Higher June 2022 Paper 2R Q23
23 Express \(\left(\dfrac{20}{x^2 - 36} - \dfrac{2}{x - 6}\right) \times \dfrac{1}{4 - x}\) as a single fraction in its simplest form.
(3)
| Scheme | Marks |
|---|---|
eg \(\dfrac{20}{x^2 - 36} - \dfrac{2(x + 6)}{x^2 - 36}\) oe or \(\dfrac{20}{(x - 6)(x + 6)} - \dfrac{2(x + 6)}{(x - 6)(x + 6)}\) oe or \(\dfrac{20(x - 6)}{(x^2 - 36)(x - 6)} - \dfrac{2(x + 6)(x - 6)}{(x^2 - 36)(x - 6)}\) or \(\dfrac{20 - 2(x + 6)}{(x^2 - 36)(4 - x)}\) oe | M1 |
eg \(\dfrac{8 - 2x}{x^2 - 36} \times \dfrac{1}{4 - x}\) or \(\dfrac{8 - 2x}{(x - 6)(x + 6)} \times \dfrac{1}{4 - x}\) or \(\dfrac{20x - 2x^2 - 48}{(x^2 - 36)(x - 6)} \times \dfrac{1}{4 - x}\) oe \(\dfrac{8 - 2x}{(x^2 - 36)(4 - x)}\) oe | M1 |
| \(\dfrac{2}{x^2 - 36}\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for writing the first two fractions with a common denominator (may be a single denominator) or multiplying both fractions by \(\dfrac{1}{4 - x}\) and writing over a common denominator
M1: for simplifying first 2 fractions to a single fraction and expanding and simplifying numerator – must be correct, and showing intention to multiply by \(\dfrac{1}{4 - x}\)
or
expanding the numerator of the full solution and writing as a single fraction
A1: oe eg \(\dfrac{2}{(x - 6)(x + 6)}\)