Higher November 2018 Paper 1 Q18
18. The intensity of a light source, \(I\) candela, is inversely proportional to the square of the distance, \(d\) metres, from the light source.
From a distance of 2 metres, a torch has a light intensity of 7 candela.
Find the light intensity of the torch from a distance of 4 metres. [5]
| Scheme | Marks | Comments |
|---|---|---|
| \(I \propto \dfrac{1}{d^2}\) or \(I = k \times \dfrac{1}{d^2}\) or equivalent | B1 | |
| \(7 = \dfrac{k}{2^2}\) | M1 | FT their equation providing it is non-linear |
| \(k = 28\) or \(I = \dfrac{28}{d^2}\) | A1 | FT their equation providing it is non-linear |
| \((I =)\ \dfrac{28}{4^2}\) | M1 | FT ‘their 28’ |
| \((I =)\ 1.75\) (candela) CAO | A1 | |
| (5) |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| \(7 \times 2^2\) seen or implied in later working | B1 | |
| Forms \(7 \times 2^2 = I \times 4^2\) | M2 | or M1 if one error |
| \(I = \dfrac{7\times4}{16}\) seen or implied; FT ‘their equation of equivalent difficulty’ | M1 | |
| \((I =)\ 1.75\) (candela) CAO | A1 |