Higher November 2023 Paper 2 Q20
20 Write
\[\frac{14}{3x - 21} + \left[(x + 4) \div \frac{2x^2 - 6x - 56}{2x + 3}\right]\]in the form \(\dfrac{ax + b}{cx + d}\) where \(a\), \(b\), \(c\) and \(d\) are integers. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{6x + 37}{6x - 42}\) | P1 | for factorising to get the numerator, eg \((x + 4)(2x - 14)\) or \(2(x + 4)(x - 7)\) or \((2x + 8)(x - 7)\) |
| P1 | For process to work with the division by \(\dfrac{2x^2 - 6x - 56}{2x + 3}\) eg multiplies by \(\dfrac{2x + 3}{2x^2 - 6x - 56}\) | |
| P1 | for two correct fractions with a common denominator, eg \(\dfrac{28}{6(x - 7)}\) and \(\dfrac{6x + 9}{6(x - 7)}\) oe or \(\dfrac{28 + 6x + 9}{6(x - 7)}\) oe | |
| A1 | oe or \(a = 6\), \(b = 37\), \(c = 6\), \(d = -42\) |
Additional guidance
P marks can be awarded in any order