Foundation January 2023 Paper 1 Q25
25
(a) Factorise \(y^2 - 2y - 48\) (2)
(b) Write down the inequality shown on the number line
(c) Solve the inequality \(7w + 6 \gt 12w + 14\) (3)
| Scheme | Marks |
|---|---|
| \((y \pm 6)(y \pm 8)\) or \(y(y + 6) - 8(y + 6)\) or \(y(y - 8) + 6(y - 8)\) | M1 |
| \((y + 6)(y - 8)\) | A1 |
| (2) |
Notes
M1: or for \((y \pm a)(y \pm b)\) where \(ab = -48\) or \(a + b = -2\)
A1: oe Allow any letter for \(y\)
| Scheme | Marks |
|---|---|
| \(x \leqslant 3\) | B1 |
| (1) |
Notes
B1: allow \(3 \geqslant x\)
Allow any letter for \(x\)
| Scheme | Marks |
|---|---|
| \(6 - 14 \gt 12w - 7w\) oe or \(7w - 12w \gt 14 - 6\) oe | M1 |
\(-8 \gt 5w\) or \(-5w \gt 8\) or \(-w \gt \dfrac{8}{5}\) or \(w \gt -\dfrac{8}{5}\) or \(w = -\dfrac{8}{5}\) oe | M1 |
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(w \lt -\dfrac{8}{5}\) | A1 |
| (3) | |
| (6 marks) |
Notes
M1: Condone = rather than > or any other sign for this mark.
M1: Condone = rather than > or any other sign for this mark.
A1: oe accept \(-\dfrac{8}{5} \gt w\)
Must have correct sign on answer line dep on M1
(sight of correct answer in working space and just \((w =)\;-\dfrac{8}{5}\) oe on answer line gains M2 only)