Higher June 2024 Paper 1 Q20
20 \(2^x = \dfrac{2^n}{\sqrt[3]{2}} \qquad 2^y = \left(\sqrt{2}\right)^5\)
Given that \(x + y = 8\)
work out the value of \(n\). (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(5\dfrac{5}{6}\) | P1 | for \(2^x = 2^{n - \frac{1}{3}}\) or \(2^y = 2^{\frac{5}{2}}\) or \(x = n - \dfrac{1}{3}\) oe or \(y = \dfrac{5}{2}\) oe or for \((2^{x + y} =)\ \dfrac{2^n}{\sqrt[3]{2}} \times \left(\sqrt{2}\right)^5\) |
| P1 | for \(2^{x + y} = 2^{n - \frac{1}{3} + \frac{5}{2}}\) or \(x + y = n - \dfrac{1}{3} + \dfrac{5}{2}\) oe or \(\dfrac{11}{2} = n - \dfrac{1}{3}\) oe | |
| A1 | oe eg \(\dfrac{35}{6}\) |