| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2013 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Factoring out constants before expansion |
| Difficulty | Moderate -0.3 This is a straightforward application of the binomial expansion for fractional powers with standard substitution. Part (a) requires routine use of the formula (1+x)^n with n=1/2 after factoring, and part (b) is a direct numerical substitution. While it requires careful algebraic manipulation and fraction arithmetic, it follows a well-practiced template with no conceptual surprises, making it slightly easier than average. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
\begin{enumerate}[label=(\alph*)]
\item Find the binomial expansion of
$$\sqrt{(9 + 8x)}, \quad |x| < \frac{9}{8}$$
in ascending powers of $x$, up to and including the term in $x^2$.
Give each coefficient as a simplified fraction.
[5]
\item Use your expansion to estimate the value of $\sqrt{11}$, giving your answer as a single fraction.
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 2013 Q1 [8]}}