Higher November 2021 Paper 1 Q15
15 Show that \(\dfrac{4x + 3}{2x} + \dfrac{3}{5}\) can be written in the form \(\dfrac{ax + b}{cx}\) where \(a\), \(b\) and \(c\) are integers. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{26x + 15}{10x}\) | M1 | for method to write at least one of the fractions with a suitable denominator, eg \(\dfrac{4x + 3}{2x} \times \dfrac{5}{5}\ \left(= \dfrac{20x + 15}{10x}\right)\) or \(\dfrac{3}{5} \times \dfrac{2x}{2x}\ \left(= \dfrac{6x}{10x}\right)\) |
| M1 | for method to combine the fractions, eg \(\dfrac{5(4x + 3)}{5 \times 2x} + \dfrac{3 \times 2x}{5 \times 2x}\) or \(\dfrac{5(4x + 3) + 3 \times 2x}{5 \times 2x}\) or \(\dfrac{20x + 15}{10x} + \dfrac{6x}{10x}\) | |
| A1 | for correct algebra leading to \(\dfrac{26x + 15}{10x}\) oe in form \(\dfrac{ax + b}{cx}\) |