A-LevelMathematicsAlgebra9709/12 · Feb/Mar 2024 · Q65 Marks
It is given that the coefficient of x³ in the expansion of (2+ax)⁴(5-ax) is 432. Find the value of the constant a.
- It is given that the coefficient of x³ in the expansion of (2+ax)⁴(5-ax) is 432. Find the value of the constant a.[5]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.
- [B1 B1] (⁴C₂)2²(ax)², (⁴C₃)2¹(ax)³ OE Expect 24a²x², 8a³x³ (may be seen in an expansion).
- [*M1] Multiply terms involving x² and x³ by 5-ax to obtain x³ term Must find two products only (may be seen in an expansion).
- [DM1] Equate coefficient of x³ to 432 and solve for a Ignore inclusion of x³ at this stage.
- [A1] Obtain a=3 only
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