| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2008 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Direct quotient expansion |
| Difficulty | Standard +0.3 This is a straightforward application of the binomial expansion requiring students to expand (1+x)^(-1/2) and (1-x)^(1/2), multiply the series, and then substitute a specific value. While it involves multiple steps and careful algebraic manipulation, it follows a standard template for C4 binomial questions with no 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 |
5 (i) Show that $\sqrt { \frac { 1 - x } { 1 + x } } \approx 1 - x + \frac { 1 } { 2 } x ^ { 2 }$, for $| x | < 1$.\\
(ii) By taking $x = \frac { 2 } { 7 }$, show that $\sqrt { 5 } \approx \frac { 111 } { 49 }$.
\hfill \mbox{\textit{OCR C4 2008 Q5 [8]}}