Higher November 2022 Paper 1 Q19
19
(a) Work out the value of \(\quad \left(\dfrac{5}{4}\right)^{-2}\) [2 marks]
(b) Work out the value of \(\quad \left(\dfrac{9}{100}\right)^{\frac{3}{2}}\) [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\left(\dfrac{4}{5}\right)^2\) or \(\dfrac{4^2}{5^2}\) or \(\left(\dfrac{25}{16}\right)^{-1}\) or \(\dfrac{1}{\left(5/4\right)^2}\) or \(\dfrac{1}{5^2/4^2}\) or \(\left(\dfrac{1}{5/4}\right)^2\) or \(\dfrac{1}{25/16}\) or \(\dfrac{1/25}{1/16}\) | M1 | missing brackets must be recovered accept a correct decimal or mixed number for any fraction eg \(\dfrac{1}{1.25^2}\) |
| \(\dfrac{16}{25}\) | A1 | oe fraction or decimal |
Additional guidance
| Ignore any attempt to convert a correct fraction into a decimal | M1A1 |
| Answer | Mark | Comments |
|---|---|---|
| \(\left(\sqrt{\dfrac{9}{100}}\right)^3\) or \(\dfrac{3^3}{10^3}\) or \(\left(\dfrac{3}{10}\right)^3\) or \(\sqrt{\dfrac{9^3}{100^3}}\) or \(\sqrt{\left(\dfrac{9}{100}\right)^3}\) or \(\dfrac{\left(\sqrt{9}\right)^3}{\left(\sqrt{100}\right)^3}\) or \(\sqrt{\dfrac{729}{1\,000\,000}}\) or \(\dfrac{\sqrt{729}}{\sqrt{1\,000\,000}}\) | M1 | oe with 0.09 for \(\dfrac{9}{100}\) or 0.3 for \(\dfrac{3}{10}\) or \(3^2\) for 9 or \(10^2\) for 100 missing brackets must be recovered |
| \(\dfrac{27}{1000}\) or 0.027 | A1 |
Additional guidance
| Ignore any attempt to convert a correct fraction into a decimal | M1A1 |
| For M1 do not allow power \(\dfrac{1}{2}\) with no square root |