June 2024 Paper 1 Q10
10 A function f is given by
\[\begin{aligned} \mathrm{f}(x) &= -\tfrac{1}{2}x + 21 & \qquad 0 &\leqslant x \leqslant 2 \\ &= ax^2 + bx & \qquad 2 &\lt x \leqslant 6 \end{aligned}\]A sketch of \(\quad y = \mathrm{f}(x) \quad\) is shown.
Work out the values of \(a\) and \(b\). [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(P\) is (2, 20) or \(y\) value of \(P\) is 20 | M1 | implied by \(4a + 2b = 20\) could be seen on diagram |
| \(4a + 2b = k\) | M1 | oe \(4a + 2b = 20\) \(k\) could be any number (including 0) but must be 20 if first M mark awarded |
| \(36a + 6b = 12\) | M1 | oe |
| \(a = -2\) or \(b = 14\) | A1 | |
| \(a = -2\) and \(b = 14\) | A1 |
Additional guidance
| \(a = -2\) and \(b = 14\) with no working | M3A2 |
| \(a = -2\) or \(b = 14\) with no working | M0A0 |