Higher January 2019 Paper 2R Q14
14
(a) Given that \(a = 3^x\) and \(b = 3^y\)
express in terms of \(a\) or \(b\) or \(a\) and \(b\),
express in terms of \(a\) or \(b\) or \(a\) and \(b\),
(i) \(3^{2x}\)
(ii) \(3^{x + 4y}\)
(iii) \(3^{y - 1}\)
(3)\(a = 3^x\) and \(b = 3^y\)
\(ab = 2187\)
\(a^2b = 177\,147\)
(b) Work out the value of \(x\) and the value of \(y\).
Show your working clearly. (3)
Show your working clearly. (3)
| Scheme | Marks |
|---|---|
| (i) Answer: \(a^2\) | B1 |
| (ii) Answer: \(ab^4\) | B1 |
(iii) Answer: \(\dfrac{1}{3}b\) | B1oe |
| (3) |
| Scheme | Marks |
|---|---|
| 177 147 ÷ 2187 (= 81) or \(a = 81\) | M1 |
| 2187 ÷ 81 (= 27) or \(b = 27\) | M1 |
| \(x = 4\), \(y = 3\) | A1 |
| (3) | |
| (6 marks) |
Notes
M1: or \(x + y = 7\),
M1: \(2x + y = 11\)
A1: \(x = 4\) and \(y = 3\)