Higher June 2018 Paper 1 Q11

(a) Expand and simplify \((2x - 1)(x + 3)(x - 5)\) (3)

(b) Solve \(3x^2 + 6x - 5 = 0\)
Show your working clearly.
Give your solutions correct to 3 significant figures. (3)

Mark scheme (a)

Scheme	Marks
\(2x^2 - x + 6x - 3\) or \(2x^2 + 5x - 3\) or \(x^2 + 3x - 5x - 15\) or \(x^2 - 2x - 15\) or \(2x^2 - 10x - x + 5\) or \(2x^2 - 11x + 5\)	M1
eg. \(2x^3 + 5x^2 - 3x - 10x^2 - 25x + 15\) or \(2x^3 - 4x^2 - 30x - x^2 + 2x + 15\) or \(2x^3 - 11x^2 + 5x + 6x^2 - 33x + 15\)	M1
\(2x^3 - 5x^2 - 28x + 15\)	A1
	(3)

M1: for expansion of any 2 of the 3 brackets (at least 3 of 4 terms correct)

M1: (dep) ft for at least half of their terms correct in second expansion (the correct number of terms must be present)

Mark scheme (a) (Alternative scheme)

Scheme	Marks
\(2x^3 - 10x^2 - x^2 + 5x + 6x^2 - 30x - 3x + 15\)	M2
\(2x^3 - 5x^2 - 28x + 15\)	A1

M2: for a complete expansion with 8 terms present, at least 4 of which must be correct

Mark scheme (b)

Scheme	Marks
\(\dfrac{-6 \pm \sqrt{96}}{6}\) or \(\dfrac{-6 \pm \sqrt{6^2 - -60}}{6}\) Accept 9.79 – 9.8(0) in place of \(\sqrt{96}\) NB: denominator must be 2 × 3 or 6 and there must be evidence for correct order of operations in the numerator	M2
0.633, −2.63	A1
	(3)
	(6 marks)

M2: If not M2 then award M1 for \(\dfrac{-6 \pm \sqrt{6^2 - 4 \times 3 \times -5}}{2 \times 3}\)

condone one sign error in substitution;

allow evaluation of individual terms e.g 36 in place of \(6^2\)

A1: dep on M1 for answers in range 0.63 to 0.633, −2.63 to −2.633
Award M2A1 for correct answer with correct working that would gain at least M1

Mark scheme (b) (Alternative scheme)

M1: for completing the square

M1: for correct method to isolate \(x\)

A1: dep on M1 for answer in range 0.63 to 0.633, −2.63 to −2.633
Award M2A1 for correct answer with correct working that would gain at least M1