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O-LevelAdditional MathematicsSeries4037/21 · May/June 2025 · Q66 Marks

Using an appropriate quadratic factorisation, find the first three terms in the binomial expansion of (9x²+12x+4)⁵, in ascending powers of x. You must simplify your coefficients.

  1. (a)Using an appropriate quadratic factorisation, find the first three terms in the binomial expansion of (9x²+12x+4)⁵, in ascending powers of x. You must simplify your coefficients.[4]
  2. (b)Find the term independent of x in the expansion of (6/x² + x/2)¹².[2]

Mark scheme

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

  1. [M2] M1 for (3x + 2)² soi
  2. [A2] A1 for any two terms correct or 2¹⁰ + 10(2⁹)(3x) + 45(2⁸)(3x)² or for 3 correct terms seen but not summed e.g. a list
  3. After M2 A0, allow SC1 for an answer of 59 049x¹⁰ + 393660x⁹ + 1180980x⁸
  4. [A1] 1024 + 15360x + 103 680x²
  5. [M1] for C(6/x²)^(12-r)(x/2)^r soi
  6. [A1] 51 963 120

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About this question

Topic
Series, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, May/June 2025 Paper 2 Variant 1, question 6.

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