Higher June 2019 Paper 1 Q12
12.
(a) Find the value of each of the following.
(i) \(0{\cdot}8^{-1}\) [1]
(ii) \(625^{\frac{1}{4}}\) [1]
(iii) \(\left(\dfrac{1}{64}\right)^{\frac{2}{3}}\) [2]
(b) Write \(81\times\dfrac{3^0}{27^2}\) as a power of 3. [2]
(c) Simplify \(\dfrac{\left(5ab^4\right)^3}{a^2}\). [3]
| Scheme | Marks | Comments |
|---|---|---|
| (a)(i) \(\dfrac{5}{4}\) oe | B1 | Accept e.g. 1.25, \(\dfrac{10}{8}\) etc |
| (a)(ii) 5 | B1 | Accept \(\pm5\) |
| (a)(iii) Sight of \(\left(\dfrac{1}{4}\right)^2\) or \(\dfrac{1}{\sqrt[3]{4096}}\) oe | B1 | |
| \(\dfrac{1}{16}\) | B1 | Ignore attempts to convert the fraction to a decimal |
| Scheme | Marks | Comments |
|---|---|---|
| \(3^4\times\dfrac{3^0}{(3^3)^2}\) oe, si | B1 | |
| \(3^{-2}\) | B1 | a final answer of \(\dfrac{1}{9}\) or \(\dfrac{1}{3^2}\) without wrong working implies first B1 only |
| Scheme | Marks | Comments |
|---|---|---|
| \(125ab^{12}\) | B3 | Mark final answer B2 for any two elements of \(125ab^{12}\) correct in their final answer e.g. \(5^3ab^{12}\) or \(\dfrac{125a^3b^{12}}{a^2}\) or B1 for any one element of \(125ab^{12}\) correct in their final answer or for \(\dfrac{5^3a^3b^{12}}{a^2}\) seen at some stage |
| (9) |