Higher November 2022 Paper 3 Q22
22 Simplify fully \(\quad \dfrac{2}{x + 1} + \dfrac{7 - 5x}{3} + 4x\)
Give your answer as a single fraction. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{6}{3(x + 1)}\) or \(\dfrac{(7 - 5x)(x + 1)}{3(x + 1)}\) or \(\dfrac{3 \times 4x(x + 1)}{3(x + 1)}\) | M1 | oe one correct term with possible common denominator |
| \(\dfrac{6}{3(x + 1)}\) and \(\dfrac{(7 - 5x)(x + 1)}{3(x + 1)}\) and \(\dfrac{3 \times 4x(x + 1)}{3(x + 1)}\) | M1dep | oe all terms correct with common denominator may be a single fraction |
| \(\dfrac{6}{3(x + 1)} + \dfrac{7x + 7 - 5x^2 - 5x}{3(x + 1)} + \dfrac{12x^2 + 12x}{3(x + 1)}\) | M1dep | oe all terms correct with common denominator and brackets on numerator expanded |
| \(\dfrac{7x^2 + 14x + 13}{3(x + 1)}\) | A1 | SC3 \(7x^2 + 14x + 13\ (= 0)\) or \(\dfrac{7x^2 + 14x + 13}{3x + 1}\) |
Additional guidance
Do not award A mark if further incorrect simplification is seen after a correct answer
\(3(x + 1)\) can be \(3x + 3\) throughout