Higher June 2023 Unit 1 Q14
14. The table below shows some of the values of \(y = x + \dfrac{1}{x}\) for values of \(x\) from 0·2 to 4.
| \(x\) | 0·2 | 0·5 | 0·8 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|
| \(y = x + \dfrac{1}{x}\) | 5·2 | 2·05 | 2 | 2·5 | \(3{\cdot}\dot{3}\) | 4·25 |
(a)
(i) Complete the table by finding the value of \(y\) for \(x = 0{\cdot}5\). [1]
(ii) On the graph paper below, draw the graph of \(y = x + \dfrac{1}{x}\) for values of \(x\) from 0·2 to 4. [2]
(b) Use your graph to solve the equation \(x + \dfrac{1}{x} = 3\). [2]
| Scheme | Marks | Comments |
|---|---|---|
| (i) 2·5 | B1 | |
| (ii) At least 6 correct plots and no incorrect plot. | P1 | FT ‘their (0·5, 2·5)’. Allow ‘±½ a small square’. |
| A smooth curve drawn through their plots. | C1 | FT ‘their 7 plots’ OR a curve through the 6 given plots and through (0·5, 2·5). Allow for the intention to pass through their plots (± 1 small square horizontal OR vertical). The curve should NOT intercept the \(y\)-axis. |
| Scheme | Marks | Comments |
|---|---|---|
| Two correct readings from their graph. | B2 | For reference, \(x\) = 0·4 AND 2·6 to 1d.p. B1 for one correct reading. Strict FT ‘their graph’. If more than two points of intersection, award B1 for one correct answer, B2 for a complete set of answers. If no marks, award SC1 for drawing the line \(y = 3\). |