4MA0 Higher January 2014 Paper 3 Q14
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)
| 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) |
Notes
M1: ft from \(kt^2 = 50\) with \(k \ne 1\)
A1: Also accept \(\pm 10\)