Higher June 2024 Unit 1 Q16
16.
(a) Simplify \(\dfrac{4y^2 + 8xy}{y^2 - 4x^2}\). [4]
(b) Make \(f\) the subject of the following formula. [5]\[\sqrt{hf^2 - m} = 3f\]
| Scheme | Marks | Comments |
|---|---|---|
| (Numerator) \(4y(y + 2x)\) | B1 | |
| (Denominator) \((y + 2x)(y - 2x)\) | B2 | B1 for \((y \ldots 2x)(y \ldots 2x)\) |
| \(\dfrac{4y}{y - 2x}\) or equivalent. | B1 | Mark final answer. FT provided no more than one previous error and provided simplification required. |
| Scheme | Marks | Comments |
|---|---|---|
| FT until 2nd error for equivalent level of difficulty. | ||
| Sight of \(hf^2 - m = 9f^2\) | B1 | Squaring Allow \(3^2f^2\) or \((3f)^2\) or \((3f)(3f)\) for \(9f^2\). |
| \(hf^2 - 9f^2 = m\) or equivalent | B1 | Isolating terms in \(f^2\). FT a formula with three or more terms AND with at least two terms in \(f^2\). |
| \(f^2(h - 9) = m\) or equivalent | B1 | Factorising fully. |
| \(f^2 = \dfrac{m}{h - 9}\) OR \(f^2 = \dfrac{-m}{9 - h}\) | B1 | Isolating \(f^2\). |
| \(f = \pm\sqrt{\dfrac{m}{h - 9}}\) OR \(f = \pm\sqrt{\dfrac{-m}{9 - h}}\) | B1 | Mark final answer. Allow omission of ±. |