O-LevelAdditional MathematicsPermutations and combinations4037/21 · May/June 2014 · Q68 Marks
Find the coefficient of x⁵ in the expansion of (3 - 2x)⁸.
- (a)Find the coefficient of x⁵ in the expansion of (3 - 2x)⁸.[2]
- (b)(i)Write down the first three terms in the expansion of (1 + 2x)⁶ in ascending powers of x.[2]
- (b)(ii)In the expansion of (1 + ax)(1 + 2x)⁶, the coefficient of x² is 1.5 times the coefficient of x. Find the value of the constant a.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.
- [M1] 8C3 x 3^3 x (±2x)^5 or 3^8 8C3 (± 2/3)^5 condone C5, -2x^5
- [A1] -48384 can be in expansion
- [B2,1,0] 1+12x + 60x² ignore additional terms. If B0, allow M1 for 3 correct unsimplified terms
- [B1ft] Coefficient of x correct or correct ft (12+a) soi ft their 1+12x + 60x^2
- [B1ft] Coefficient of x² correct or correct ft (60+12a) soi ft their 1+12x + 60x^2
- [M1] 1.5 × their(12 + a)= their(60+12a) no x or x²
- [A1] -4
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