4MA0 Higher January 2014 Paper 3 Q14

EdexcelHigherOld spec5 marksDirect & Inverse Proportion

14 \(D\) is directly proportional to \(t^2\)
When \(t = 4\), \(D = 8\)

(a) Find a formula for \(D\) in terms of \(t\). (3)

(b) Find the positive value of \(t\) when \(D = 50\) (2)

Mark scheme (a)

Scheme	Marks
\(D = kt^2\)	M1
\(8 = k \times 16\) oe or \(8 = k \times 4^2\)	M1
\(D = \frac{1}{2}t^2\)	A1
	(3)

Notes

M1: for \(D = kt^2\) but not for \(D = t^2\)

A1: for \(D = \frac{1}{2}t^2\) oe with \(D\) the subject
Award 3 marks if answer is \(D = kt^2\) and \(k\) is evaluated as \(\frac{1}{2}\) in part (a) or part (b)

Scheme	Marks
\(t^2 = 100\)	M1
10	A1
	(2)
	(5 marks)