Higher June 2018 Unit 1 Q11
11. Given that \(y\) is directly proportional to \(\sqrt{x}\) and that \(y = 30\) when \(x = 36\),
(a) find an expression for \(y\) in terms of \(x\), [3]
(b) use the expression you found in part (a) to complete the following table. [2]
| \(x\) | 36 | 49 | |
|---|---|---|---|
| \(y\) | 30 | 40 |
| Scheme | Marks | Comments |
|---|---|---|
| \(y = k\sqrt{x}\) OR \(y^2 = cx\) | B1 | Allow \(y\) α \(k\sqrt{x}\). (\(y\) α \(\sqrt{x}\) is insufficient.) FT from expressions of the form \(k\) x \(x^{n}\) (n ≠ 1) (equivalent difficulty only) M1 implies B1 |
| 30 = \(k\) x 6 OR 30 = \(k\) x √36 OR \(k\) = 5 OR c = 25 | M1 | |
| \((y =)\ 5\sqrt{x}\) | A1 | May be seen (explicitly) in part (b). Do not allow equivalent e.g. \(y^2 = 25x\) unless \((y =)\ 5\sqrt{x}\) seen in part (b) |
| Scheme | Marks | Comments | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| B2 | B1 for one correct value. FT from any non-linear |