| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2018 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Factoring out constants before expansion |
| Difficulty | Standard +0.3 This is a straightforward application of the binomial expansion requiring factoring out the constant (√4 = 2), then expanding (1 - 9x/4)^(1/2) to three terms using the standard formula. Part (b) requires choosing x to make 4-9x = 310, which is routine algebraic manipulation. Slightly above average difficulty due to the fractional power and the application in part (b), but still a standard C4 textbook exercise with no novel insight required. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<1 |
\begin{enumerate}
\item (a) Find the binomial series expansion of
\end{enumerate}
$$\sqrt { 4 - 9 x } , | x | < \frac { 4 } { 9 }$$
in ascending powers of $x$, up to and including the term in $x ^ { 2 }$ Give each coefficient in its simplest form.\\
(b) Use the expansion from part (a), with a suitable value of $x$, to find an approximate value for $\sqrt { 310 }$\\
Show all your working and give your answer to 3 decimal places.
\hfill \mbox{\textit{Edexcel C4 2018 Q1 [8]}}