| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2014 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Expansion up to x^3 term |
| Difficulty | Moderate -0.8 This is a straightforward application of the binomial theorem requiring only substitution into the formula and simplification. It's a standard C2 question with no problem-solving element—students simply need to recall the binomial expansion formula and perform routine algebraic manipulation to find the first four terms. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| \(1+12x\) | B1 | Both terms correct as printed (allow \(12x^1\) but not \(1^8\)) |
| \(\ldots+\frac{8(7)}{2!}\left(\frac{3x}{2}\right)^2+\frac{8(7)(6)}{3!}\left(\frac{3x}{2}\right)^3+\ldots\) or \(\ldots+{}^8C_2\left(\frac{3x}{2}\right)^2+{}^8C_3\left(\frac{3x}{2}\right)^3+\ldots\) | M1 | For either the \(x^2\) term or the \(x^3\) term. Requires correct binomial coefficient in any form with the correct power of \(x\), but the other part of the coefficient (perhaps including powers of 2 and/or 3 or signs) may be wrong or missing |
| \(\ldots+63x^2+189x^3+\ldots\) | A1A1 | A1: Either \(63x^2\) or \(189x^3\); A1: Both \(63x^2\) and \(189x^3\). Terms may be listed but must be positive |
# Question 1:
$\left(1+\frac{3x}{2}\right)^8$
| $1+12x$ | B1 | Both terms correct as printed (allow $12x^1$ but not $1^8$) |
| $\ldots+\frac{8(7)}{2!}\left(\frac{3x}{2}\right)^2+\frac{8(7)(6)}{3!}\left(\frac{3x}{2}\right)^3+\ldots$ or $\ldots+{}^8C_2\left(\frac{3x}{2}\right)^2+{}^8C_3\left(\frac{3x}{2}\right)^3+\ldots$ | M1 | For **either** the $x^2$ term **or** the $x^3$ term. Requires correct binomial coefficient in any form with the correct power of $x$, but the other part of the coefficient (perhaps including powers of 2 and/or 3 or signs) may be wrong or missing |
| $\ldots+63x^2+189x^3+\ldots$ | A1A1 | A1: **Either** $63x^2$ **or** $189x^3$; A1: **Both** $63x^2$ **and** $189x^3$. Terms may be listed but must be positive |
**[Total 4]**
---\begin{enumerate}
\item Find the first 4 terms, in ascending powers of $x$, of the binomial expansion of
\end{enumerate}
$$\left( 1 + \frac { 3 x } { 2 } \right) ^ { 8 }$$
giving each term in its simplest form.\\
\hfill \mbox{\textit{Edexcel C2 2014 Q1 [4]}}