June 2024 Paper 3 Q1
1 Simplify each of the following.
(a) \(\left(2a^2\right)^3 \times \frac{3}{4}a^{-1}\) [2]
(b) \(\dfrac{4x^2 - 9}{\left(2x^2 + 5x - 12\right)(2x + 3)}\) [2]
| Scheme | Marks | AO |
|---|---|---|
| \(6a^5\) | B2 | 1.1 1.1 |
| [2] |
Notes
B2: B1 for 6 or \(a^5\) in their final answer or for \(8a^6 \times \frac{3}{4}a^{-1}\)
\(\frac{24}{4}a^5\) as a final answer is B1 B0
| Scheme | Marks | AO |
|---|---|---|
| \(\dfrac{(2x-3)(2x+3)}{(2x-3)(x+4)(2x+3)}\) | M1 | 1.1 |
| \(\dfrac{1}{x+4}\) | A1 | 1.1 |
| [2] |
Notes
M1: M1 for either \(4x^2 - 9 = (2x-3)(2x+3)\) or \(2x^2 + 5x - 12 = (2x-3)(x+4)\)
A correct answer www implies M1
A1: oe, for example, \((x+4)^{-1}\)
Do not ISW if further incorrect simplification occurs e.g. \(\frac{1}{x+4} = \frac{1}{x} + \frac{1}{4}\) is A0