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O-LevelAdditional MathematicsPermutations and combinations4037/22 · Oct/Nov 2025 · Q36 Marks

Find the exact value of the term independent of x in the expansion of (2+3/x)¹⁰ (1-4x²)².

  1. Find the exact value of the term independent of x in the expansion of (2+3/x)¹⁰ (1-4x²)².[6]

Mark scheme

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

  1. [B3] 2¹⁰ +10x2⁹x(3/x)+45x2⁸x(3/x)² oe, soi
  2. [B2] for 3 terms for 2¹⁰ +10x2⁹x(3/x)+45x2⁸x(3/x)² oe, soi
  3. [B1] for two correct terms in 2¹⁰+10x2⁹x(3/x)+45x2⁸x(3/x)² oe, soi
  4. [B1] and 1-8x²+16x⁴ soi
  5. [M2 FT their expansions for M2 or M1] 2¹⁰ +their15360×their(-8)+their103680×their16
  6. [M1 FT] for any two correct terms in this sum
  7. [A1] 1537024

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About this question

Topic
Permutations and combinations, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2025 Paper 2 Variant 2, question 3.

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