| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Find n and constants from given terms |
| Difficulty | Moderate -0.3 This is a straightforward binomial expansion question requiring standard application of the binomial theorem formula. Part (a) uses the coefficient of x to find k, part (b) substitutes k into the x² term, and part (c) applies the same formula for x⁴. All three parts are routine calculations with no problem-solving insight needed, making it slightly easier than average but still requiring careful algebraic manipulation. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| \(k = \frac{3}{2}\) | M1, A1 | Attempts to use the binomial expansion to find a value for \(k\); Correct answer only |
| Answer | Marks | Guidance |
|---|---|---|
| \(p = \frac{405}{4}\) | M1, A1 | Uses the binomial expansion to find an equation for \(p\) using their \(k\); Correct answer only |
| Answer | Marks | Guidance |
|---|---|---|
| \(q = \frac{8505}{4}\) | M1, A1 | Identifies the correct term and uses their value of \(k\) to find the value of \(q\); Correct answer only |
### Part a:
$k = \frac{3}{2}$ | M1, A1 | Attempts to use the binomial expansion to find a value for $k$; Correct answer only
### Part b:
$p = \frac{405}{4}$ | M1, A1 | Uses the binomial expansion to find an equation for $p$ using their $k$; Correct answer only
### Part c:
$q = \frac{8505}{4}$ | M1, A1 | Identifies the correct term and uses their value of $k$ to find the value of $q$; Correct answer onlyThe first 3 terms, in ascending powers of $x$, in the binomial expansion of $(1 + kx)^{10}$ are given by
$$1 + 15x + px^2$$
where $k$ and $p$ are constants.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $k$ [2]
\item Find the value of $p$ [2]
\item Given that, in the expansion of $(1 + kx)^{10}$, the coefficient of $x^4$ is $q$, find the value of $q$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel AS Paper 1 Q11 [6]}}