4MA0 Higher June 2014 Paper 4R Q12
12
(a) Factorise \(\;2t^2 - 7t + 3\) (2)
(b) Rearrange the formula \(y = a - bx^2\) to make \(x\) the subject. (3)
| Scheme | Marks |
|---|---|
| M1 | |
| \((2t - 1)(t - 3)\) | A1 |
| (2) |
Notes
M1: \((2t \pm 1)(t \pm 3)\) or \((2t \pm 3)(t \pm 1)\)
NB. Accept \(1t\) in place of \(t\)
A1: cao
| Scheme | Marks |
|---|---|
| \(bx^2 = a - y\) or \(-bx^2 = y - a\) | M1 |
| \(x^2 = \dfrac{a - y}{b}\) or \(x^2 = \dfrac{y - a}{-b}\) or \(x^2 = -\dfrac{y - a}{b}\) | M1 |
| \(x = \pm\sqrt{\dfrac{a - y}{b}}\) | A1 |
| (3) | |
| (5 marks) |
Notes
M1: for isolating \(bx^2\) (or \(-bx^2\))
M1: for isolating \(x^2\)
A1: or \(x = \pm\sqrt{\dfrac{y - a}{-b}}\) or \(x = \pm\sqrt{-\dfrac{y - a}{b}}\)
(condone omission of \(\pm\))