Higher November 2018 Paper 2 Q27
27 The point \(\left(3, \dfrac{1}{64}\right)\) lies on the curve \(\quad y = k^x \quad\) where \(k\) is a constant.
Show that the point \(\left(\dfrac{1}{2}, \dfrac{1}{2}\right)\) lies on the curve. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{1}{64} = k^3\) or \(\sqrt[3]{\dfrac{1}{64}}\) | M1 | oe equation in \(k\) |
| (\(k =\)) \(\dfrac{1}{4}\) or (\(k =\)) 0.25 | A1 | must see working for M1 implied by \(\quad y = \left(\dfrac{1}{4}\right)^x\) \(\left(\dfrac{1}{4}\right)^3 = \dfrac{1}{64}\) is M1A1 |
| \(\left(\dfrac{1}{4}\right)^{\frac{1}{2}} = \dfrac{1}{2}\) or \(0.25^{\frac{1}{2}} = 0.5\) | A1 | must see working for M1A1 allow \(\sqrt{\dfrac{1}{4}} = \dfrac{1}{2}\) or \(\sqrt{0.25} = 0.5\) |