A-LevelMathematicsSeries9709/12 · May/June 2011 · Q25 Marks
Find the terms in x² and x³ in the expansion of (1 – ½x)⁶.
- (i)Find the terms in x² and x³ in the expansion of (1 – ½x)⁶.[3]
- (ii)Given that there is no term in x³ in the expansion of (k + 2x)(1 – ½x)⁶, find the value of the constant k.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.
- [3] (i) Term in x² ⁶C₂ × (±3x/2)² = 135x²/4; M1 For either unsimplified term; A1 co; Term in x³ ⁶C₃ × (±3x/2)³ = −540x³/8; A1 co (omission or error with “−” can still gain 2 out of 3)
- [2] (ii) Term in x³ = 270x³/4 + 135kx³/2; M1 considers exactly 2 terms in x³; A1 co; → k = 1.
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