| 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 This is a straightforward two-part question testing basic binomial theorem recall. Part (i) is direct calculation of a binomial coefficient, and part (ii) requires identifying the correct term in a standard binomial expansion with simple substitution. Both are routine textbook exercises requiring minimal problem-solving, making this easier than average for A-level. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 10 cao | 1 | [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(-720\ [x^3]\) | 4 marks total | Condone \(-720x\) etc; allow equivalent marks for the \(x^3\) term as part of a longer expansion |
| B3 for 720 \([x^3]\) or for \(10 \times 9 \times -8\ [x^3]\) | B3 | |
| or M2 for \(10 \times 3^2 \times (-2)^3\) oe or ft from (i) | M2 | e.g. M2 for \(3^5\left(\ldots10\times\left(\frac{-2}{3}\right)^3\ldots\right)\) or M1 for \(10\times\left(\frac{-2}{3}\right)^3\) etc |
| or M1 for two of these three elements correct or ft; condone \(x\) still included | M1 |
## Question 5(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| 10 cao | 1 | [1] |
---
## Question 5(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $-720\ [x^3]$ | 4 marks total | Condone $-720x$ etc; allow equivalent marks for the $x^3$ term as part of a longer expansion |
| B3 for 720 $[x^3]$ or for $10 \times 9 \times -8\ [x^3]$ | B3 | |
| or M2 for $10 \times 3^2 \times (-2)^3$ oe or ft from (i) | M2 | e.g. M2 for $3^5\left(\ldots10\times\left(\frac{-2}{3}\right)^3\ldots\right)$ or M1 for $10\times\left(\frac{-2}{3}\right)^3$ etc |
| or M1 for two of these three elements correct or ft; condone $x$ still included | M1 | |
---5 (i) Evaluate ${ } ^ { 5 } \mathrm { C } _ { 3 }$.\\
(ii) Find the coefficient of $x ^ { 3 }$ in the expansion of $( 3 - 2 x ) ^ { 5 }$.
\hfill \mbox{\textit{OCR MEI C1 Q5 [5]}}