Foundation November 2020 Paper 2 Q22
22 Here is the graph of \(\quad y = x^2 - 7x + 10 \quad\) for values of \(x\) from 0 to 7
(a) Write down the roots of \(\quad x^2 - 7x + 10 = 0\) [2 marks]
(b) Write down the \(x\)-coordinate of the turning point of the curve. [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| 2 and 5 with no other roots | B2 | either order B1 at least one correct root with up to one incorrect root SC1 (2, 0) or (5, 0) or (2, 5) or (5, 2) |
Additional guidance
| \(x = 2\) and \(x = 5\) | B2 |
| 2, 5 or 5, 2 | B2 |
| (2, 0) and (5, 0) and 2 and 5 | SC1 |
| (2, 0) and (5, 0) and \(-2\) and \(-5\) | B0 |
| 2, 0 and 5, 0 (both pairs imply coordinates) | SC1 |
| 2, 0 or 5, 0 (one pair implies roots) | B1 |
| (0, 2) and (0, 5) | B0 |
| 0, 2 and 0, 5 (both pairs imply coordinates) | B0 |
| 0, 2 or 0, 5 (one pair implies roots) | B1 |
| Both answers embedded \(2^2 - 7 \times 2 + 10 = 0\) and \(5^2 - 7 \times 5 + 10 = 0\) | B1 |
| \((x - 2)(x - 5)\) | B0 |
| Answer | Mark | Comments |
|---|---|---|
| 3.5 | B1 | oe |
Additional guidance
| \(x = 3.5\) | B1 |
| \(3.5x\) | B0 |
| Ignore any \(y\)-coordinate even with brackets omitted eg \((3.5, -2.25)\) or \(3.5, -2\) or \(x = 3.5\;\; y = -2.25\) or \(x = 3.5\;\; y = 2\) | B1 |
| \((-2.25, 3.5)\) | B0 |