Higher January 2021 Paper 2 Q21
21 Write \(\dfrac{25x^2 - 64}{5x^2 - 13x - 6} \times \dfrac{x^2 - 8x + 15}{5x + 8} - (x - 7)\)
as a single fraction in its simplest form.
Show clear algebraic working.
(4)
| Scheme | Marks |
|---|---|
| \(\dfrac{(5x - 8)(5x + 8)}{(5x + 2)(x - 3)} \times \dfrac{(x - 5)(x - 3)}{5x + 8}\) or eg \(\dfrac{(5x - 8)(x - 5)}{(5x + 2)}(-(x - 7))\) | M2 |
\(\dfrac{(5x - 8)(x - 5) - (x - 7)(5x + 2)}{5x + 2}\) oe or \(\dfrac{5x^2 - 25x - 8x + 40 - (5x^2 - 35x + 2x - 14)}{5x + 2}\) oe or \(\dfrac{(25x^2 - 64)(x^2 - 8x + 15) - (x - 7)(5x^2 - 13x - 6)(5x + 8)}{(5x^2 - 13x - 6)(5x + 8)}\) oe or \(\dfrac{(5x - 8)(x^2 - 8x + 15) - (x - 7)(5x + 2)(x - 3)}{(5x + 2)(x - 3)}\) oe or \(\dfrac{(25x^2 - 64)(x - 5) - (x - 7)(5x + 2)(5x + 8)}{(5x + 2)(5x + 8)}\) oe | M1 |
Working required Answer: \(\dfrac{54}{5x + 2}\) | A1 |
| (4) | |
| (4 marks) |
Notes
M2: For factorising at least 2 of the quadratics correctly – could be implied by 2 factors cancelled correctly (M1 For factorising at least 1 of the 3 quadratics correctly)
M1: (indep (ft if M2 awarded)) For writing the fractions over a common denominator with or without brackets removed – need not be in simplest form
Could be written as 2 separate fractions over a common denominator
A1: dep on M3