4MA0 Higher January 2017 Paper 4R Q20
20 \((3 + \sqrt{c})(2\sqrt{c} - 3) = 1 + k\sqrt{c}\)
where \(c\) and \(k\) are prime numbers.
(a) Find the value of \(c\) and the value of \(k\). (3)
\[p^m = \frac{1}{p \times \sqrt[3]{p^2}}\]
(b) Find the value of \(m\). (3)
| Scheme | Marks |
|---|---|
| \(6\sqrt{c} - 9 + 2c - 3\sqrt{c}\) or \(3\sqrt{c} - 9 + 2c\) | M1 |
| \(c = 5\) | A1 |
| \(k = 3\) | B1 |
| (3) |
Notes
M1: Accept \(\sqrt{c}\sqrt{c}\) or \((\sqrt{c})^2\) instead of \(c\)
| Scheme | Marks |
|---|---|
| \(\dfrac{1}{p \times p^{\frac{2}{3}}}\) or \(p^{m + 1 + \frac{2}{3}} = 1\) | M1 |
| \(\dfrac{1}{p^{\frac{5}{3}}}\) or \(p^{-\frac{5}{3}}\) or \(m + 1 + \dfrac{2}{3} = 0\) | M1 |
| \(-\dfrac{5}{3}\) | A1 |
| (3) | |
| (6 marks) |
Notes
A1: \(p^{-\frac{5}{3}}\) gains M2 only