| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Form (1+bx)^n expansion |
| Difficulty | Easy -1.2 This is a straightforward binomial expansion question requiring direct application of the binomial theorem formula. Part (a) is routine calculation with no problem-solving required, and part (b) tests basic knowledge that the expansion is valid for all x when the exponent is a positive integer. This is easier than average A-level content. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| \(1 + \left(\frac{3}{2}\right)(4x) + \frac{3(\cdot1)}{2}(4x)^2 + \frac{3(\cdot1)(\cdot3)}{3 \cdot 2}(4x)^3 + \ldots\) | M1 | |
| \(1 + 6x + 6x^2 - 4x^3 + \ldots\) | A3 | |
| \(\ | x\ | < \frac{1}{4}\) |
$1 + \left(\frac{3}{2}\right)(4x) + \frac{3(\cdot1)}{2}(4x)^2 + \frac{3(\cdot1)(\cdot3)}{3 \cdot 2}(4x)^3 + \ldots$ | M1 |
$1 + 6x + 6x^2 - 4x^3 + \ldots$ | A3 |
$\|x\| < \frac{1}{4}$ | B1 | (5)\begin{enumerate}[label=(\alph*)]
\item Expand $(1 + 4x)^5$ in ascending powers of $x$ up to and including the term in $x^5$, simplifying each coefficient. [4]
\item State the set of values of $x$ for which your expansion is valid. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q1 [5]}}