Higher November 2018 Paper 1 Q14
14
(a) Work out the value of \(\left(\dfrac{16}{81}\right)^{\frac{3}{4}}\) (2)
\(3^a = \dfrac{1}{9} \qquad 3^b = 9\sqrt{3} \qquad 3^c = \dfrac{1}{\sqrt{3}}\)
(b) Work out the value of \(a + b + c\) (2)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{8}{27}\) | M1 | for showing the 4th root of 16 as 2 and the 4th root of 81 as 3 or \(\dfrac{8}{n}\ (n \neq 27)\) or \(\dfrac{n}{27}\ (n \neq 8)\) or an intention to find the 4th root and cube, eg. \(\sqrt[4]{\left(\dfrac{16}{81}\right)^3}\) or \(\left(\sqrt[4]{\dfrac{16}{81}}\right)^3\) oe |
| A1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| 0 | M1 | for writing \(\dfrac{1}{9} = 3^{-2}\), \(9\sqrt{3} = 3^{2.5}\), \(\dfrac{1}{\sqrt{3}} = 3^{-0.5}\) as powers of 3, with at least 2 correct or for working out \(\dfrac{1}{9} \times 9\sqrt{3} \times \dfrac{1}{\sqrt{3}} = 1\) |
| A1 | cao |