Higher January 2023 Paper 2 Q22
22 Solve the inequality \(\;6x^2 + 37x \leqslant 35\)
Show clear algebraic working.
(3)
| Scheme | Marks |
|---|---|
\((6x - 5)(x + 7)\;(= 0)\) or \(\dfrac{-37 \pm \sqrt{37^2 - 4 \times 6 \times -35}}{2 \times 6}\) \(6\left[\left(x + \dfrac{37}{12}\right)^2 - \left(\dfrac{37}{12}\right)^2\right]\ldots\) oe | M1 |
| \(\dfrac{5}{6}\) oe and \(-7\) | A1 |
Working must be seen for both accuracy marks as asked for in question Answer: \(-7 \leqslant x \leqslant \dfrac{5}{6}\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: A correct method to solve the quadratic equation \(6x^2 + 37x - 35\;(= 0)\) using any correct method (if factorising, allow brackets which expanded give 2 out of 3 terms correct) (if using formula allow one sign error in substitution and some simplification – allow as far as \(\dfrac{-37 \pm \sqrt{1369 + 840}}{12}\)) or completing the square as far as shown on left
A1: dep on M1
correct critical values (allow 0.83…)
A1: dep on M1
oe eg \(-7 \leqslant x \leqslant 0.83\ldots\), \(\left[-7, \dfrac{5}{6}\right]\) Accept \(x \leqslant \dfrac{5}{6}\), \(x \geqslant -7\)