| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2010 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Expansion up to x^2 term |
| Difficulty | Easy -1.2 This is a straightforward application of the binomial theorem requiring only direct substitution into the formula and basic arithmetic. It's a standard C2 question with no problem-solving element—students simply need to recall the binomial expansion formula and compute three terms with simple coefficients. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((3-x)^6 = 3^6 + 3^5 \times 6 \times (-x) + 3^4 \times \binom{6}{2} \times (-x)^2\) | M1 | For either the \(x\) term or \(x^2\) term; requires correct binomial coefficient in any form with correct power of \(x\) |
| \(= 729,\quad -1458x,\quad +1215x^2\) | B1, A1, A1 | B1 for 729; A1 for \(-1458x\) (simplified, \(x\) required); Final A1 c.a.o. for \(+1215x^2\) |
## Question 1:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(3-x)^6 = 3^6 + 3^5 \times 6 \times (-x) + 3^4 \times \binom{6}{2} \times (-x)^2$ | M1 | For either the $x$ term or $x^2$ term; requires correct binomial coefficient in any form with correct power of $x$ |
| $= 729,\quad -1458x,\quad +1215x^2$ | B1, A1, A1 | B1 for 729; A1 for $-1458x$ (simplified, $x$ required); Final A1 c.a.o. for $+1215x^2$ |
---\begin{enumerate}
\item Find the first 3 terms, in ascending powers of $x$, of the binomial expansion of
\end{enumerate}
$$( 3 - x ) ^ { 6 }$$
and simplify each term.\\
\hfill \mbox{\textit{Edexcel C2 2010 Q1 [4]}}