4MA0 Higher January 2017 Paper 3R Q11

EdexcelHigherOld spec8 marksIndices Simultaneous Equations

(a) Solve \[\begin{aligned} 7x + 2y &= 16 \\ 5x - 2y &= 20 \end{aligned}\] Show clear algebraic working. (3)

(b) Expand and simplify \(\;(k + 9)(k - 5)\) (2)

Mark scheme (a)

Scheme	Marks
e.g. \(12x = 36\) or \(24y = -60\)	M1
e.g. 7 × “3” + \(2y\) = 16 or \(7x + 2 \times -2.5 = 16\)	M1
\(x = 3\) oe, \(y = -2.5\)	A1
	(3)

Notes

M1: for addition of given equations or a complete method to eliminate \(y\) or \(x\) (condone one arithmetic error)

M1: (dep) for method to find second variable

A1: dep on M1 for both values correct.
NB. Candidates showing no working score zero

Mark scheme (b)

Scheme	Marks
\(k^2 + 9k - 5k - 45\)	M1
\(k^2 + 4k - 45\)	A1
	(2)

Notes

M1: for 3 terms correct or all 4 terms correct ignoring signs or
\(k^2 + 4k + \ldots\) or … \(+ 4k - 45\)
(corrected from the printed mark scheme: “\(y^2 + 4k + \ldots\)”)

Mark scheme (c)

Scheme	Marks
eg \(\left(\dfrac{1}{8x^6y^3}\right)^{-\frac{1}{3}}\) or \(\left(\dfrac{8x^6y^8}{y^5}\right)^{\frac{1}{3}}\) or \(\left(\dfrac{y^{\frac{-5}{3}}}{0.5x^{-2}y^{\frac{-8}{3}}}\right)\) oe	M1oe
eg \((8x^6y^3)^{\frac{1}{3}}\) or \(\left(\dfrac{1}{8^{\frac{-1}{3}}x^{-2}y^{-1}}\right)\) or \(\left(\dfrac{2x^2y^{\frac{8}{3}}}{y^{\frac{5}{3}}}\right)\) oe	M1oe
\(2x^2y\)	A1oe
	(3)
	(8 marks)

Notes

M1oe: any one of
correct simplification of \(y\) term or
reciprocal or
cube root of at least all variables

M1oe: any two of
correct simplification of \(y\) term or
reciprocal or
cube root of at least all variables

A1oe: e.g. \(\left(\dfrac{y}{0.5x^{-2}}\right)\) SCB2 for \(\left(\dfrac{1}{2x^2y}\right)\) or \(ax^ny^m\) with 2 of \(a = 2\), \(n = 2\), \(m = 1\)

NB: do not accept decimal powers unless recurring dot is shown