Standard +0.8 This requires systematic case analysis of two modulus expressions with different critical points (x = -1/2 and x = 2), solving quadratic inequalities in each region, and combining solutions. More demanding than routine single-modulus problems but follows standard technique for A-level.
State or imply non-modular inequality \((2x+1)^2 < (3(x-2))^2\), or corresponding quadratic equation, or pair of linear equations \((2x+1) = \pm3(x-2)\)
B1
EITHER method
Make reasonable solution attempt at 3-term quadratic e.g. \(5x^2 - 40x + 35 = 0\) or solve two linear equations for \(x\)
M1
Obtain critical values \(x = 1\) and \(x = 7\)
A1
State final answer \(x < 1\) and \(x > 7\)
A1
Obtain critical value \(x = 7\) from graphical method, or by inspection, or by solving a linear equation or inequality
B1
OR method
Obtain critical value \(x = 1\) similarly
B2
State final answer \(x < 1\) and \(x > 7\)
B1
Total: 4
## Question 1:
| Answer | Mark | Guidance |
|--------|------|----------|
| State or imply non-modular inequality $(2x+1)^2 < (3(x-2))^2$, or corresponding quadratic equation, or pair of linear equations $(2x+1) = \pm3(x-2)$ | B1 | EITHER method |
| Make reasonable solution attempt at 3-term quadratic e.g. $5x^2 - 40x + 35 = 0$ or solve two linear equations for $x$ | M1 | |
| Obtain critical values $x = 1$ and $x = 7$ | A1 | |
| State final answer $x < 1$ and $x > 7$ | A1 | |
| Obtain critical value $x = 7$ from graphical method, or by inspection, or by solving a linear equation or inequality | B1 | OR method |
| Obtain critical value $x = 1$ similarly | B2 | |
| State final answer $x < 1$ and $x > 7$ | B1 | |
**Total: 4**
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