Higher June 2023 Paper 1 Q6
6
(a) Simplify \(\quad (2c^4d^7)^3\) (2)
(b) Find the value of \(\;5y^0\;\) where \(\;y \gt 0\) (1)
(c) Factorise fully \(\quad 16a^2b^3 + 20a^3b\) (2)
(d)
(i) Factorise \(\quad x^2 + 9x - 22\) (2)
(ii) Hence solve \(\quad x^2 + 9x - 22 = 0\) (1)
| Scheme | Marks |
|---|---|
| \(8c^{12}d^{21}\) | B2 |
| (2) |
Notes
B2: (B1 for 2 correct terms as part of a product)
| Scheme | Marks |
|---|---|
| 5 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(4a^2b(4b^2 + 5a)\) | B2 |
| (2) |
Notes
B2: B1 for any correct partial factorisation with at least 2 factors, or the correct common factor with no more than 1 error inside the bracket
| Scheme | Marks |
|---|---|
| (i) \((x \pm 11)(x \pm 2)\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \((x + 11)(x - 2)\) | A1 |
| (2) | |
| (ii) Answer: −11, 2 | B1ft |
| (1) | |
| (8 marks) |
Notes
M1: for \((x \pm 11)(x \pm 2)\)
or for \((x + a)(x + b)\) with \(ab = -22\) or \(a + b = 9\)
A1: for correct factors
B1ft: ft dep on factorising in the form \((x + p)(x + q)\)