Standard +0.8 This requires understanding modulus inequalities and systematically considering multiple cases (four sign combinations). Students must square both sides correctly, solve a quadratic inequality, then verify solutions against case conditions—more demanding than routine single-modulus problems but standard for P3 level.
EITHER: State or imply non-modular inequality \((2x-5)^2 > (3(2x+1))^2\), or corresponding quadratic equation, or pair of linear equations \((2x-5) = \pm 3(2x+1)\)
B1
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations for \(x\)
M1
Obtain critical values \(-2\) and \(\frac{1}{4}\)
A1
State final answer \(-2 < x < \frac{1}{4}\)
A1
OR: Obtain critical value \(x = -2\) from graphical method, or by inspection, or by solving a linear equation or inequality
(B1)
Obtain critical value \(x = \frac{1}{4}\) similarly
(B2)
State final answer \(-2 < x < \frac{1}{4}\)
(B1)
Do not condone \(\leqslant\) for \(<\)
Total: 4
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| EITHER: State or imply non-modular inequality $(2x-5)^2 > (3(2x+1))^2$, or corresponding quadratic equation, or pair of linear equations $(2x-5) = \pm 3(2x+1)$ | B1 | |
| Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations for $x$ | M1 | |
| Obtain critical values $-2$ and $\frac{1}{4}$ | A1 | |
| State final answer $-2 < x < \frac{1}{4}$ | A1 | |
| OR: Obtain critical value $x = -2$ from graphical method, or by inspection, or by solving a linear equation or inequality | (B1) | |
| Obtain critical value $x = \frac{1}{4}$ similarly | (B2) | |
| State final answer $-2 < x < \frac{1}{4}$ | (B1) | Do not condone $\leqslant$ for $<$ |
| **Total: 4** | | |
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