Higher November 2018 Paper 2 Q19
19 Solve \(22 \lt \dfrac{m^2 + 7}{4} \lt 32\)
Show all your working. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(9 \lt m \lt 11\) \(-11 \lt m \lt -9\) | M1 | for a correct method to begin rearranging to solve for \(m^2\) eg \(88 \lt m^2 + 7\) or \(m^2 + 7 \lt 128\) or \(81 \lt m^2 \lt 121\) |
| M1 | for a complete method to \(m^2 = 81\) or \(m^2 = 121\) or better | |
| M1 | for a set of critical values: at least two out of 9, 11, \(-9\), \(-11\) | |
| M1 | for selecting a correct inequality for one set of critical values eg \(9 \lt m\) and \(m \lt -9\) or \(m \lt 11\) and \(-11 \lt m\) or \(9 \lt m\) and \(m \lt 11\) or a set of inequalities with some error eg \(9\ ?\ m\ ?\ 11\) and \(-11\ ?\ m\ ?\ -9\) where ? is an incorrect inequality symbol like \(9 \lt m \leqslant 11\) or \(9 \geqslant m \geqslant 11\) or answer given as \(\pm 9 \lt m \lt \pm 11\) | |
| A1 | \(9 \lt m \lt 11\) and \(-11 \lt m \lt -9\) given as boundaries of \(m\) |
Additional guidance
It is insufficient to just multiply all three elements by 4; some rearrangement must occur such as showing as two separate inequalities or isolating \(m^2\)
Accept an inequality used in place of “=”.
\(m^2\) must be isolated at this stage.
Do not award if other values are also given eg 10
Could be shown as \(9 \lt m \lt 11\) or \(-11 \lt m \lt -9\) or \(-11 \lt m \lt 11\)
Accept with an “and” or an “or” or neither