Higher June 2025 Paper 1 Q12
12 Express \(\dfrac{5}{4} + \dfrac{x - 3}{6x}\) as a single fraction in its simplest form.
(3)
| Scheme | Marks |
|---|---|
eg \(\dfrac{5(6x)}{24x} + \dfrac{4(x - 3)}{24x}\) oe or \(\dfrac{5(6x)}{4(6x)} + \dfrac{4(x - 3)}{4(6x)}\) oe or \(\dfrac{30x}{24x} + \dfrac{4(x - 3)}{24x}\) oe or \(\dfrac{30x + 4(x - 3)}{24x}\) oe or \(\dfrac{15x}{12x} + \dfrac{2(x - 3)}{12x}\) oe or \(\dfrac{15x + 2(x - 3)}{12x}\) oe | M1 |
eg \(\dfrac{30x + 4x - 12}{24x}\) oe or \(\dfrac{30x}{24x} + \dfrac{4x - 12}{24x}\) oe or \(\dfrac{30x}{24x} + \dfrac{4x}{24x} - \dfrac{12}{24x}\) oe or \(\dfrac{34x}{24x} - \dfrac{12}{24x}\) oe or \(\dfrac{34x - 12}{24x}\) oe or \(\dfrac{15x + 2x - 6}{12x}\) oe | M1 |
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(\dfrac{17x - 6}{12x}\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for two correct fractions with common denominator
or
a single correct fraction
M1: for correct fraction(s) with bracket(s) expanded correctly
A1: oe but must be simplified eg \(\dfrac{-6 + 17x}{12x}\)
do not ISW incorrect simplification eg \(\dfrac{17x - 6}{12x} = \dfrac{11}{12}\) is M2A0