October 2020 Paper 2 Q6

OCR MEICurrent spec4 marksBinomial Expansion

(a) Find the first three terms in ascending powers of \(x\) of the binomial expansion of \((1 + 4x)^{\frac{1}{2}}\). [3]

(b) State the range of values of \(x\) for which this expansion is valid. [1]

Mark scheme (a)

Scheme	Marks	AO
\(1 + \left(\frac{1}{2}\right)(4x) + \left(\frac{1}{2}\right)\left(-\frac{1}{2}\right)\dfrac{(4x)^2}{2!}\)	M1	2.1
\(1 + 2x - 2x^2\) isw cao	A1 A1	1.1 1.1
	[3]

M1: ignore extra terms, allow one error

A1: two of three terms correct

A1: all three terms correct, ignore extra terms

if M0 allow SC2 for 2 of first three terms correct

Scheme	Marks	AO
\(\|x\| < \dfrac{1}{4}\) oe	B1	1.1
	[1]