| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2025 |
| Session | October |
| Marks | 4 |
| Topic | Binomial Theorem (positive integer n) |
| Type | Single binomial expansion |
| Difficulty | Standard +0.3 This is a straightforward binomial expansion problem requiring students to identify which term is constant, set up the equation using the binomial coefficient, and solve for a. While it involves multiple steps (finding r=4, calculating C(6,4), solving a^4=256), these are all standard techniques with no conceptual difficulty beyond routine A-level binomial theorem application. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
\textbf{In this question you must show detailed reasoning.}
Consider the expansion of $\left(\frac{x^2}{2} + \frac{a}{x}\right)^6$. The constant term is 960.
Find the possible values of $a$. [4]
\hfill \mbox{\textit{SPS SPS FM 2025 Q5 [4]}}