4MA0 Higher January 2014 Paper 3 Q18
18
(a) \(x = 9 \times 10^{2m}\) where \(m\) is an integer.
Find, in standard form, an expression for \(\sqrt{x}\) (2)
Find, in standard form, an expression for \(\sqrt{x}\) (2)
(b) \(y = 9 \times 10^{2n}\) where \(n\) is an integer.
Find, in standard form, an expression for \(y^{\frac{3}{2}}\)
Give your answer as simply as possible. (3)
Find, in standard form, an expression for \(y^{\frac{3}{2}}\)
Give your answer as simply as possible. (3)
| Scheme | Marks |
|---|---|
| \(3 \times 10^m\) | B2 |
| (2) |
Notes
B2: B1 for \(3 \times \sqrt{10^{2m}}\) or \(3 \times 10^{km}\) where \(k \ne 1\)
or \(a \times 10^m\) where \(a \ne 3\)
| Scheme | Marks |
|---|---|
\(\left((9)^{\frac{3}{2}} =\right) 27\) or 2.7 | B1 |
| \(27 \times 10^{3n}\) oe | M1 |
| \(2.7 \times 10^{3n + 1}\) | A1 |
| (3) | |
| (5 marks) |