June 2019 Paper 2 Q13
13 Simplify fully \(\quad \dfrac{x - x^3}{2x + 2x^2}\)
You must show your working. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(x(1 - x^2)\) or \(2x(1 + x)\) or \(x(2 + 2x)\) or \(\dfrac{1 - x^2}{2 + 2x}\) | M1 | implied by 2nd M1 oe factorisation eg \(-x(x^2 - 1)\) |
| \(x(1 + x)(1 - x)\) or \(\dfrac{x(1 - x^2)}{2x(1 + x)}\) or \(\dfrac{1 - x^2}{2(1 + x)}\) or \(\dfrac{(1 + x)(1 - x)}{2 + 2x}\) | M1dep | implies M2 oe factorisation eg \(-x(x + 1)(x - 1)\) |
| \(\dfrac{x(1 + x)(1 - x)}{2x(1 + x)}\) or \(\dfrac{(1 + x)(1 - x)}{2(1 + x)}\) or \(\dfrac{x(1 - x)}{2x}\) | M1dep | implies M3 oe factorisation eg \(\dfrac{-x(x + 1)(x - 1)}{2x(1 + x)}\) |
| \(\dfrac{1 - x}{2}\) with M3 seen | A1 | oe simplest form eg \(\dfrac{1}{2}(1 - x)\) or \(\dfrac{1}{2} - \dfrac{1}{2}x\) or \(\dfrac{-x + 1}{2}\) |
Additional guidance
| \(\dfrac{x(1 + x)(1 - x)}{2x(1 + x)}\) or \(\dfrac{(1 + x)(1 - x)}{2(1 + x)}\) or \(\dfrac{x(1 - x)}{2x}\) is sufficient working | M3 |
| \(2(x + x^2)\) with no further work | M0 |
| \(\dfrac{x - 1}{-2}\) with M3 seen or \(-\dfrac{1}{2}(x - 1)\) with M3 seen or \(\dfrac{-(x - 1)}{2}\) with M3 seen | M3A1 |