Foundation June 2023 Paper 1 Q23
23 Erika tries to sketch the graph \(\quad y = \dfrac{1}{x} \quad\) with \(\;x \neq 0\)
Make two different criticisms of her sketch. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Any two from: Reference to graph passing through point where \(x = 0\) Reference to graph being incorrect for negative \(x\) values Reference to the graph stopping before the end of the axes/axis | B2 | B1 any one correct reference eg the graph touches the \(y\)-axis eg the graph to the left of the \(y\)-axis should be below the \(x\)-axis eg the graph should go to the ends of the axes |
Additional guidance
| Ignore non-contradictory, irrelevant responses alongside a correct response | |
| Draws correct graph | B2 |
| Draws graph with one section correct for positive values of \(x\) or negative values of \(x\) | B1 for that section |
| ‘It isn’t the graph of \(y = \dfrac{1}{x}\)’ scores B0, but B1 may still be scored for the other criticism | |
| ‘There are no numbers on the axes’ scores B0, but B1 may still be scored for the other criticism | |
| Mark for graph touching \(y\)-axis | |
| You cannot have \(x = 0\) | B1 |
| The line in the top right should be moved to the right | B1 |
| It says \(x\) doesn’t \(= 0\) but it (the sketch) does | B1 |
| One line is touching the \(y\)-axis | B1 |
| The lines should be symmetrical | B0 |
| You cannot have \(y = 0\) | B0 |
| One line is touching the \(y\)-axis but the other isn’t | B0 |
| Mark for negative values being in the wrong quadrant | |
| There shouldn’t be anything in the top-left section | B1 |
| There should be something in the bottom-left section | B1 |
| It is the graph of \(y = \dfrac{1}{x^2}\) | B1 |
| It should have rotational symmetry | B1 |
| It should be symmetrical about \(y = x\) | B1 |
| It should be symmetrical about \(y = -x\) | B1 |
| It should be symmetrical | B0 |
| One should be negative | B0 |
| The bit on the left is wrong | B0 |
| The negative values are plotted incorrectly | B0 |
| Reference to the graph stopping before the end of the axes | |
| It stops before the end of the axes | B1 |
| The lines don’t go far enough | B1 |
| The lines need to be higher up | B0 |