June 2018 Paper 1 Q15
15 Here is the graph of \(\quad y = 3x - x^2 \quad\) for values of \(x\) from \(-1\) to 4
By drawing a suitable linear graph on the grid, work out approximate solutions to
\[x^2 - 4x + 2 = 0\][4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(2 - x\) or \(x - 2\) | M1 | do not award M1 if you see evidence of incorrect method for finding a linear expression |
| \(y = 2 - x\) accurately drawn | M1 | |
| 3.4 | A1 | accept 3.3 to 3.5 |
| 0.6 | A1 | accept 0.5 to 0.7 |
Additional guidance
| For the first M1, start by looking for evidence of a correct method. eg \(\ x^2 - 4x + 2 + 3x - x^2 = -x + 2\) or \(x^2 - 4x + 2 = 0 \ \rightarrow\ x^2 - 3x - x + 2 = 0 \ \rightarrow\ -x + 2 = 3x - x^2\) | |
| Attempts to solve \(x^2 - 4x + 2 = 0\) by using the quadratic formula or by completing the square or by drawing a new quadratic graph (for \(y = x^2 - 4x + 2\)) score 0 marks You might see work which uses the quadratic formula or completing the square which leads to answers of \(2 \pm \sqrt{2}\) … and if this follows working using a correct method to find the linear graph, it can be ignored (they could be using it as a check on their answers obtained graphically), but if it looks like it is their main method, then award 0 marks, as stated above.. Ignore any \(y\) coordinates that might accompany the final \(x\) values. |