Higher June 2024 Paper 6 Q14
14 The sketch shows the coordinate axes and the point (0, 10).
Not to scale
The distance from the point (0, 10) to a point (12, \(t\)) is 12.5 units.
Work out the two possible values of \(t\).
You must show your working and you may use the sketch to help. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 13.5 and 6.5 with correct working | 5 | ‘Correct working’ requires evidence of Pythagoras or quadratic Accept \(\frac{27}{2}\) and \(\frac{13}{2}\) | |
| M2 for [\(h^2 =\)] \(12.5^2 - 12^2\) or better or M1 for \(12^2 + h^2 = 12.5^2\) or better | Allow other letters or \(t - 10\) for \(h\) and allocate marks as per main method | ||
| B1 for \(h = 3.5\) AND | Accept -3.5 or ±3.5 | ||
| M1 for 10 + their 3.5 soi by 13.5 or 10 – their 3.5 soi by 6.5 | Their 3.5 from use of Pythagoras | ||
| If 0, 1 or 2 scored, instead award SC3 for both 13.5 and 6.5 as answers with no or insufficient working If 0 or 1 scored, instead award SC2 for either 13.5 or 6.5 as answer with no working or insufficient working | Alternative method 1: M3 for \(t^2 - 20t + 87.75 = 0\) or M2 for \(144 + t^2 - 20t + 100 = 156.25\) or M1 for \(12^2 + (t - 10)^2 = 12.5^2\) AND M1 for correct method to solve their 3-term quadratic | ||