Moderate -0.8 This is a straightforward quadratic inequality requiring factorization to (x-9)(x+2)>0 and identifying regions where the product is positive. It's a standard C1 exercise with routine technique and no problem-solving insight needed, making it easier than average but not trivial.
\((x \pm a)(x \pm b)\) with \(ab=18\), or \(x = \frac{7 \pm \sqrt{49--72}}{2}\), or \(\left(x-\frac{7}{2}\right)^2 \pm \left(\frac{7}{2}\right)^2 - 18\)
M1
For attempting to find critical values. Factors alone OK; \(x=\) must appear for formula/completing the square
\((x-9)(x+2)\) or \(x = \frac{7 \pm 11}{2}\) or \(x = \frac{7}{2} \pm \frac{11}{2}\)
A1
Factors alone OK. Formula or completing the square need \(x=\) as written
\(x > 9\) or \(x < -2\), choosing "outside"
M1
For choosing outside region. Must have two different critical values. Note: \(-2 > x > 9\) is M1A0; \(-2 < x < 9\) is M0A0
Final answer with strict inequalities
A1
Use of \(\geq\) in final answer gets A0
## Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(x \pm a)(x \pm b)$ with $ab=18$, or $x = \frac{7 \pm \sqrt{49--72}}{2}$, or $\left(x-\frac{7}{2}\right)^2 \pm \left(\frac{7}{2}\right)^2 - 18$ | M1 | For attempting to find critical values. Factors alone OK; $x=$ must appear for formula/completing the square |
| $(x-9)(x+2)$ or $x = \frac{7 \pm 11}{2}$ or $x = \frac{7}{2} \pm \frac{11}{2}$ | A1 | Factors alone OK. Formula or completing the square need $x=$ as written |
| $x > 9$ or $x < -2$, choosing "outside" | M1 | For choosing outside region. Must have two different critical values. Note: $-2 > x > 9$ is M1A0; $-2 < x < 9$ is M0A0 |
| Final answer with strict inequalities | A1 | Use of $\geq$ in final answer gets A0 |
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