June 2022 Paper 2 Q5
5 Work out all the negative integer values of \(x\) for which \(\quad 3x^2 \lt 48\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(-3 \quad -2 \quad -1\) with no other values | B3 | any order B2 \(-3 \quad -2 \quad -1\) with one other value or any two of \(-3 \quad -2 \quad -1\) with no other values or inequality for which the only integer values are \(-3 \quad -2 \quad -1\) eg \(-4 \lt x \lt 0\) or \(-3 \leqslant x \leqslant -1\) or \(-4 \lt x \leqslant -1\) B1 \(-4 \lt x \lt 4\) or \(-3 \quad -2 \quad -1 \quad (0) \quad 1 \quad 2 \quad 3\) with no other values or one of \(-3 \quad -2 \quad -1\) with no other values or \(x^2 \lt \dfrac{48}{3}\) or \(x^2 \lt 16\) or \(3(x + 4)(x - 4) \lt 0\) or \((x + 4)(x - 4) \lt 0\) |
Additional guidance
| B1 may be awarded for correct work with no, or incorrect answer, even if this is seen amongst multiple attempts | |
| Answer \(-3 \quad -2 \quad -1\) with no other values (no need to check working) | B3 |
| \(-4 \lt x \lt 0\) is equivalent to the two inequalities \(x \gt -4 \quad x \lt 0\) etc | B2 |
| For B1 allow equivalent factorised inequalities or equivalent inequalities with coefficient 1 for \(x^2\) eg1 \((3x + 12)(x - 4) \lt 0\) eg2 \(3(4 + x)(4 - x) \gt 0\) eg3 \(x^2 - \dfrac{48}{3} \lt 0\) | B1 B1 B1 |
| \((-4, 0)\) or \([-3, -1]\) etc | B2 |
| \((-4, 4)\) | B1 |
| Only \(x \gt -4\) or only \(x \lt \pm 4\) or only \(x \lt 4\) | B0 |
| Condone B3 response in working with any inequality on answer line | B3 |
| Condone B3 response in working with 3 on answer line (3 is likely to be the number of integers) | B3 |
| Only invalid inequalities with no or incorrect answer | B0 |
| Only equations with no or incorrect answer | B0 |