Foundation June 2024 Paper 1R Q22

EdexcelFoundationCurrent spec9 marksFactorising Linear Inequalities

(a) Simplify \(\quad g^9 \div g^2\) (1)

(b) Expand \(\quad 5k^2(k^3 + 4)\) (2)

(c)

(i) Factorise \(\quad x^2 - 2x - 63\) (2)

(ii) Hence, solve \(\quad x^2 - 2x - 63 = 0\) (1)

(d) Solve the inequality \(\quad 7 - 2y \lt 3y - 12\) (3)

Scheme	Marks
\(g^7\)	B1
	(1)

Scheme	Marks
\(5k^5 + 20k^2\)	B2
	(2)

Mark scheme (c)

Scheme	Marks
(i) \((x \pm 7)(x \pm 9)\)	M1
Correct answer scores full marks (unless from obvious incorrect working) Answer: \((x + 7)(x - 9)\)	A1
(ii) Answer: –7, 9	B1
	(3)

Notes

M1: for \((x \pm 7)(x \pm 9)\)
or for \((x + a)(x + b)\) where \(ab = -63\) or \(a + b = -2\) where \(a\) and \(b\) are integers

A1: for correct factors

B1: must ft from (c)(i) dep on factorising in the form \((x + p)(x + q)\) where \(p\) and \(q\) are integers

Mark scheme (d)

Scheme	Marks
\(-2y - 3y \lt -12 - 7\) or \(7 + 12 \lt 3y + 2y\) or \(7 \lt 5y - 12\) or \(7 - 5y \lt -12\) or \(-2y \lt 3y - 19\) or \(19 - 2y \lt 3y\)	M1
\(-5y \lt -19\) or \(19 \lt 5y\) or \(-y \lt \dfrac{-19}{5}\) or \(y \lt \dfrac{19}{5}\) or \(y = \dfrac{19}{5}\) oe	M1
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(y \gt \dfrac{19}{5}\)	A1
	(3)
	(9 marks)

Notes

M1: for rearrangement with \(y\) terms on one side and numerical terms on the other in a correct inequality or the correct simplification of \(y\) terms or numbers on one side in a correct inequality

sign can be = or the incorrect inequality sign

M1: for the correct simplification of \(y\) terms on one side and numbers on the other side in a correct inequality or a correct inequality with the wrong sign

sign can be = or the incorrect inequality sign

A1: oe eg \(y \gt 3.8\) or \(3.8 \lt y\)
Must be given as the correct inequality on the answer line