Higher June 2018 Paper 4 Q20
20 Solve this equation, giving your answers correct to 1 decimal place.
\[\frac{5}{x + 2} + \frac{3}{x - 3} = 2\][6]| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| −0.3 5.3 | 6 | B1 for \((x + 2)(x - 3)\) oe seen | likely seen in \(2(x + 2)(x - 3)\) implied by \(x^2 - x - 6\) |
| M1 for \(5(x - 3) + 3(x + 2)\) oe or better | implied by \(5x - 15 + 3x + 6\) or \(8x - 9\) | ||
| M1FT for \(2x^2 - 10x - 3\) [= 0] or FT their correct attempt to form a quadratic equation with at most two errors | \(2x^2 - 10x - 3\) [=0] seen scores 3 marks, condone e.g. \(2x^2 - 10x = 3\) for 3 marks | ||
| M1FT for \(\dfrac{-(-10) \pm \sqrt{(-10)^2 - 4 \times 2 \times -3}}{2 \times 2}\) oe condoning at most two errors or better FT their ‘quadratic equation’ | for completing the square see additional guidance | ||
| A1 for each of −0.3 or 5.3 or for both answers correct but to more than 1dp. or A1FT for two answers correct to 1 d.p. FT from their ‘quadratic equation’ | For A1 the correct answers are −0.28388… and 5.28388… and can be rounded or truncated. Note: for A1FT they must get M1 first. | ||