| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2022 |
| Session | June |
| Marks | 3 |
| 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 factorial simplification and direct application of the binomial coefficient formula. Part (a) is trivial arithmetic (100!/98! = 100×99 = 9900), and part (b) requires only recognizing that the coefficient is C(100,98) = C(100,2) = 4950, using the same calculation. No problem-solving or insight required—pure routine recall and computation. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\frac{100!}{98!} = \frac{100 \times 99 \times 98!}{98!}\) | M1 | oe |
| \(= 9900\) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\left[_{100}C_{98}\right] = 4950\) | B1 | Allow for \(4950x^{98}\) seen |
## Question 2:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{100!}{98!} = \frac{100 \times 99 \times 98!}{98!}$ | M1 | oe |
| $= 9900$ | A1 | cao |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\left[_{100}C_{98}\right] = 4950$ | B1 | Allow for $4950x^{98}$ seen |
---2
\begin{enumerate}[label=(\alph*)]
\item Determine the value of $\frac { 100 ! } { 98 ! }$.
\item Find the coefficient of $x ^ { 98 }$ in the expansion of $( 1 + x ) ^ { 100 }$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 1 2022 Q2 [3]}}