Higher November 2021 Paper 1 Q21
21.
(a) Expand and simplify \((3x + 2)^3\). [3]
(b) Simplify \(\dfrac{4x^2 - 1}{6x^2 - 13x + 5}\). [5]
| Scheme | Marks | Comments |
|---|---|---|
| \((3x + 2)^3 = (3x + 2)(3x + 2)(3x + 2)\) and attempting to multiply out one pair of brackets | S1 | \(27x^3 + 8\) is S0 |
| \(27x^3 + 54x^2 + 36x + 8\) or simplified equivalent | B2 | Mark final answer B1 for \((9x^2 + 6x + 6x + 4)(3x + 2)\) or better or for a final answer with at most one incorrect coefficient NB: Correct unsimplified equivalent for B1 may be \(27x^3 + 18x^2 + 18x^2 + 12x + 18x^2 + 12x + 12x + 8\) |
| Scheme | Marks | Comments |
|---|---|---|
| \((2x + 1)(2x - 1)\) | B2 | Allow for \(4\left(x^2 - \dfrac{1}{4}\right) = 4\left(x - \dfrac{1}{2}\right)\left(x + \dfrac{1}{2}\right)\) B1 for sight of \((2x)^2 - 1^2\); allow for sight of \((2x)^2 - 1\) |
| \(6x^2 - 13x + 5 = (2x - 1)(3x - 5)\) soi | B2 | B1 for \(6x^2 - 13x + 5 = (2x \ldots 1)(3x \ldots 5)\) |
| \(\dfrac{2x + 1}{3x - 5}\) | B1 | CAO; mark final answer |
| (8) |