Higher June 2019 Paper 1 Q18
18
(a) Express \(\sqrt{3} + \sqrt{12}\) in the form \(a\sqrt{3}\) where \(a\) is an integer. (2)
(b) Express \(\left(\dfrac{1}{\sqrt{3}}\right)^7\) in the form \(\dfrac{\sqrt{b}}{c}\) where \(b\) and \(c\) are integers. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(3\sqrt{3}\) | M1 | for working unambiguously with \(\sqrt{12}\), eg \(\sqrt{4 \times 3}\) or \(\sqrt{4} \times \sqrt{3}\) or \(2\sqrt{3}\) |
| A1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{\sqrt{3}}{81}\) | M1 | for simplifying the power eg \((\sqrt{3})^7 = 27\sqrt{3}\) |
| M1 | for method to rationalise the denominator eg multiplying by \(\dfrac{\sqrt{3}}{\sqrt{3}}\) | |
| A1 | for \(\dfrac{\sqrt{3}}{81}\) or equivalent fraction in form \(\dfrac{\sqrt{b}}{c}\), eg \(\dfrac{\sqrt{2187}}{2187}\) |
Additional guidance
May be seen as the first step