Higher November 2024 Paper 2 Q14
14 Given that \(\dfrac{3^{2n + 3}}{3^4} = 3^3 \times 3^{1 - 2n}\)
find the value of \(n\)
Show your working clearly.
(3)
| Scheme | Marks |
|---|---|
eg \(3^{2n + 3 - 4}\left(= 3^3 \times 3^{1 - 2n}\right)\) or \(3^{2n - 1}\left(= 3^3 \times 3^{1 - 2n}\right)\) or \(\left(3^{2n + 3} =\right) 3^7 \times 3^{1 - 2n}\) or \(\left(\dfrac{3^{2n + 3}}{3^4} =\right) 3^{4 - 2n}\) or \(\left(3^{2n + 3} =\right) 3^3 \times 3^{5 - 2n}\) or \(\dfrac{3^{2n}}{3^4} = 3^{1 - 2n}\) (division by 3³) This is not an exhaustive list or \(2n + 3 - 4\) (= ….) or (… =) \(3 + 1 - 2n\) or \(2n - 1\) (=…) or (... =) \(4 - 2n\) (no other options for this) | M1 |
| eg \(3^{2n + 3 - 4} = 3^{3 + 1 - 2n}\) or \(3^{2n + 3} = 3^{8 - 2n}\) or \(3^{2n - 1} = 3^{4 - 2n}\) or \(2n + 3 - 4 = 3 + 1 - 2n\) oe eg \(2n - 1 = 4 - 2n\) | M1 |
Working required Answer: \(\dfrac{5}{4}\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: For one rule of indices used to correctly combine two or more of the given expressions (do not need part in brackets)
(must include algebra)
or
For one of the 4 expressions shown, providing it is clear that they apply to the LHS or to the RHS
M1: A correct single power of 3 on both sides or a correct equation in \(n\) without indices
(some students may go straight to this and gain M2)
A1: oe dep on M1