Higher November 2023 Paper 2 Q24
24 Simplify fully \(\quad \dfrac{8x^2 + 4}{5x} \times \dfrac{3x}{14x^2 + 7}\)
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(4(2x^2 + 1)\) or \(7(2x^2 + 1)\) or \(\dfrac{8x^2 + 4}{5} \times \dfrac{3}{14x^2 + 7}\) | M1 | |
| \(\dfrac{4(2x^2 + 1)}{5x} \times \dfrac{3x}{7(2x^2 + 1)}\) or \(\dfrac{4(2x^2 + 1)}{5} \times \dfrac{3}{7(2x^2 + 1)}\) or \(\dfrac{4}{5x} \times \dfrac{3x}{7}\) | M1dep | \(\dfrac{4}{5x} \times \dfrac{3x}{7}\) must follow \(4(2x^2 + 1)\) and \(7(2x^2 + 1)\) |
| \(\dfrac{12}{35}\) with M2 seen | A1 | |
| Alternative method 2 | ||
| \(\dfrac{24x^3 + 12x}{70x^3 + 35x}\) or \(\dfrac{x(24x^2 + 12)}{x(70x^2 + 35)}\) or \(\dfrac{24x^2 + 12}{70x^2 + 35}\) | M1 | |
| \(\dfrac{12x(2x^2 + 1)}{35x(2x^2 + 1)}\) or \(\dfrac{12(2x^3 + x)}{35(2x^3 + x)}\) or \(\dfrac{12(2x^2 + 1)}{35(2x^2 + 1)}\) | M1dep | |
| \(\dfrac{12}{35}\) with M2 seen | A1 | |
Additional guidance
Up to M2 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts