| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2009 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Product of separate expansions |
| Difficulty | Standard +0.3 This is a standard C4 binomial expansion question requiring routine application of the generalised binomial theorem, followed by division of series (or multiplication by (1+x)^{-3}), and stating validity conditions. While it involves multiple parts and algebraic manipulation, it follows a predictable template with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
3 (i) Expand $( 1 + 2 x ) ^ { \frac { 1 } { 2 } }$ as a series in ascending powers of $x$, up to and including the term in $x ^ { 3 }$.\\
(ii) Hence find the expansion of $\frac { ( 1 + 2 x ) ^ { \frac { 1 } { 2 } } } { ( 1 + x ) ^ { 3 } }$ as a series in ascending powers of $x$, up to and including the term in $x ^ { 3 }$.\\
(iii) State the set of values of $x$ for which the expansion in part (ii) is valid.
\hfill \mbox{\textit{OCR C4 2009 Q3 [9]}}