| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2015 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Multiply by polynomial |
| Difficulty | Standard +0.3 This is a straightforward application of the binomial expansion for negative/fractional powers followed by polynomial multiplication. Part (i) requires routine use of the formula (1+x)^n with n=-1/3, and stating the validity condition |2x|<1 is standard. Part (ii) involves multiplying the expansion by (1-3x) and collecting terms, which is mechanical algebra. Slightly above average difficulty due to the fractional power and two-part structure, but no novel insight required. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
**Question 3:** [2 marks]
Apply expression from line 51 with n=10 upper floors, p=7 people, answer to 2 d.p.3 (i) Find the first three terms of the binomial expansion of $\frac { 1 } { \sqrt [ 3 ] { 1 - 2 x } }$. State the set of values of $x$ for which\\
the expansion is valid. the expansion is valid.\\
(ii) Hence find $a$ and $b$ such that $\frac { 1 - 3 x } { \sqrt [ 3 ] { 1 - 2 x } } = 1 + a x + b x ^ { 2 } + \ldots$.
\hfill \mbox{\textit{OCR MEI C4 2015 Q3 [8]}}