Higher November 2024 Paper 5 Q21
21
(a) Work out.
\(\left(\dfrac{1}{8}\right)^{\frac{1}{3}}\) [1]
(b) \(2^x \times 4^y = 16\)
Show that \(y = 2 - \dfrac{x}{2}\). [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{1}{2}\) oe | 1 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(2^x \times 2^{2y} = 2^4\) | M2 | B1 for \(2^{2y}\) or \(2^4\) | For M2 accept equivalent work with all terms in other bases e.g. 4 Accept \((2^2)^y\) for \(2^{2y}\) Allow B1 for writing one other term correctly in base 4 or base 16 e.g. [\(2^x =\)] \(4^{\frac{x}{2}}\) or [\(4^y =\)] \(16^{\frac{y}{2}}\) |
| \(x + 2y = 4\) | M1 | M1 dep on M2 | For M1 accept correct equivalent equation |
| one further step leading to \(y = 2 - \frac{x}{2}\) | A1 | ||