Higher June 2025 Paper 2 Q19
19 Solve the inequality \(4x^2 + 4x - 15 \lt 0\)
Show clear algebraic working.
(3)
| Scheme | Marks |
|---|---|
\((2x - 3)(2x + 5)\) or \(\dfrac{-4 \pm \sqrt{4^2 - 4 \times 4 \times -15}}{2 \times 4}\) or \(4\left[\left(x + \dfrac{1}{2}\right)^2 - \left(\dfrac{1}{2}\right)^2\right] - 15(= 0)\) or \(4\left(x + \dfrac{4}{2 \times 4}\right)^2 - \dfrac{4^2}{4 \times 4} + -15(= 0)\) | M1 |
| 1.5, – 2.5 oe | A1 |
| \(-2.5 \lt x \lt 1.5\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for a correct method to solve the quadratic equation \(4x^2 + 4x - 15 = 0\)
Allow \((4x - 6)(x + 2.5)\) or \((4x + 10)(x - 1.5)\) or \((4x - 6)(4x + 10)\) leading to \((x - 1.5)(x + 2.5)\) or \((4x - 6)(4x + 10)\) leading to correct values of \(x\)
Do not allow \((x - 1.5)(x + 2.5)\) without previous working
(If using formula allow some simplification – allow as far as \(\dfrac{-4 \pm \sqrt{16 + 240}}{8}\))
A1: oe dep on M1
A1: oe dep on M1
Allow \(x \gt -2.5\) (and) \(x \lt 1.5\) oe
Allow any variable as long as used all the way through