Higher June 2024 Paper 1R Q17
17
(a) \(\left(\sqrt[4]{k^{12}}\right)^5 = k^n\)
Find the value of \(n\) (1)
Find the value of \(n\) (1)
(b) Express \(\dfrac{7}{2 - \sqrt{3}}\) in the form \(\sqrt{c} + d\) where \(c\) and \(d\) are integers.
Show your working clearly. (3)
Show your working clearly. (3)
| Scheme | Marks |
|---|---|
| 15 | B1 |
| (1) |
Notes
B1: accept \(k^{15}\)
| Scheme | Marks |
|---|---|
| eg \(\dfrac{7(2 + \sqrt{3})}{(2 - \sqrt{3})(2 + \sqrt{3})}\) or \(\dfrac{7(-2 - \sqrt{3})}{(2 - \sqrt{3})(-2 - \sqrt{3})}\) | M1 |
eg \(\dfrac{14 + 7\sqrt{3}}{4 + 2\sqrt{3} - 2\sqrt{3} - 3}\) or \(\dfrac{14 + 7\sqrt{3}}{4 - 3}\) or \(\dfrac{14 + 7\sqrt{3}}{1}\) or \(\dfrac{-14 - 7\sqrt{3}}{-4 - 2\sqrt{3} + 2\sqrt{3} + 3}\) or \(\dfrac{-14 - 7\sqrt{3}}{-4 + 3}\) or \(\dfrac{-14 - 7\sqrt{3}}{-1}\) | M1 |
Working required Answer: \(\sqrt{147} + 14\) | A1 |
| (3) | |
| (4 marks) |
Notes
M1: for multiplying the numerator and denominator of the fraction by \(2 + \sqrt{3}\) or \(-2 - \sqrt{3}\)
M1: dep on previous M1
A1: dep on M2
SCB1 for \(\sqrt{147} + 14\) gained with no method marks awarded
SCB2 for \(\sqrt{147} + 14\) gained with 1st M1 awarded