Foundation June 2023 Paper 2R Q23
23
(a) Solve \(9 - 4x \gt 17\) (2)
(b) Write down the three inequalities that represent the shaded region \(R\) (3)
| Scheme | Marks |
|---|---|
\(-4x \gt 17 - 9\) or \(-4x \gt 8\) or \(9 - 17 \gt 4x\) or \(-8 \gt 4x\) or \(\dfrac{9}{4} - x \gt \dfrac{17}{4}\) oe or \(-\dfrac{9}{4} + x \lt -\dfrac{17}{4}\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \(x \lt -2\) | A1 |
| (2) |
Notes
M1: for a correct first step
Condone = rather than > or any other sign for this mark.
A1: oe eg \(-2 \gt x\)
(sight of correct answer in working space and just \((x =)\) –2 on answer line gains M1 only)
| Scheme | Marks |
|---|---|
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \(y \geqslant 2\) \(x \leqslant 6\) \(y \leqslant x\) | B3 |
| (3) | |
| (5 marks) |
Notes
B3: for all 3 correct
Allow \(2 \leqslant y\), \(6 \geqslant x\) and \(x \geqslant y\)
B2 for 2 correct
B1 for 1 correct
Allow < and > signs
SCB2: \(y \leqslant 2\), \(y \geqslant x\) and \(x \geqslant 6\) (for all 3)
Allow < and > signs