Higher November 2018 Paper 2 Q22
22 Simplify fully \(\quad \dfrac{x^5 - 4x^3}{3x - 6}\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(3(x - 2)\) or \(x^3(x^2 - 4)\) or \(x^2(x^3 - 4x)\) or \(x(x^4 - 4x^2)\) or \((x^4 + 2x^3)(x - 2)\) or \(x^3(x + 2)(x - 2)\) or \(x^2(x^2 + 2x)(x - 2)\) or \(x(x^3 + 2x^2)(x - 2)\) | M1 | numerator or denominator factorised oe eg \(x^2(x + 2)(x^2 - 2x)\) |
| \(3(x - 2)\) and \(x^3(x + 2)(x - 2)\) or \(3(x - 2)\) and \((x^4 + 2x^3)(x - 2)\) or \(3(x - 2)\) and \(x^2(x^2 + 2x)(x - 2)\) or \(3(x - 2)\) and \(x(x^3 + 2x^2)(x - 2)\) | A1 | numerator and denominator factorised each with factor \((x - 2)\) |
| \(\dfrac{x^3(x + 2)}{3}\) or \(\dfrac{x^2(x^2 + 2x)}{3}\) or \(\dfrac{x(x^3 + 2x^2)}{3}\) or \(\dfrac{x^4 + 2x^3}{3}\) | A1 | oe fully simplified expression eg \(\dfrac{1}{3}x^3(x + 2)\) or \(\dfrac{x^4}{3} + \dfrac{2x^3}{3}\) |
Additional guidance
| \(\dfrac{x^3(x + 2)}{3}\) followed by further incorrect work | M1A1A0 |
| \(\dfrac{x^3 \times (x + 2)}{3}\) or \(\dfrac{1}{3} \times x^3(x + 2)\) | M1A1A0 |
| \(3 \times (x - 2)\) and \(x^3 \times (x + 2) \times (x - 2)\) | M1A1 |
| \(3 \times (x - 2)\) or \(x^3 \times (x^2 - 4)\) | M1 |
| \(1(3x - 6)\) or \(-1(6 - 3x)\) | M0 |
| \(-3(2 - x)\) | M1 |
| \(-3(2 - x)\) and \(-x^3(x + 2)(2 - x)\) | M1A1 |