Higher November 2018 Paper 1 Q17
17 Here is a sketch of a curve.
The equation of the curve is \(y = x^2 + ax + b\) where \(a\) and \(b\) are integers.
The points \((0, -5)\) and \((5, 0)\) lie on the curve.
Find the coordinates of the turning point of the curve. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| \((2, -9)\) | P1 | substitutes \(x = 0\), \(y = -5\) into \(y = x^2 + ax + b\) \((b = -5)\) or substitutes \(x = 5\), \(y = 0\) into \(y = x^2 + ax + b\) \((0 = 25 + 5a + b)\) or starts process to find other intercept, eg writes \(y = (x - 5)(x - k)\) |
| P1 | for complete process to find two intercepts, eg. substitutes the second point into \(y = x^2 + ax + b\) and solves to find \(a\ (= -4)\) and \(b\ (= -5)\) or substitutes \(x = 0\), \(y = -5\) into \(y = (x - 5)(x - k)\) and solves to find \(k\ (= -1)\) | |
| P1 | (dep on P2) for factorising or completing the square of \(x^2 + \text{``}{-}4\text{''}x + \text{``}{-}5\text{''}\) and identifying the \(x\)-coordinate of the turning point or for a complete process to find the \(x\)-coordinate of the turning point, eg \((5 + \text{``}{-}1\text{''})/2\) | |
| A1 | cao |
Additional guidance
\(x\)-coordinate of 2 with no or incorrect working gets NO marks