Foundation June 2025 Paper 2 Q26
26
(a) Solve the inequality \(7 - 3t \lt 2t + 15\) (2)
The region R, shown shaded in the diagram, is bounded by three straight lines.
(b) Write down three inequalities that define the region R (3)
| Scheme | Marks |
|---|---|
| \(-3t - 2t \lt 15 - 7\) or \(-5t \lt 8\) oe or \(7 - 15 \lt 2t + 3t\) or \(-8 \lt 5t\) oe or \(t = -1.6\) or \(t \lt -1.6\) | M1 |
| Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: \(t \gt -1.6\) | A1 |
| (2) |
Notes
M1: for correctly isolating terms in \(t\) on one side and number terms on the other side (use of = or any inequality symbol or variable is permitted)
A1: oe eg \(-1.6 \lt t\) or \(t \gt -\dfrac{8}{5}\) or \(-\dfrac{8}{5} \lt t\) oe
Must have correct inequality symbol on answer line
NB Sight of correct answer in working space and just \((t =)-1.6\) oe on answer line gains M1 only
| Scheme | Marks |
|---|---|
| \(x \geqslant 2\) | B1 |
| \(y \geqslant 3\) | B1 |
| \(x + y \leqslant 9\) | B1 |
| (3) | |
| (5 marks) |
Notes
B1: oe allow \(x \gt 2\) or \(2 \lt x\)
B1: oe allow \(y \gt 3\) or \(3 \lt y\)
B1: oe allow \(x + y \lt 9\) or \(y \lt 9 - x\) or \(9 \gt x + y\)
SC B2 for all of \(x \leqslant 2\), \(y \leqslant 3\), \(x + y \geqslant 9\) oe
or
\(x \lt 2\), \(y \lt 3\), \(x + y \gt 9\)
SC B1 for all of \(x = 2\), \(y = 3\), \(x + y = 9\) oe