Moderate -0.3 This is a standard C4 binomial expansion question with routine application steps: extract the factor, apply the formula with fractional power, and state validity |x/4| < 1. Part (iii) requires recognizing 399 = 400 - 1 = 100(4 - 0.01), which is straightforward substitution. Slightly easier than average due to being a textbook-style multi-part question with clear signposting and no conceptual surprises.
5. (i) Expand \(( 4 - x ) ^ { \frac { 1 } { 2 } }\) in ascending powers of \(x\) up to and including the term in \(x ^ { 2 }\), simplifying each coefficient.
(ii) State the set of values of \(x\) for which your expansion is valid.
(iii) Use your expansion with \(x = 0.01\) to find the value of \(\sqrt { 399 }\), giving your answer to 9 significant figures.
5. (i) Expand $( 4 - x ) ^ { \frac { 1 } { 2 } }$ in ascending powers of $x$ up to and including the term in $x ^ { 2 }$, simplifying each coefficient.\\
(ii) State the set of values of $x$ for which your expansion is valid.\\
(iii) Use your expansion with $x = 0.01$ to find the value of $\sqrt { 399 }$, giving your answer to 9 significant figures.\\
\hfill \mbox{\textit{OCR C4 Q5 [9]}}