Higher November 2024 Paper 2 Q20
20 Solve the inequality \(10x^2 + 11x - 21 \lt 0\)
Show clear algebraic working.
(3)
| Scheme | Marks |
|---|---|
\((10x + 21)(x - 1)\) or \(\dfrac{-11 \pm \sqrt{(11)^2 - 4 \times 10 \times -21}}{2 \times 10}\) \(10\left[\left(x + \dfrac{11}{20}\right)^2 - \dfrac{121}{400}\right] - 21\;(= 0)\) oe | M1 |
| (\(x\) =) 1, (\(x\) =) −2.1 | A1 |
| Working required Answer: \(-2.1 \lt x \lt 1\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: A correct method to solve the quadratic; correct factors or correct substitution into the formula or can be simplified as far as \(\dfrac{-11 \pm \sqrt{121 + 840}}{20}\) or correctly completing the square.
\((10)(x + 2.1)(x - 1)\) is not a correct factorisation – it is working backwards from calculator answers.
A1: dep on M1 for correct critical values
A1: dep on M1
oe eg \(x \gt -2.1\) (and) \(x \lt 1\) (do not penalise ‘or’)
or \(\dfrac{-21}{10} \lt x \lt 1\) etc
including the open interval (–2.1, 1) or ]–2.1, 1[