1MA0 Higher November 2014 Paper 2 Q22
22
(a) Simplify fully \(\dfrac{2x^2 - 5x + 3}{x^2 + 5x - 6}\) (3)
(b) Make \(m\) the subject of \[\frac{m}{v} - \frac{t}{b} = \frac{m - t}{R}\] (4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(\dfrac{(2x - 3)(x - 1)}{(x + 6)(x - 1)}\) | \(\dfrac{2x - 3}{x + 6}\) | 3 | M1 for \((2x - 3)(x - 1)\) M1 for \((x + 6)(x - 1)\) A1 cao |
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(\dfrac{mb - tv}{vb} = \dfrac{m - t}{R}\) \(mbR - tvR = mvb - tvb\) \(mbR - mvb = tvR - tvb\) \(m(bR - vb) = tvR - tvb\) OR \(\dfrac{m}{v} - \dfrac{t}{b} = \dfrac{m}{R} - \dfrac{t}{R}\) \(\dfrac{m}{v} - \dfrac{m}{R} = \dfrac{t}{b} - \dfrac{t}{R}\) \(\dfrac{mR - mv}{vR} = \dfrac{tR - tb}{bR}\) \(\dfrac{m(R - v)}{vR} = \dfrac{tR - tb}{bR}\) | \(m = \dfrac{tv(R - b)}{b(R - v)}\) | 4 | M1 for putting LHS over a common denominator with at least one correct numerator (ignore signs) or for showing an intention to multiply each term on both sides by \(R\) or \(v\) or \(b\) M1 for rearranging correctly to isolate terms in \(m\) M1 for factorising with common factor \(m\) from 2 terms A1 for \(m = \dfrac{tv(R - b)}{b(R - v)}\) oe |