| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2008 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Multiply by polynomial |
| Difficulty | Moderate -0.3 This is a straightforward application of the binomial expansion for negative/fractional powers followed by polynomial multiplication. Part (i) is standard bookwork requiring the formula with n=-1/2, and part (ii) simply multiplies the result by (1+2x). The validity condition |2x|<1 is routine. This is slightly easier than average as it follows a predictable template with no problem-solving insight required. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
| Answer | Marks | Guidance |
|---|---|---|
| 100th term is therefore even | M1 A1 | for reason; www |
Even, odd, odd, even, odd, odd recurs
100th term is therefore even | M1 A1 | for reason; www2 (i) Find the first three terms in the binomial expansion of $\frac { 1 } { \sqrt { 1 - 2 x } }$. State the set of values of $x$ for which the expansion is valid.\\
(ii) Hence find the first three terms in the series expansion of $\frac { 1 + 2 x } { \sqrt { 1 - 2 x } }$.
\hfill \mbox{\textit{OCR MEI C4 2008 Q2 [8]}}