Higher June 2023 Paper 2 Q15

EdexcelHigherCurrent spec7 marksIndices Solving Simple Equations

(a) Simplify fully \(\quad \left(32a^{15}\right)^{\frac{3}{5}}\) (2)

(b) Express \(\;\left(\dfrac{1}{10x}\right)^{-3}\;\) in the form \(\;px^n\;\) where \(p\) and \(n\) are integers. (2)

Scheme	Marks
\(8a^9\)	B2
	(2)

Mark scheme (b)

Scheme	Marks
\(1000x^3\)	B2
	(2)

B2: for a fully correct answer.

(B1 for final answer or final line of working with: 1000 or \(x^3\) as part of a product or \((10x)^3\) or \(\dfrac{1}{1000x^3}\) )

Mark scheme (c)

Scheme	Marks
eg \(30 \times \dfrac{1 - 2y}{3} = 30 \times \dfrac{4}{5} - 30 \times \dfrac{2y - 1}{2}\) oe or eg \(\dfrac{10(1 - 2y)}{30} = \dfrac{6 \times 4}{30} - \dfrac{15(2y - 1)}{30}\) oe or eg \(\dfrac{1 - 2y}{3} = \dfrac{2 \times 4}{10} - \dfrac{5(2y - 1)}{10}\) oe or eg \(10(1 - 2y) = 3 \times 2 \times 4 - 3 \times 5(2y - 1)\) oe or eg \(\dfrac{10(1 - 2y) + 15(2y - 1)}{30} = \dfrac{4}{5}\) or \(\dfrac{2(1 - 2y)}{6} + \dfrac{3(2y - 1)}{6} = \dfrac{4}{5}\) oe (as above)	M1
eg \(10 - 20y = 24 - 30y + 15\) oe eg \(10y = 29\) or \(50 - 100y + 150y - 75 = 120\) oe or \(10 - 20y + 30y - 15 = 24\) oe \(2 - 4y + 6y - 3 = 4.8\)	M1
Working required Answer: 2.9	A1
	(3)
	(7 marks)

M1: For clear intention to multiply all terms by 30 (or 3 × 5 × 2) or a multiple of 30 oe in an equation

or to express all terms over 30 (or 3 × 5 × 2) or a multiple of 30 oe in an equation

writing RHS over 10 or a multiple of 10 or ‘cross multiplying’ in an equation

bringing terms in \(y\) on LHS side and leaving \(\dfrac{4}{5}\) on RHS and writing terms on LHS over 6 or a multiple of 6 in an equation

[if expanded numerators, allow one error]

M1: (ft if only one error)
Expanding brackets and multiplying by denominator with no more than one error in total

A1: oe eg \(\dfrac{29}{10}\) or \(2\dfrac{9}{10}\) dep on M2