4MA0 Higher January 2016 Paper 4 Q18
18 \(y\) is directly proportional to \(\sqrt{x}\)
When \(x = 49\), \(y = 4\)
(a) Find a formula for \(y\) in terms of \(x\). (3)
(b) Calculate the value of \(x\) when \(y = 12\) (2)
| Scheme | Marks |
|---|---|
| \(y = k\sqrt{x}\) or \(cy = \sqrt{x}\) | M1 |
| \(4 = k \times \sqrt{49}\) or \(4c = \sqrt{49}\) | M1 |
| \(y = \dfrac{4}{7}\sqrt{x}\) | A1 |
| (3) |
Notes
A1: Accept \(y = 0.571(1428)\sqrt{x}\)
Note: Award M2A1 if answer given is \(y = k\sqrt{x}\) with \(k\) evaluated as \(\dfrac{4}{7}\) in (a) or (b).
M2 for \(k = \dfrac{4}{7}\)
| Scheme | Marks |
|---|---|
| \(12 = \text{"}\dfrac{4}{7}\text{"} \times \sqrt{x}\) (\(\sqrt{x} = 21\)) | M1 |
| 441 | A1 |
| (2) |
Notes
M1: Allow ft if M1 scored in (a) but not if \(k = 1\)
A1: ft from \(12 = \text{"}\dfrac{4}{7}\text{"} \times \sqrt{x}\) but not if \(k = 1\)