4MA0 Higher January 2015 Paper 3R Q20
20 \(R\) is inversely proportional to the square of \(c\).
When \(c = 4\), \(R = 30\)
(a) Find a formula for \(R\) in terms of \(c\). (3)
(b) Calculate the positive value of \(c\) when \(R = 1920\) (2)
| Scheme | Marks |
|---|---|
| \(R = \dfrac{k}{c^2}\) | M1 |
| \(30 = \dfrac{k}{4^2}\) or \(k = 480\) oe | M1 |
| \(R = \dfrac{480}{c^2}\) oe | A1 |
| (3) |
Notes
M1: for \(R = \dfrac{k}{c^2}\) but not for \(R = \dfrac{1}{c^2}\)
Also award for correct equation in \(R\), \(c^2\) and a constant or for \(R\) = numerical value ÷ \(c^2\)
M1: for \(30 = \dfrac{k}{4^2}\) or for correct substitution into an equation which scores the first method mark (may be implied by correct evaluation of the constant)
A1: Award 3 marks if answer is \(R = \dfrac{k}{c^2}\) but \(k\) is evaluated in part (b). SCB2 for correct formula for \(c\) in terms of \(R\).
| Scheme | Marks |
|---|---|
| \(c^2 = \dfrac{480}{1920}\) or \(c^2 = \dfrac{30}{1920} \times 4^2\) | M1ft |
| 0.5oe | A1 |
| (2) | |
| (5 marks) |
Notes
M1ft: for substitution and rearrangement into form \(c^2 = \dfrac{k}{1920}\) with their value of \(k\) substituted except for \(k = 1\)
A1: accept ±0.5