June 2025 Paper 2 Q9
9
\[\begin{aligned} \mathrm{f}(x) &= x^2 + px & \qquad x &\leqslant 1 \\ &= 2p - \tfrac{1}{2}x & \qquad x &\gt 1 \end{aligned}\]A sketch of \(\quad y = \mathrm{f}(x) \quad\) is shown.
Work out the value of \(p\). [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(1 + p = 2p - \dfrac{1}{2}\) | M1 | oe equation eg \(1^2 + p \times 1 = 2p - \dfrac{1}{2} \times 1\) |
| \(\dfrac{3}{2}\) or 1.5 | A1 | oe value eg \(1\dfrac{1}{2}\) |