4MA0 Higher June 2015 Paper 4R Q14
14 \(V\) is inversely proportional to the square of \(t\)
\(V = 28\) when \(t = 2.5\)
(a) Express \(V\) in terms of \(t\) (3)
(b) Work out the value of \(V\) when \(t = 6.25\) (2)
| Scheme | Marks |
|---|---|
| \(V = \dfrac{k}{t^2}\) | M1 |
\(28 = \dfrac{k}{2.5^2}\) oe or \(k = 28 \times 2.5^2\) or \(k = 175\) | M1 |
| \(V = \dfrac{175}{t^2}\) | A1 |
| (3) |
Notes
M1: Allow \(Vt^2 = k\) or \(t^2 = \dfrac{k}{V}\)
Do not allow \(V = \dfrac{1}{t^2}\)
M1: For correct substitution in a correct equation
Implies first M1
Award M2 if k = 175 stated unambiguously in (a) or (b)
A1: Only award if \(V\) is the subject.
Award M2A1 if \(V = \dfrac{k}{t^2}\) on answer line and \(k\) evaluated as 175 in part (a) or part (b)
| Scheme | Marks |
|---|---|
| \(V = \dfrac{\text{"}175\text{"}}{6.25^2}\) | M1 |
| 4.48 | A1 |
| (2) |
Notes
M1: ft for \(k\) if \(k \gt 1\)