| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2020 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Expand and state validity |
| Difficulty | Moderate -0.8 This is a straightforward application of the binomial expansion formula for fractional powers requiring recall of the standard formula and validity condition |x| < 1 (adjusted for the coefficient). The calculation is routine with minimal steps, making it easier than average but not trivial since it involves fractional indices. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(1 + \left(\frac{1}{2}\right)(4x) + \left(\frac{1}{2}\right)\left(-\frac{1}{2}\right)\frac{(4x)^2}{2!}\) | M1 | ignore extra terms, allow one error; if M0 allow SC2 for 2 of first three terms correct |
| \(1 + 2x - 2x^2\) isw cao | A1 | two of three terms correct |
| A1 | all three terms correct, ignore extra terms |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \( | x | < \frac{1}{4}\) oe |
## Question 6:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $1 + \left(\frac{1}{2}\right)(4x) + \left(\frac{1}{2}\right)\left(-\frac{1}{2}\right)\frac{(4x)^2}{2!}$ | M1 | ignore extra terms, allow one error; if M0 allow SC2 for 2 of first three terms correct |
| $1 + 2x - 2x^2$ isw cao | A1 | two of three terms correct |
| | A1 | all three terms correct, ignore extra terms |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $|x| < \frac{1}{4}$ oe | B1 | or $|x| \leq \frac{1}{4}$ oe |
---6
\begin{enumerate}[label=(\alph*)]
\item Find the first three terms in ascending powers of $x$ of the binomial expansion of $( 1 + 4 x ) ^ { \frac { 1 } { 2 } }$.
\item State the range of values of $x$ for which this expansion is valid.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2020 Q6 [4]}}