4MA0 Higher January 2014 Paper 3 Q16
16 Given that \(y\) is positive, make \(y\) the subject of \(\;y = \sqrt{ay^2 + n}\)
Show clear algebraic working.
(5)
| Scheme | Marks |
|---|---|
| \(y^2 = ay^2 + n\) | M1 |
\(y^2 - ay^2 = n\) or \(1 = a + \dfrac{n}{y^2}\) or \(1 - a = \dfrac{n}{y^2}\) | M1 |
| \(y^2(1 - a) = n\) | M1 |
| \(y^2 = \dfrac{n}{1 - a}\) | M1 |
| \(\sqrt{\dfrac{n}{1 - a}}\) | A1 |
| (5) | |
| (5 marks) |
Notes
M1: isolate terms in \(y^2\) or divide through by \(y^2\)
M1: take out \(y^2\) as a common factor
M1: \(y^2\) as subject
A1: accept \(\sqrt{\dfrac{-n}{a - 1}}\)