| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Basic committee/group selection |
| Difficulty | Easy -1.2 This is a straightforward two-part question testing basic recall of combination notation and direct application of the binomial theorem. Part (i) is a simple calculation of 5C3 = 10, and part (ii) requires identifying the correct term in the binomial expansion using the formula, yielding coefficient 80. Both parts are routine textbook exercises requiring no problem-solving or insight, making this easier than average. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| (i) 0 www | 2 | M1 for \(\frac{5\times4\times3}{3\times2\times(1)}\) or \(\frac{5\times4}{2\times(1)}\) or for 1 5 10 10 5 1 seen |
| (ii) 80 www or ft \(8 \times\) their (i) | 2 | B2 for \(80x^3\); M1 for \(2^3\) or \((2x)^3\) seen |
## Question 11:
**(i)** 0 www | **2** | M1 for $\frac{5\times4\times3}{3\times2\times(1)}$ or $\frac{5\times4}{2\times(1)}$ or for 1 5 10 10 5 1 seen
**(ii)** 80 www or ft $8 \times$ their (i) | **2** | B2 for $80x^3$; M1 for $2^3$ or $(2x)^3$ seen | Total: **4**
---11 (i) Calculate ${ } ^ { 5 } \mathrm { C } _ { 3 }$.\\
(ii) Find the coefficient of $x ^ { 3 }$ in the expansion of $( 1 + 2 x ) ^ { 5 }$.
\hfill \mbox{\textit{OCR MEI C1 Q11 [4]}}