Higher June 2023 Unit 2 Q11
11. Make \(x\) the subject of the formula \(ax^2 + x^2 = b\). [3]
| Scheme | Marks | Comments | ||||||
|---|---|---|---|---|---|---|---|---|
| \(x^2(a + 1) = b\) OR \(-x^2(a + 1) = -b\) OR \(x^2(-a - 1) = -b\) | B1 | FT until 2nd error. \(x^2\) or \(-x^2\) factorised. | ||||||
| \(x^2 = \frac{b}{a+1}\) OR \(-x^2 = \frac{-b}{-a-1}\) | B1 | Isolating the \(x^2\) or \(-x^2\). Allow a FT from \(2x^2 = \frac{b}{a}\). | ||||||
| \(x = \pm\sqrt{\frac{b}{a+1}}\) | B1 | B0 for √\([b \div (a + 1)]\) (use of the division sign). Allow omission of \(\pm\). Mark final answer. Note:
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