Higher November 2018 Paper 2 Q21
21 \(y\) is inversely proportional to \(\sqrt{x}\)
\(y = 4 \quad\) when \(\quad x = 9\)
(a) Work out an equation connecting \(y\) and \(x\). [3 marks]
(b) Work out the value of \(y\) when \(\quad x = 25\) [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(y = \dfrac{k}{\sqrt{x}}\) | M1 | oe equation implied by \(\quad 4 = \dfrac{k}{\sqrt{9}}\) oe |
| (\(k =\)) \(4 \times \sqrt{9}\) or (\(k =\)) 12 | M1dep | oe |
| \(y = \dfrac{12}{\sqrt{x}}\) | A1 | oe equation |
| Alternative method 2 | ||
| \(ky = \dfrac{1}{\sqrt{x}}\) | M1 | oe equation implied by \(\quad 4k = \dfrac{1}{\sqrt{9}}\) oe |
| (\(k =\)) \(\dfrac{1}{\sqrt{9}} \div 4\) or (\(k =\)) \(\dfrac{1}{12}\) | M1dep | oe |
| \(\dfrac{1}{12}y = \dfrac{1}{\sqrt{x}}\) | A1 | oe equation |
Additional guidance
| Alt 1 (\(k =\)) 12 or (\(k \propto\)) 12 with no incorrect working | M1M1 |
| Condone use of \(\propto\) for up to M1M1A0 eg (Alt 1) \(y \propto \dfrac{k}{\sqrt{x}}\) M1 \(k \propto 12\) M1dep \(y \propto \dfrac{12}{\sqrt{x}}\) A0 | |
| \(y = \dfrac{12}{\sqrt{x}}\) oe | M1M1A1 |
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{12}{\sqrt{25}}\) or \(\dfrac{\text{their } k}{\sqrt{25}}\) | M1 | oe their \(k\) from (a) |
| 2.4 or \(\dfrac{12}{5}\) or \(2\dfrac{2}{5}\) | A1ft | ft \(\dfrac{\text{their } k}{5}\) |
Additional guidance
| \(y \propto 2.4\) | M1A0 |
| \(y = \dfrac{\frac{4}{3}}{\sqrt{x}}\) in (a) \(\dfrac{\frac{4}{3}}{\sqrt{25}}\) M1 \(\dfrac{4}{15}\) (allow [0.266, 0.267]) A1ft |