Higher November 2024 Paper 6 Q18
18 \(y\) is inversely proportional to \(x^2\).
Find the percentage decrease in \(y\) when \(x\) is increased by 25%. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 36 | 4 | M3 for \(\left(1 - \frac{1}{1.25^2}\right)\) [× 100] oe soi \(\frac{9}{25}\) oe or M2 for \(\frac{1}{1.25^2}\) [× 100] oe soi \(\frac{16}{25}\) oe or 64 or M1 for 1.25 [× 100] oe or for \(y = \frac{k}{x^2}\) oe | Alternative method following a valid combination of values where \(x_1^2 y_1 = k\) eg \(x_1 = 4\), \(y_1 = 10\), \(k = 160\) M3 for \(\frac{y_1 - y_2}{y_1}\) [×100] or M2 for \(\frac{\textit{their } k}{(1.25x_1)^2}\) soi or M1 for \(1.25x_1\) soi eg continued \(\frac{10 - 6.4}{10}\) [×100] \(\frac{160}{5^2}\) soi by 6.4 1.25 × 4 soi by 5 |