| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Finding unknown power and constant |
| Difficulty | Standard +0.3 This is a straightforward application of the binomial expansion formula where students equate coefficients to find unknowns. While it requires careful algebraic manipulation and solving simultaneous equations, the method is standard and commonly practiced in C4. The verification of k in part (ii) is routine once a and n are found. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
3. The first four terms in the series expansion of $( 1 + a x ) ^ { n }$ in ascending powers of $x$ are
$$1 - 4 x + 24 x ^ { 2 } + k x ^ { 3 }$$
where $a , n$ and $k$ are constants and $| a x | < 1$.\\
(i) Find the values of $a$ and $n$.\\
(ii) Show that $k = - 160$.\\
\hfill \mbox{\textit{OCR C4 Q3 [8]}}