| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Standard binomial expansion coefficient |
| Difficulty | Easy -1.2 Both parts are direct applications of standard techniques: (i) requires simple polynomial multiplication and collecting terms, (ii) is a routine binomial coefficient calculation using the formula. These are textbook exercises testing basic recall and arithmetic with minimal problem-solving required, making them easier than average A-level questions. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(x^3\) | 2 | Ignore any other terms in expansion; M1 for \(-3[x^3]\) and \(7[x^3]\) soi |
| (ii) \(x^2\) www | 3 | M1 for \(\frac{7\times6}{2}\) or 21 or for Pascal's triangle seen with 1 7 21 … row and M1 for \(2^2\) or 4 or \(\{2x\}^2\) |
## Question 12:
**(i)** $x^3$ | **2** | Ignore any other terms in expansion; M1 for $-3[x^3]$ and $7[x^3]$ soi
**(ii)** $x^2$ www | **3** | M1 for $\frac{7\times6}{2}$ or 21 or for Pascal's triangle seen with 1 7 21 … row and M1 for $2^2$ or 4 or $\{2x\}^2$ | Total: **5**
---12 (i) Find the coefficient of $x ^ { 3 }$ in the expansion of $\left( x ^ { 2 } - 3 \right) \left( x ^ { 3 } + 7 x + 1 \right)$.\\
(ii) Find the coefficient of $x ^ { 2 }$ in the binomial expansion of $( 1 + 2 x ) ^ { 7 }$.
\hfill \mbox{\textit{OCR MEI C1 Q12 [5]}}