| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Standard binomial expansion coefficient |
| Difficulty | Easy -1.2 This is a straightforward C1 binomial theorem question requiring only direct application of the combination formula and the binomial expansion formula. Part (i) is pure recall/calculation of 8C3, and part (ii) is a standard textbook exercise with no problem-solving element—just substitute into the binomial coefficient formula with the given term. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| (i) | 2 | M1 for \(\frac{8\times7\times6}{3\times2\times1}\) or more simplified |
| (ii) \(-7\) or ft from \(-\frac{\text{their (i)}}{8}\) | 2 | M1 for 7 or ft their (i)/8 or for \(56\times(-1/2)^3\) o.e. or ft; condone \(x^3\) in answer or in M1 expression; 0 in qn for just Pascal's triangle seen |
## Question 14:
**(i)** | **2** | M1 for $\frac{8\times7\times6}{3\times2\times1}$ or more simplified
**(ii)** $-7$ or ft from $-\frac{\text{their (i)}}{8}$ | **2** | M1 for 7 or ft their (i)/8 or for $56\times(-1/2)^3$ o.e. or ft; condone $x^3$ in answer or in M1 expression; 0 in qn for just Pascal's triangle seen | Total: **4**
---14 (i) Find the value of ${ } ^ { 8 } \mathrm { C } _ { 3 }$.\\
(ii) Find the coefficient of $x ^ { 3 }$ in the binomial expansion of $\left( 1 - \frac { 1 } { 2 } x \right) ^ { 8 }$.
\hfill \mbox{\textit{OCR MEI C1 Q14 [4]}}