Foundation June 2024 Paper 2R Q22

EdexcelFoundationCurrent spec8 marksIndices Solving Simple Equations

(a) Solve \(\quad \dfrac{2f}{3} = 4f - 17\)
Show clear algebraic working. (3)

(b) Simplify \(\quad (e + 12)^0\) where \(e \gt 0\) (1)

(d) Factorise fully \(\quad 20x^5y + 12x^3y^4\) (2)

Mark scheme (a)

Scheme	Marks
eg \(2f = 12f - 51\) or \(\dfrac{f}{3} = \dfrac{4}{2}f - \dfrac{17}{2}\) or \(\dfrac{f}{3} = 2f - \dfrac{17}{2}\) or \(0.3f = 2f - 8.5\) or \(f = 6f - \dfrac{51}{2}\) or \(f = 6f - 25.5\) or \(17 = 4f - \dfrac{2}{3}f\) or \(17 = 4f - 0.6f\) or \(17 = 4f - 0.7f\) or \(\dfrac{2}{3}f - 4f = -17\) or \(0.6f - 4f = -17\) or \(0.7f - 4f = -17\)	M1
eg \(-10f = -51\) or \(10f = 51\) or \(\dfrac{5f}{3} = \dfrac{17}{2}\) or \(5f = \dfrac{51}{2}\) or \(17 = \dfrac{10f}{3}\) or \(3.3f = 17\) or \(-\dfrac{10f}{3} = -17\) or \(-3.3f = -17\)	M1
Working required Answer: \(\dfrac{51}{10}\)	A1
	(3)

Notes

M1: for a correct first step – multiplying both sides by 3 correctly and expanding to find \(2f = 12f - 51\) or \(2f = -51 + 12f\) or writing the RHS as 2 terms each over 2
(Allow decimals to 1dp or better – rounded or truncated)

M1: for a correct 2 term equation in the form \(af = b\)
ft the following equations only \(2f = 12f - 17\) oe, \(2f = 4f - 51\) oe, \(6f = 12f - 51\) oe
(Allow decimals to 1dp or better – rounded or truncated)

A1: (dep on at least M1) oe

Scheme	Marks
1	B1
	(1)

Mark scheme (c)

Scheme	Marks
\(3a^3h^4\)	B2
	(2)

Notes

B2: for \(3a^3h^4\) oe

B1 for a product in the form \(ka^ph^q\) where 2 from \(k\), \(p\) or \(q\) are correct (allow multiplication signs) eg \(5a^3h^4\) or \(\dfrac{12a^3h^4}{4}\) (Allow \(3a^3\) or \(a^3h^4\) or \(3h^4\) as long as not added to any other term)

Mark scheme (d)

Scheme	Marks
\(4x^3y(5x^2 + 3y^3)\)	B2
	(2)
	(8 marks)

Notes

B2: for \(4x^3y(5x^2+3y^3)\)
B1 for any correct factorisation with at least a 2 term factor outside the bracket eg \(2x^3y(10x^2 + 6y^3)\) or \(x^3y(20x^2 + 12y^3)\) or \(2x(10x^4y + 6x^2y^4)\) or \(4y(5x^5 + 3x^3y^3)\) or \(4x^3(5x^2y + 3y^4)\) etc or the correct highest common factor and a 2 term expression with at most one incorrect term eg \(4x^3y(5x^2 + \ldots)\) or \(4x^3y(\ldots + 3y^3)\)