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O-LevelAdditional MathematicsSeries4037/22 · Oct/Nov 2013 · Q68 Marks

Find the coefficient of x³ in the expansion of (1 – 2x)⁶.

  1. (a)(i)Find the coefficient of x³ in the expansion of (1 – 2x)⁶.[2]
  2. (a)(ii)Find the coefficient of x³ in the expansion of (1 + x/2)(1 – 2x)⁶.[3]
  3. (b)Expand (2√x + 1/√x)⁴ in a series of powers of x with integer coefficients.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.

  1. [B1] -8 or 20 ±40 implies ±2×20 or +160 hence B1
  2. [B1] -160(x³) isw OK if seen in expansion
  3. [B1] 60(x²) Can be implied
  4. [M1] (i) + 1/2 (their 60)
  5. [A1] -130(x³)
  6. [B3,2,1,0] 16x² +32x+24+8/x+1/x² oe Terms must be evaluated (allow 24x⁰). B2 for 4 terms correct. B1 for 2 or 3 terms correct. ISW once expansion is seen.

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About this question

Topic
Series, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2013 Paper 2 Variant 2, question 6.

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