Higher June 2024 Paper 1 Q12
12
(a) Factorise fully \(\quad 6y^2 - 5y - 4\) (2)
(b) Express \(\;\dfrac{2x + 1}{4x} + \dfrac{7 - 5x}{3x}\;\) as a single fraction in its simplest form. (3)
| Scheme | Marks |
|---|---|
| \((2y \pm 1)(3y \pm 4)\) or \((2y \pm 4)(3y \pm 1)\) or \(2y(3y - 4) + 1(3y - 4)\) or \(3y(2y + 1) - 4(2y + 1)\) | M1 |
| Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: \((2y + 1)(3y - 4)\) | A1 |
| (2) |
Notes
M1: NB factors must be in the form \((ay + b)\) where \(a\) and \(b\) are integers
Condone use of a different letter to \(y\)
A1: or \((3y - 4)(2y + 1)\)
Ignore further working if solving a quadratic to find roots.
| Scheme | Marks |
|---|---|
\(\dfrac{3(2x + 1)}{12x} + \dfrac{4(7 - 5x)}{12x}\) or \(\dfrac{3x(2x + 1)}{12x^2} + \dfrac{4x(7 - 5x)}{12x^2}\) or \(\dfrac{3(2x + 1) + 4(7 - 5x)}{12x}\) oe or \(\dfrac{3x(2x + 1) + 4x(7 - 5x)}{12x^2}\) oe | M1 |
\(\dfrac{6x + 3 + 28 - 20x}{12x}\) oe or \(\dfrac{6x^2 + 3x + 28x - 20x^2}{12x^2}\) oe or \(\dfrac{31x - 14x^2}{12x^2}\) oe | M1 |
Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: \(\dfrac{31 - 14x}{12x}\) | A1 |
| (3) | |
| (5 marks) |
Notes
M1: for two correct fractions with common denominator with the intention to add
or
a single correct fraction
NB \(12x\) can be written as \((3)(4x)\) or \((4)(3x)\) for this mark
or
\(12x^2\) can be written as \((3x)(4x)\) for this mark
M1: for a correct single fraction with all brackets expanded
A1: or \(\dfrac{14x - 31}{-12x}\)