OCR C4 2008 June — Question 5 8 marks

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2008
SessionJune
Marks8
PaperDownload PDF ↗
TopicGeneralised Binomial Theorem
TypeDirect quotient expansion
DifficultyStandard +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.
Spec1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions

5
  1. Show that \(\sqrt { \frac { 1 - x } { 1 + x } } \approx 1 - x + \frac { 1 } { 2 } x ^ { 2 }\), for \(| x | < 1\).
  2. By taking \(x = \frac { 2 } { 7 }\), show that \(\sqrt { 5 } \approx \frac { 111 } { 49 }\).

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]}}