AS June 2019 Paper 1 Q6
6
(a) On the axes provided, sketch the graph of\[x = \cosh(y + b)\]
where \(b\) is a positive constant. [4 marks]
(b) Determine the minimum distance between the graph of \(x = \cosh(y + b)\) and the \(y\)-axis. [1 mark]
| Scheme | Marks | AO |
|---|---|---|
| Draws a \(\cup\) shape or \(\subset\) or \(\cap\) or \(\supset\) in any position. Condone a graph which appears to have an asymptote and/or a cusp. | B1 | 1.2 |
| Draws a \(\cup\) shape in any orientation or position with the vertex not positioned on an axis. Condone a half graph drawn. Condone a graph which appears to have an asymptote and/or a cusp. | M1 | 3.1a |
| Draws a \(\subset\) shape. The line of symmetry must be parallel to the \(x\)-axis. Condone a half graph drawn, i.e. only the upper half or only the lower half of the \(\subset\) shape Condone a graph which appears to have an asymptote and/or a cusp. | M1 | 3.1a |
| Draws a correct sketch of \(x = \cosh(y + b)\) with \(x\)-intercept identified as \((\cosh b, 0)\) Ignore incorrect vertex coordinates. Do not condone a half graph, or a graph with asymptotes or a cusp. NMS can score 4/4 | A1 | 1.1b |
Typical solution
| Scheme | Marks | AO |
|---|---|---|
| Deduces the correct minimum distance between the graph of \(x = \cosh(y + b)\) and the \(y\)-axis as 1 | B1 | 2.2a |
| (5 marks) |