June 2025 Paper 3 Q1
1
(a) Express \(3x^2 - 12x + 17\) in the form \(a(x - b)^2 + c\) where \(a\), \(b\) and \(c\) are constants. [3]
(b) State the coordinates of the minimum point of the curve \(y = 3x^2 - 12x + 17\). [1]
(c) State the equation of the normal to the curve \(y = 3x^2 - 12x + 17\) at its minimum point. [1]
| Scheme | Marks | AO |
|---|---|---|
| \(\{3\}(x\ \{-2\})^2\ \{+5\}\) | B3 | 1.1 1.1 1.1 |
| [3] |
Notes
B3: B2 for 2 correct \(\{\ \}\) components, B1 for 1 correct \(\{\ \}\) component must be of the form \(\pm a(x \pm b)^2 \pm c\) with terms simplified. Award B1 for explicitly stating \(a = 3\), B1 for explicitly stating \(b = 2\) and B1 for explicitly stating \(c = 5\)
SC B2 for \(3(x - 2) + 5\) but no marks for any other non-squared expression
| Scheme | Marks | AO |
|---|---|---|
| \((2, 5)\) | B1FT | 1.2 |
| [1] |
Notes
B1FT: Correct answer or follow through from their answer to part (a) of the form \(\pm a(x \pm b)^2 \pm c\)
Allow \(x = 2\), \(y = 5\) or 2,5
| Scheme | Marks | AO |
|---|---|---|
| \(x = 2\) | B1FT | 1.1 |
| [1] |
Notes
B1FT: Correct answer or follow through their consistent \(x\)-value from parts (a) and (b)
Must be an equation