Higher June 2022 Paper 2 Q22
22 Find algebraically the set of values of \(x\) for which
\[x^2 - 49 \gt 0 \qquad \textbf{and} \qquad 5x^2 - 31x - 72 \gt 0\](5)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(x \lt -7,\ x \gt 8\) | M1 | for method to solve \(x^2 - 49 \gt 0\) eg \((x + 7)(x - 7)\) or 7 and \(-7\) |
| A1 | for \(x \lt -7\) and \(x \gt 7\) | |
| M1 | for method to solve \(5x^2 - 31x - 72 \gt 0\) eg \((5x \pm 9)(x \pm 8)\) or \(\dfrac{--31 \pm \sqrt{(-31)^2 - 4 \times 5 \times (-72)}}{2 \times 5}\) or 8 and \(-1.8\) oe | |
| A1 | for \(x \lt -1.8\) and \(x \gt 8\) | |
| A1 | cao |
Additional guidance
accept use of = or incorrect inequality symbol for both the M marks
This may be implied by a suitable diagram