| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2007 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Expand and state validity |
| Difficulty | Moderate -0.5 This is a straightforward application of the binomial theorem for fractional powers requiring recall of the formula and basic algebraic manipulation. The validity condition (|3x| < 1) follows directly from the standard rule. While it involves a fractional index, it's a routine textbook exercise with no problem-solving or novel insight required, making it slightly easier than average. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
Find the first four terms in the binomial expansion of $(1+3x)^{-1/3}$.
State the range of values of $x$ for which the expansion is valid. [5]5 Find the first four terms in the binomial expansion of $( 1 + 3 x ) ^ { \frac { 1 } { 3 } }$.\\
State the range of values of $x$ for which the expansion is valid.
\hfill \mbox{\textit{OCR MEI C4 2007 Q5 [5]}}