| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Product with linear term |
| Difficulty | Moderate -0.3 This is a straightforward application of the binomial expansion for negative powers with standard follow-through parts. Part (a) requires direct substitution into the binomial formula, part (b) is simple algebraic manipulation multiplying by (1+x), and part (c) involves routine substitution. All techniques are standard C4 material with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<1 |
$$f(x) = (1 + 3x)^{-1}, \quad |x| < \frac{1}{3}.$$
\begin{enumerate}[label=(\alph*)]
\item Expand $f(x)$ in ascending powers of $x$ up to and including the term in $x^3$. [3]
\item Hence show that, for small $x$,
$$\frac{1 + x}{1 + 3x} \approx 1 - 2x + 6x^2 - 18x^3.$$ [2]
\item Taking a suitable value for $x$, which should be stated, use the series expansion in part $(b)$ to find an approximate value for $\frac{101}{103}$, giving your answer to 5 decimal places. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q4 [8]}}