Higher January 2023 Paper 2R Q26
26 Write
\(\dfrac{4x^2 - 17x - 15}{2x - 1} \times \dfrac{2x^2 - 7x + 3}{x^2 - 25} + (29 - 4x)\)
as a single fraction in its simplest form.
(4)
| Scheme | Marks |
|---|---|
eg \(\dfrac{(4x + 3)(x - 5)}{2x - 1} \times \dfrac{(2x - 1)(x - 3)}{(x + 5)(x - 5)}\) or eg \(\dfrac{(4x + 3)(x - 3)}{x + 5}\;(+(29 - 4x))\) | M2 |
eg \(\dfrac{(4x + 3)(x - 3) + (29 - 4x)(x + 5)}{x + 5}\) oe or eg \(\dfrac{4x^2 - 9x - 9 + 145 + 9x - 4x^2}{x + 5}\) oe | M1 |
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(\dfrac{136}{x + 5}\) | 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: for writing the correct fractions over a common denominator of \((x + 5)\) with or without brackets removed – need not be in simplest form. Could be written as 2 separate fractions.