Higher June 2023 Paper 2 Q19

EdexcelHigherCurrent spec3 marksCompleting the Square

19 Express \(\;3x^2 - 6x + 5\;\) in the form \(\;a(x - b)^2 + c\)

(3)

Mark scheme

Scheme	Marks
\(3(x^2 - 2x)\)….. or \(3(x^2 - 2x + \ldots..)\) oe or	M1
\(3(x - 1)^2\)…… or \(3\left[(x - 1)^2 \ldots\ldots\right]\) oe	M1
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(3(x - 1)^2 + 2\)	A1
	(3)
	(3 marks)

M1: (where …… is any number or no number)

A1: (if student continues to solve a quadratic equation, ISW)

Scheme	Marks
\(ax^2 - 2abx + ab^2 + c\)	M1
Any 2 of the following: \(a = 3\) or \(2ab = 6\) or \(ab^2 + c = 5\) oe	M1
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(3(x - 1)^2 + 2\)	A1
	(3 marks)

M1: for multiplying out \(a(x - b)^2 + c\) to obtain \(ax^2 - 2abx + ab^2 + c\) oe

M1: for equating coefficients with any 2 of \(a = 3\) or \(2ab = 6\) or \(ab^2 + c = 5\) oe seen

A1: (if student continues to solve a quadratic equation, ISW)