4400 Higher November 2007 Paper 3 Q19

EdexcelHigherOld spec9 marksDirect & Inverse Proportion

19 A wind turbine generates a power of \(P\) kilowatts when the wind speed is \(w\) m/s.
\(P\) is proportional to \(w^3\).
\(P = 300\) when \(w = 12\)

(a) Find a formula for \(P\) in terms of \(w\). (3)

(b) Calculate the value of \(P\) when \(w = 7.5\)
Give your answer correct to 3 significant figures. (2)

(c) When the wind speed is \(x\) m/s, the wind turbine generates twice as much power as it does when the wind speed is 10 m/s.
Calculate the value of \(x\).
Give your answer correct to 3 significant figures. (4)

Scheme	Marks
\(P = kw^3\)	M1
\(300 = k \times 12^3\)	M1
\(P = \frac{25}{144}w^3\)	A1
	(3)

Scheme	Marks
\(\text{“}\frac{25}{144}\text{”} \times 7.5^3\)	M1
73.2	A1ft
	(2)

Mark scheme (c)

Scheme	Marks
\(\text{“}\frac{25}{144}\text{”} \times 10^3\) (= 174)	M1
\(2 \times \text{“}\frac{25}{144}\text{”} \times 10^3 = \text{“}\frac{25}{144}\text{”} \times w^3\)	M1
\(\sqrt[3]{2000}\)	M1
12.6	A1
	(4)
	(9 marks)

Notes

M1: “\(\frac{25}{144}\)” can be \(k\)

M1: \(2 \times \text{“}174\text{”} = \text{“}0.174\text{”} \times w^3\) or \(2000 = w^3\)

M1: or \(10 \times \sqrt[3]{2}\) M3