4MA0 Higher June 2013 Paper 4 Q16
16 The pressure \(P\), of water leaving a cylindrical pipe, is inversely proportional to the square of the radius, \(r\), of the pipe.
\(P = 22.5\) when \(r = 2\)
(a) Find a formula for \(P\) in terms of \(r\). (3)
(b) Calculate the value of \(P\) when \(r = 1.5\) (1)
(c) Calculate the value of \(r\) when \(P = 10\) (2)
| Scheme | Marks |
|---|---|
| \(P = \text{“}k\text{”} / r^2\) | M1 |
| \(22.5 = \text{“}k\text{”} / 2^2\) | M1 |
| \(P = 90 / r^2\) | A1 |
| (3) |
Notes
M1: \(k \neq 1\)
M1: \(k \neq 1\)
| Scheme | Marks |
|---|---|
| 40 | B1 ft |
| (1) |
Notes
B1 ft: from “\(k\)” ÷ \(1.5^2\) \(k \neq 1\)
| Scheme | Marks |
|---|---|
\(10 = \text{“}k\text{”} / r^2\) \((r =)\ \sqrt{\text{“}k\text{”}/10}\) | M1 |
| 3 | A1 ft |
| (2) |
Notes
M1: \(k \neq 1\)
A1 ft: ignore ±