AS June 2019 Paper 1 Q4
4 The line \(L\) has polar equation
\[r = \frac{k}{\sin\theta}\]where \(k\) is a positive constant.
(a) Sketch \(L\). [1 mark]
(b) State the minimum distance between \(L\) and the point \(O\). [1 mark]
| Scheme | Marks | AO |
|---|---|---|
| Draws a horizontal line above the point \(O\), parallel to the initial line. Ignore a vertical axis through \(O\). Ignore an extension of the initial line. Accept a freehand ‘straight’ line – mark intention. A deliberate curve, e.g. parabolic, is B0. | B1 | 1.1b |
Typical solution
| Scheme | Marks | AO |
|---|---|---|
| States the correct minimum distance as \(k\) Treat an answer of \(k = 0\) as two responses, one correct and one incorrect (B0). Condone \(r = k\) Ignore any value of \(\theta\), e.g. \(\theta = \frac{\pi}{2}\) Must be simplified, e.g. \(k - 0\) is B0, but \(k - 0 = k\) is B1. | B1 | 1.1b |
| (2 marks) |