June 2025 Paper 2 Q1
1
In this question you must show detailed reasoning.
Solve the inequality \(x^2 + 3x \leqslant 10\). [3]
| Scheme | Marks | AO |
|---|---|---|
| DR | ||
| \((x - 2)(x + 5)\,[\leqslant 0]\) | M1 | 1.1 |
| \(x = -5\) or \(x = 2\) | A1 | 1.1 |
| \(-5 \leqslant x \leqslant 2\) | A1 | 1.1 |
| [3] |
Notes
M1: Rearrange and attempt to solve quadratic inequality or equation
Some evidence of finding critical values (e.g. factorising or formula etc.) must be seen. This mark is not implied by correct answers.
A1: For both values (may be seen later e.g. embedded in an incorrectly formed inequality or implied by the final A1)
A1: Condone equivalent forms, e.g. \(x \leqslant 2\) and \(x \geqslant -5\) but do not accept open interval(s)
Answers only without working scores 0/3