| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2024 |
| Session | February |
| Marks | 4 |
| Topic | Binomial Theorem (positive integer n) |
| Type | Single coefficient given directly |
| Difficulty | Moderate -0.3 This is a straightforward application of the binomial theorem requiring students to set up the general term, identify the correct term for x^8, equate the coefficient to the given value, and solve for k. While it involves some algebraic manipulation and potentially large numbers, it's a standard textbook exercise with a clear method and no conceptual challenges beyond basic binomial expansion. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
2.
The coefficient of $x ^ { 8 }$ in the expansion of $( 2 x + k ) ^ { 12 }$, where $k$ is a positive integer, is 79200000.\\
Determine the value of $k$.\\
\hfill \mbox{\textit{SPS SPS SM Pure 2024 Q2 [4]}}