Higher June 2024 Paper 2R Q26
26 Write \(\;4 - \left[(3x - 5) \div \dfrac{3x^2 + x - 10}{4x - 1}\right]\;\) as a single fraction in its simplest form.
(4)
| Scheme | Marks |
|---|---|
\((3x - 5)(x + 2)\) or \(\dfrac{4\left(3x^2 + x - 10\right) - (3x - 5)(4x - 1)}{3x^2 + x - 10}\) oe or \(\dfrac{27x - 45}{3x^2 + x - 10}\) | M1 |
\(\dfrac{4x - 1}{x + 2}\) implies first M1 or \(\dfrac{4\left(3x^2 + x - 10\right) - (3x - 5)(4x - 1)}{(3x - 5)(x + 2)}\) or \(\dfrac{27x - 45}{(3x - 5)(x + 2)}\) | M1 |
\(\dfrac{4(x + 2) - (4x - 1)}{x + 2}\) or \(\dfrac{4x + 8 - 4x + 1}{x + 2}\) or \(\dfrac{4(x + 2)}{x + 2} - \dfrac{4x - 1}{x + 2}\) or \(\dfrac{4x + 8}{x + 2} - \dfrac{4x - 1}{x + 2}\) or \(\dfrac{9(3x - 5)}{(3x - 5)(x + 2)}\) | M1 |
Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: \(\dfrac{9}{x + 2}\) | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for correctly factorising \(3x^2 + x - 10\) to give \((3x - 5)(x + 2)\)
(may be seen later on in working)
OR
combining 2 fractions into a correct single fraction
M1: for inverting and cancelling giving a correct fraction
OR
for a correct single fraction where the denominator is factorised
M1: for a correct single fraction or two correct fractions with a common denominator
OR
for a correct fully factorised single fraction