4400 Higher June 2006 Paper 3 Q20
20 Make \(R\) the subject of the formula \(A = \pi(R + r)(R - r)\)
(4)
| Scheme | Marks |
|---|---|
| \(A = \pi(R^2 - r^2)\) or \(\dfrac{A}{\pi} = (R + r)(R - r)\) | M1 |
| \(A = \pi R^2 - \pi r^2\) or \(\dfrac{A}{\pi} = R^2 - r^2\) | M1 |
| \(R^2 = \dfrac{A + \pi r^2}{\pi}\) or \(R^2 = \dfrac{A}{\pi} + r^2\) | M1 |
| \(\sqrt{\dfrac{A + \pi r^2}{\pi}}\) or \(\sqrt{\dfrac{A}{\pi} + r^2}\) oe | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for \(R^2 - r^2\) seen or division by \(\pi\)
M1: for \(A = \pi R^2 - \pi r^2\) or \(\dfrac{A}{\pi} = R^2 - r^2\). This M1 also implies the first M1
M1: for \(R^2 = \dfrac{A + \pi r^2}{\pi}\) or \(R^2 = \dfrac{A}{\pi} + r^2\). ft if \((R + r)(R - r)\) expanded as \(R^2 - r\) to a maximum of 3 marks
A1: Condone omission of ±
Do not award if followed by further incorrect ‘simplifying’