Higher November 2024 Paper 1 Q11
11 Kate was asked to factorise \(x^2 + 5x + 6\) in the form \((x + a)(x + b)\)
Kate says,
“The sum of \(a\) and \(b\) must be 6 and the product of \(a\) and \(b\) must be 5”
(a) Explain what is wrong with Kate’s statement. (1)
(b) Factorise fully \(2m^2 - 2\) (2)
(c) Factorise fully \(ax + bx - ay - by\) (2)
| Answer | Mark | Mark scheme |
|---|---|---|
| Explanation | C1 | for explanation Acceptable examples the sum must be 5 and the product must be 6 she had the sum and the product the wrong way round it should be the other way around \(a\) and \(b\) must be multiplied together to make 6 Not acceptable examples the answer should be \((x + 3)(x + 2)\) the product of \(a\) and \(b\) is not 5 |
| Answer | Mark | Mark scheme |
|---|---|---|
| \(2(m - 1)(m + 1)\) | M1 | for a correct partial factorisation, eg \(2(m^2 - 1)\) or \((2m - 2)(m + 1)\) or \((m - 1)(2m + 2)\) |
| A1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| \((a + b)(x - y)\) | M1 | for a correct partial factorisation, eg \(x(a + b) - y(a + b)\) or \(x(a + b) + y(-a - b)\) or \(a(x - y) + b(x - y)\) |
| A1 | for \((a + b)(x - y)\) oe |