June 2023 Paper 1 Q2
2 Express \(\dfrac{5x+1}{x^2-x-12}\) in partial fractions. [4]
| Scheme | Marks | AO |
|---|---|---|
| \(x^2 - x - 12 = (x-4)(x+3)\) | B1 | 1.1a |
| \(\dfrac{5x+1}{x^2-x-12} = \dfrac{A}{x-4} + \dfrac{B}{x+3}\) \(5x + 1 = A(x+3) + B(x-4)\) | M1 | 1.1a |
| Substitute \(x = -3\) giving \(B = 2\) | M1 | 1.1b |
| substitute \(x = 4\) giving \(A = 3\) \(\dfrac{5x+1}{x^2-x-12} = \dfrac{3}{x-4} + \dfrac{2}{x+3}\) | A1 | 1.1b |
| [4] |
Notes
B1: both factors seen
M1: setting up partial fractions using their factors. May be implied by correct expression as final answer.
M1: method for finding either \(A\) or \(B\) soi
A1: both \(A\) and \(B\) correct if clear which denominator they apply to
ISW if an error made only in the transcription to final answer