| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | October |
| Marks | 7 |
| Topic | Binomial Theorem (positive integer n) |
| Type | Substitution into binomial expansion |
| Difficulty | Moderate -0.8 Part (i) is a straightforward binomial expansion requiring only formula application and arithmetic. Part (ii) requires the insight to substitute x = 3y + y² and then identify the y³ term, which adds modest problem-solving beyond routine expansion, but this is still a standard Further Maths technique with clear methodology and limited steps. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
\begin{enumerate}[label=(\roman*)]
\item Find the binomial expansion of $(2 + x)^5$, simplifying the terms. [4]
\item Hence find the coefficient of $y^3$ in the expansion of $(2 + 3y + y^2)^5$. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2020 Q1 [7]}}