4MA0 Higher June 2017 Paper 3 Q15
15 \(P\) is directly proportional to \(r^3\)
\(P = 343\) when \(r = 3.5\)
Find a formula for \(P\) in terms of \(r\).
(3)
| Scheme | Marks |
|---|---|
| \(P = kr^3\) | M1 |
| \(343 = k \times 3.5^3\) oe or \(k = 8\) or \(m \times 343 = 3.5^3\) oe or \(m = 0.125\) oe | M1 |
| \(P = 8r^3\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: Allow \(mP = r^3\)
Do not allow \(P = r^3\)
M1: for correct substitution into a correct equation.
Implies first M1
A1: for \(P = 8r^3\) oe (\(P\) must be the subject)
(Award M2A0 for correct equation with \(r\) as subject given as final answer)
Award M2A1 if \(P = kr^3\) on the answer line and \(k\) evaluated as 8
Award M2A0 if \(P \propto 8r^3\) is given as final answer