| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Topic | Generalised Binomial Theorem |
| Type | Finding unknown power and constant |
| Difficulty | Standard +0.3 This is a straightforward application of the binomial expansion where students equate coefficients of x and x² to form two simultaneous equations. The algebra is routine (solving n(n-1)a²/2 = -6 and na = 6), requiring only basic manipulation skills. While it involves the generalised binomial theorem, the problem-solving demand is minimal—it's a standard textbook exercise that's slightly easier than average due to its mechanical nature. |
| Spec | 4.04c Scalar product: calculate and use for angles4.04d Angles: between planes and between line and plane |
6. In this question you must show detailed reasoning.
Given that
$$( 1 + a x ) ^ { n } = 1 + 6 x - 6 x ^ { 2 } + \ldots$$
where $a$ and $n$ are constants, find the values of $a$ and $n$.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q6 [6]}}