Moderate -0.8 This is a straightforward quadratic inequality requiring factorization (or quadratic formula) followed by standard inequality reasoning with critical values. It's a routine C1 exercise with no complications, making it easier than average but not trivial since students must correctly identify the solution interval.
For factors giving at least two out of three terms correct when expanded and collected; or use of formula or completing the square with at most one error (comp square must reach \([5](x-a)^2 \leq b\) or \((5x-c)^2 \leq d\) stage); if correct: \(5(x-2.8)^2 \leq 51.2\) or \((x-2.8)^2 \leq 10.24\) or \((5x-14)^2 \leq 256\)
Boundary values \(-0.4\) oe and \(6\) soi
A1
A0 for just \(\frac{28 \pm \sqrt{1024}}{10}\)
\(-0.4 \leq x \leq 6\) oe
A2
May be separate inequalities; mark final answer. A1 for one end correct e.g. \(x \leq 6\) or for \(-0.4 < x < 6\) oe; or B1 for \(a \leq x \leq b\) ft their boundary values; condone unsimplified but correct \(\frac{28-\sqrt{1024}}{10} \leq x \leq \frac{28+\sqrt{1024}}{10}\); allow A1 for \(-0.4 \leq 0 \leq 6\); condone errors in inequality signs during working towards final answer
[4]
## Question 3:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(5x+2)(x-6)$ | M1 | For factors giving at least two out of three terms correct when expanded and collected; or use of formula or completing the square with at most one error (comp square must reach $[5](x-a)^2 \leq b$ or $(5x-c)^2 \leq d$ stage); if correct: $5(x-2.8)^2 \leq 51.2$ or $(x-2.8)^2 \leq 10.24$ or $(5x-14)^2 \leq 256$ |
| Boundary values $-0.4$ oe and $6$ soi | A1 | A0 for just $\frac{28 \pm \sqrt{1024}}{10}$ |
| $-0.4 \leq x \leq 6$ oe | A2 | May be separate inequalities; mark final answer. A1 for one end correct e.g. $x \leq 6$ or for $-0.4 < x < 6$ oe; or B1 for $a \leq x \leq b$ ft their boundary values; condone unsimplified but correct $\frac{28-\sqrt{1024}}{10} \leq x \leq \frac{28+\sqrt{1024}}{10}$; allow A1 for $-0.4 \leq 0 \leq 6$; condone errors in inequality signs during working towards final answer |
| **[4]** | | |
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