A-LevelMathematicsSeries9709/12 · May/June 2023 · Q24 Marks
The coefficient of x⁴ in the expansion of (x + a)⁶ is p and the coefficient of x² in the expansion of (ax + 3)⁴ is q. It is given that p + q = 276. Find the possible values of the constant a.
- Find the possible values of the constant a.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [B1] [Coefficient of x⁴ = p =] 15a² May be seen in an expansion or with x⁴.
- [B1] [Coefficient of x² = q =] 54a² May be seen in an expansion or with x².
- [M1] Equating their p + their q to 276 leading to an equation in a² only No x terms and no extra terms. If p and q are not identified then it needs to be clear from the expansion that the appropriate coefficients are being used. 69a² = 276 implies the first 3 marks.
- [A1] a = ±2 CAO
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