Higher June 2024 Paper 3 Q15
15
(a) Simplify fully \(\dfrac{(a - 3)^2}{5(a - 3)}\) (1)
(b) Factorise \(3k^2 + 11k - 4\) (2)
(c) Simplify fully \(\dfrac{4 - x^2}{x^2 + 3x} \div \dfrac{x + 2}{x + 3}\) (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{a - 3}{5}\) | B1 | for \(\dfrac{a - 3}{5}\) oe |
| Answer | Mark | Mark scheme |
|---|---|---|
| \((3k - 1)(k + 4)\) | M1 | for \((3k \pm 1)(k \pm 4)\) oe or for brackets which when expanded give 2 out of 3 terms correct |
| A1 | cao |
Additional guidance
Accept \(3k(k + 4) - (k + 4)\)
Accept \(k(3k - 1) + 4(3k - 1)\)
Accept \((1 - 3k)(-k - 4)\)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{2 - x}{x}\) | M1 | for factorisation eg \((4 - x^2 =)\ (2 - x)(2 + x)\) and \((x^2 + 3x =)\ x(x + 3)\) or for inversion and multiplication (condone incorrect factorising) eg \(\dfrac{4 - x^2}{x^2 + 3x} \times \dfrac{x + 3}{x + 2}\) oe |
| M1 | for factorisation of both quadratics and inversion and multiplication, eg \(\dfrac{(2 - x)(2 + x)}{x(x + 3)} \times \dfrac{x + 3}{x + 2}\) allow sign errors in one bracket | |
| A1 | for \(\dfrac{2 - x}{x}\) or \(\dfrac{2}{x} - 1\) |