Higher June 2023 Paper 1 Q15

EdexcelHigherCurrent spec6 marksIndices

(a) \(\sqrt{2} \div \dfrac{8^3}{16^{\frac{3}{2}}} = 2^n\)

Work out the value of \(n\)
Show your working clearly. (3)

(b) Find 4% of \(\;4.5 \times 10^{157}\)
Give your answer in standard form. (3)

Mark scheme (a)

M1: for one of \(\sqrt{2} = 2^{\frac{1}{2}}\) or \(8^3 = 2^9\) or \(16^{\frac{3}{2}} = 2^6\)

M1: for all of

\(\sqrt{2} = 2^{\frac{1}{2}}\) and \(8^3 = 2^9\) and \(16^{\frac{3}{2}} = 2^6\)

OR \(2^{\frac{1}{2}} \div 2^3\)

A1: oe, dep on M1

Mark scheme (b)

Scheme	Marks
\(0.04 \times 4.5 \times 10^{157}\) oe	M1
\(4 \times 10^{-2} \times 4.5 \times 10^{157}\) (= \(18 \times 10^{155}\)) or \(0.18 \times 10^{157}\) oe	M1
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(1.8 \times 10^{156}\)	A1
	(3)
	(6 marks)

A1: SCB1 for \(18 \times 10^{156} = 1.8 \times 10^{157}\)
or \(18 \times 10^{157} = 1.8 \times 10^{158}\)