4400 Higher June 2008 Paper 3 Q17
17 The distance, \(d\) kilometres, of the horizon from a person is directly proportional to the square root of the person’s height, \(h\) metres, above sea level.
When \(h = 225\), \(d = 54\)
(a) Find a formula for \(d\) in terms of \(h\). (3)
(b) Calculate the distance of the horizon from a person whose height above sea level is 64 metres. (1)
(c) Calculate the height above sea level of a person, when the distance of the horizon is 61.2 kilometres. (2)
| Scheme | Marks |
|---|---|
| \(d = k\sqrt{h}\) | M1 |
| \(54 = 15k\) | M1 |
| \(3.6\sqrt{h}\) oe | A1 |
| (3) |
Notes
M1: for \(d = k\sqrt{h}\) but not for \(d = \sqrt{h}\)
Also award for \(d =\) some numerical value \(\times \sqrt{h}\)
M1: for \(54 = 15k\)
Also award for \(54 = k\sqrt{225}\)
A1: for \(3.6\sqrt{h}\) oe
Award 3 marks if answer is \(d = k\sqrt{h}\) but \(k\) is evaluated as 3.6 oe in any part
| Scheme | Marks |
|---|---|
| 28.8 | B1 |
| (1) |
Notes
B1: ft from “3.6” × 8 except for \(k = 1\), if at least M1 scored in (a) (1 d.p. accuracy or better in follow through)
| Scheme | Marks |
|---|---|
| \(\sqrt{h} = \dfrac{61.2}{\text{“}3.6\text{”}}\) | M1 |
| 289 | A1 |
| (2) | |
| (6 marks) |
Notes
M1: for \(\sqrt{h} = \dfrac{61.2}{\text{“}3.6\text{”}}\) except for \(k = 1\)
A1: cao