Specimen 2020 Paper 1 Q10
10 \(\mathrm{f}(x) = \left(\dfrac{9x}{2}\right)^{-1}\)
\(\mathrm{g}(x) = \sqrt{1 - px^3} \qquad\) where \(p\) is a constant.
Given that \(\ \mathrm{f}\left(\dfrac{1}{3}\right) = \mathrm{g}\left(\dfrac{1}{3}\right)\ \) work out the value of \(p\). [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{9}{2} \times \dfrac{1}{3}\) or \(\dfrac{3}{2}\) or \(\dfrac{2}{9x}\) | M1 | oe |
| \(\dfrac{2}{3}\) | A1 | |
| their \(\dfrac{2}{3} = \sqrt{1 - p \times \left(\dfrac{1}{3}\right)^3}\) | M1dep | oe |
| \(\left(\text{their } \dfrac{2}{3}\right)^2 = 1 - p \times \left(\dfrac{1}{3}\right)^3\) | M1dep | oe |
| 15 | A1 |