Higher June 2018 Paper 1 Q15
15
(a) Factorise \(a^2 - b^2\) (1)
(b) Hence, or otherwise, simplify fully \((x^2 + 4)^2 - (x^2 - 2)^2\) (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \((a - b)(a + b)\) | B1 | cao |
Additional guidance
Accept reversed brackets
| Answer | Mark | Mark scheme |
|---|---|---|
| \(12(x^2 + 1)\) | M1 | for using ‘\(a\)’ \(= x^2 + 4\) and ‘\(b\)’ \(= x^2 - 2\) OR multiplying out both brackets, at least one fully correct |
| M1 | (dep) for a correct expression for (‘\(a\)’ + ‘\(b\)’)(‘\(a\)’ − ‘\(b\)’) with no additional brackets, simplified or unsimplified eg \((x^2 + 4 + x^2 - 2)(x^2 + 4 - x^2 + 2)\) or \((2x^2 + 2) \times 6\) OR ft for a correct expression without brackets, simplified or unsimplified eg \(x^4 + 8x^2 + 16 - x^4 + 4x^2 - 4\) | |
| A1 | for \(12(x^2 + 1)\) or \(12x^2 + 12\) oe |
Additional guidance
M1 (first): Correct 4 terms if not simplified or 3 terms if simplified