4400 Higher June 2009 Paper 4 Q21
21
(a) Solve \(2x^2 + 3x - 1 = 0\)
Give your solution(s) correct to 3 significant figures. (3)
Give your solution(s) correct to 3 significant figures. (3)
(b) Solve \(\dfrac{2}{x} - \dfrac{1}{x + 1} = 1\) (4)
| Scheme | Marks |
|---|---|
| \(\dfrac{-3 \pm \sqrt{3^2 - 4 \times 2 \times (-1)}}{2 \times 2}\) | M1 |
| \(\dfrac{-3 \pm \sqrt{17}}{4}\) | M1 |
| 0.281 and \(-1.78\) | A1 |
| (3) |
Notes
M1: allow one sign error
A1: both answers rounding to 0.281 & \(-1.78\)
(answer only gains no marks)
| Scheme | Marks |
|---|---|
| \(\dfrac{2(x + 1) - x}{x(x + 1)} = 1\) | M1 |
| \(2(x + 1) - x = x(x + 1)\) | M1 |
| \(x^2 - 2 = 0\) oe | M1 |
| \(\pm\sqrt{2}\) or \(\pm 1.41...\) | A1 |
| (4) | |
| (7 marks) |
Notes
M1: \(\dfrac{2(x + 1)}{x} - 1 = x + 1\) or \(2 - \dfrac{x}{x + 1} = x\)
M1: removal of denominator
M1: correct gathering of terms
A1: answer rounding to \(\pm 1.41\)
(answer only gains no marks)