June 2017 Paper 1 Q13
13 Solve \(\qquad x^{-\frac{1}{4}} = 0.2\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Handling the negative power first ... \(\dfrac{1}{x^{\frac{1}{4}}} = 0.2\) or \(\dfrac{1}{x^{\frac{1}{4}}} = \dfrac{1}{5}\) or \(\dfrac{1}{0.2} = x^{\frac{1}{4}}\) or \(5 = x^{\frac{1}{4}}\) or \(\dfrac{1}{\sqrt[4]{x}} = 0.2\) or \(\sqrt[4]{x} = \dfrac{1}{0.2}\) | M1 | Handling the 4th root first ... \(x^{-1} = 0.2^4\) or \(x = 0.2^{-4}\) |
| All of these are valid 2nd steps following any of the above 1st steps \(\dfrac{1}{x} = 0.2^4\) or \(\dfrac{1}{x} = \dfrac{1}{5^4}\) or \(x = 5^4\) or \(x = \dfrac{1}{0.2^4}\) or \(x = \left(\dfrac{1}{0.2}\right)^4\) | M1 | |
| (\(x\) =) 625 | A1 |
Additional guidance
The two method marks are for handling the negative power and for handling the 4th root ... and an error in one of the 1st steps does not mean that you cannot give credit for a correct 2nd step
eg \(-\sqrt[4]{x} = 0.2\) (incorrect) followed by \(x = 0.2^4 = 0.0016\) scores M0 M1
\(-\sqrt[4]{x} = 0.2\) (incorrect) followed by \(-x = 0.2^4 = 0.0016\), \(x = -0.0016\) is M0 M0 because the 4th power of \(-\sqrt[4]{x}\) would be a positive quantity
\(\dfrac{1}{0.0016}\) scores M1 M1 A0 0.0016 or \(\dfrac{1}{625}\) will score M1 M0 A0 unless other valid working seen