Foundation November 2024 Paper 2 Q21
21
(a) Show that \((x + 3)(x - 5) = x^2 - 2x - 15\). [1]
(b) The diagram shows a sketch of the graph \(y = (x + 3)(x - 5)\).
Complete the diagram by adding the values of the three intercepts with the axes. [2]
(c) The minimum point on the graph is marked T.
Write down the coordinates of the point T. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(x^2 + 3x - 5x - 15\) [\(= x^2 - 2x - 15\)] | 1 | All four terms must be seen Could be seen in a grid | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(-15\) [\(y\)-intercept] | 1 | Allow \((0, -15)\) | |
| \(-3\) and 5 [roots] | 1 | Must be in correct place. | Allow \((-3, 0)\) and \((5, 0)\) |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \((1, -16)\) | 2 | B1FT for 1 | B1FT is mid-point of their two roots from 21(b) provided one is positive and one negative. Their 1 must be > 0 |
| B1FT for \(-16\) | B1FT for their value of \(x\) their \(-16\) must be \(< 0\) | ||