Higher June 2025 Paper 6 Q21
21 The graph of \(y = -3x\) intersects the graph of \(x^2 + y^2 = 70\) at two points.
Work out the exact coordinates of the two points.
You must show your working. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \((-\sqrt{7}, 3\sqrt{7})\) and \((\sqrt{7}, -3\sqrt{7})\) exact form only with correct working | 5 | Correct working requires evidence of at least M2 For \(y\) values accept \(\pm\sqrt{63}\) and for \(x\) values accept \(\frac{\pm\sqrt{63}}{3}\) | |
| M3 for \(x^2 = 7\) or M2 for \(x^2 + 9x^2 = 70\) or \(10x^2 = 70\) or \(10x^2 - 70 = 0\) or M1 for \(x^2 + (-3x)^2 = 70\) | If \(x = -\sqrt{7}\) and \(\sqrt{7}\) seen after M2, award M3A1 Condone omission of brackets if recovered | ||
| A1 for \(x = -\sqrt{7}\) and \(\sqrt{7}\) or for one correct point | For A1 and SC1, condone –2.65 to –2.64, 2.64 to 2.65, –7.94 to –7.93, 7.93 to 7.94 | ||
| If 0 or 1 scored, instead award SC2 for \((-\sqrt{7}, 3\sqrt{7})\) and \((\sqrt{7}, -3\sqrt{7})\) with no or insufficient working If 0 scored, instead award SC1 for both \(x\) values or for one correct point with no or insufficient working | Apply similar scheme for working in terms of \(y\). | ||