Foundation June 2019 Paper 1 Q27
27 Rearrange \(\quad x = 2y - 6 \quad\) to make \(y\) the subject. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 – add 6 to both sides first | ||
| \(x + 6 = 2y\) or \(-x - 6 = -2y\) or \(\dfrac{x + 6}{2}\) or \(\dfrac{x}{2} + 3\) or \(\dfrac{1}{2}(x + 6)\) | M1 | oe |
| \(y = \dfrac{x + 6}{2}\) or \(y = \dfrac{x}{2} + 3\) or \(y = \dfrac{1}{2}(x + 6)\) | A1 | allow order reversed do not allow further incorrect work eg attempts to divide only the 6 by 2 Condone \(y = (x + 6) \div 2\) for M1A1 |
| Alternative method 2 – divide both sides by 2 first | ||
| \(\dfrac{x}{2} = y - \dfrac{6}{2}\) or \(\dfrac{x}{2} = y - 3\) or \(\dfrac{x + 6}{2}\) or \(\dfrac{x}{2} + 3\) or \(\dfrac{1}{2}(x + 6)\) | M1 | allow \(\dfrac{2y}{2}\) for \(y\) |
| \(y = \dfrac{x + 6}{2}\) or \(y = \dfrac{x}{2} + 3\) or \(y = \dfrac{1}{2}(x + 6)\) | A1 | allow order reversed do not allow further incorrect work eg attempts to divide only the 6 by 2 Condone \(y = (x + 6) \div 2\) for M1A1 |
| Alternative method 3 – flow diagram | ||
| \(y \rightarrow 2y \rightarrow 2y - 6\) \(\quad \leftarrow x + 6 \leftarrow x\) | M1 | allow \(2 \times y\) or \(y \times 2\) for \(2y\) ignore any operations seen on arrows |
| \(y = \dfrac{x + 6}{2}\) or \(y = \dfrac{x}{2} + 3\) or \(y = \dfrac{1}{2}(x + 6)\) | A1 | allow order reversed do not allow further incorrect work eg attempts to divide only the 6 by 2 Condone \(y = (x + 6) \div 2\) for M1A1 |
Additional guidance
Allow 0.5 for \(\dfrac{1}{2}\) throughout