4MA0 Higher June 2016 Paper 3R Q6
6
(a) Solve the inequalities \(-4 \lt 3x + 5 \leqslant 11\) (3)
(b) Write down the integer values of \(x\) which satisfy \(-4 \lt 3x + 5 \leqslant 11\) (2)
| Scheme | Marks |
|---|---|
\(-9 \lt 3x \leqslant 6\) or \(3x \gt -9\) and \(3x \leqslant 6\) or \(-\dfrac{4}{3} \lt x + \dfrac{5}{3} \leqslant \dfrac{11}{3}\) or \(x + \dfrac{5}{3} \gt -\dfrac{4}{3}\) and \(x + \dfrac{5}{3} \leqslant \dfrac{11}{3}\) or \(x \gt -3\) or \(x \leqslant 2\) | M2 |
| \(-3 \lt x \leqslant 2\) | A1 |
| (3) |
Notes
M2: For both ends correct for \(3x\) or \(x + \dfrac{5}{3}\) or one end correct for \(x\)
M1 for one end correct for \(3x\) or \(x + \dfrac{5}{3}\), eg \(3x \gt -9\) or \(3x \leqslant 6\) or
answers of \(x = -3\) & \(x = 2\)
A1: Accept \(x \gt -3\), \(x \leqslant 2\)
| Scheme | Marks |
|---|---|
| – 2, – 1, 0, 1, 2 | B2ft |
| (2) |
Notes
B2ft: B1 for five correct values and one incorrect value or four correct values with no incorrect value
Only ft from an inequality in the form \(a \lt x \leqslant b\)