Foundation June 2023 Paper 1 Q26
26 Here is a table of values for \(y = \dfrac{6}{x} - 2x\).
| \(x\) | \(-4\) | \(-3\) | \(-2\) | \(-1\) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|---|
| \(y\) | 6.5 | 4 | 1 | \(-4\) | 4 | \(-1\) | \(-4\) | \(-6.5\) |
(a) Draw the graph of \(y = \dfrac{6}{x} - 2x\) for \(-4 \leqslant x \leqslant 4,\ x \ne 0\).
[3]
(b) Use your graph to find the positive solution of \(\dfrac{6}{x} - 2x = 0\).
Give your answer to 1 decimal place. [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Two accurate curves | 3 | B2 for 7 or 8 points plotted accurately or B1 for 5 or 6 points plotted accurately | Ignore the curve beyond points but the curve must not cross or touch the y-axis tolerance \(\pm\dfrac{1}{2}\) small square from correct points radially no excessive feathering, no ruled lines, no excessive ‘tram lines’ overlay gives guidance only |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| A correct and accurate reading from their graph | 1FT DEP. | Dep. on a graph in (a) with at least one positive solution and strict FT their curve. | If curve crosses x-axis between two grid lines accept either grid line value as correct answer If their curve has more than one positive solution accept any of their correct solutions Do not accept answers to more than 1d.p., \(\sqrt{3}\) or answers clearly rounded from this. Condone whole numbers where appropriate e.g. 2 for 2.0 Do not accept 0 as positive. |