108

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About this question

Topic
Series, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.
Source
O-Level Additional Mathematics, May/June 2025 Paper 2 Variant 2, question 10.

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