Higher January 2022 Paper 2R Q13
13 \(a = \sqrt{8} + 4\)
\(b = \sqrt{8} - 4\)
\((a - b)(a + b)\) can be written in the form \(y\sqrt{4y}\)
Find the value of \(y\)
Show your working clearly.
(3)
| Scheme | Marks |
|---|---|
\(\sqrt{8} + 4 - \left(\sqrt{8} - 4\right)(= 8)\) and \(\sqrt{8} + 4 + \left(\sqrt{8} - 4\right)\left(= 2\sqrt{8} = 4\sqrt{2}\right)\) or \((a + b)(a - b) = a^2 - b^2\) and \((\sqrt{8} + 4)^2 - (\sqrt{8} - 4)^2\) | M1 |
| \((\text{‘}{8}\text{’})(\text{‘}{2\sqrt{8}}\text{’})\) or \(\sqrt{2048}\) or \(16\sqrt{8}\) or \(32\sqrt{2}\) or \(8\sqrt{32}\) or \(8\sqrt{8 \times 4}\) oe | M1 |
| Working required Answer: 8 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for correct substitutions into expression for \(a + b\) and \(a - b\)
or expand the expression to get \(a^2 - b^2\) and substitute into this expression.
M1: (dep M1)
A1: (dep both M marks)