4400 Higher November 2010 Paper 4 Q15

EdexcelHigherOld spec6 marksStandard Form

(a) Work out \((9 \times 10^8) \times (4 \times 10^6)\)
Give your answer in standard form. (1)

(b) \(x = 7 \times 10^m\) and \(y = 5 \times 10^n\), where \(m\) and \(n\) are integers.

(i) It is given that \(xy = 3.5 \times 10^{12}\)
Show that \(m + n = 11\)

(ii) It is also given that \(\dfrac{x}{y} = 1.4 \times 10^{27}\)
Find the value of \(m\) and the value of \(n\).

(5)

Scheme	Marks
\(3.6 \times 10^{15}\)	B1
	(1)

Mark scheme (b)

Scheme	Marks
(i) Correct expression for \(xy\) stated or clearly implied with 7 × 5 evaluated eg \(35 \times 10^{m + n}\) \(3.5 \times 10^{(1)} \times 10^m \times 10^n\)	M1
States or clearly implies that \(xy = 3.5 \times 10^{m + n + 1}\) oe or \(3.5 \times 10^{(1)} \times 10^{m + n}\) oe or \(m + n + 1\)*	A1
(ii) \(m - n = 27\) oe	B1
\(2m = 38\) or \(2n = -16\)	M1
\(m = 19\) \(\quad n = -8\)	A1
	(5)
	(6 marks)

Notes

A1: SC If A1 not scored, award B1 for \(35 \times 10^{11}\) seen.
*dep on \((3.5 \times)\ 10^{(1)} \times 10^m \times 10^n = (3.5 \times)\ 10^{12}\)

B1: for \(m - n = 27\) oe inc \(m = n + 27\)

M1: Adding or subtracting \(m + n = 11\) and \(m - n = 27\)

A1: for both values correct
Award 3 marks for both values correct, unless clearly obtained by an incorrect method.