Standard +0.3 This is a standard modulus inequality requiring case-by-case analysis based on critical points x = -2 and x = 1/3. Students must consider three intervals, square both sides or use sign analysis, then combine solution sets. Slightly above average difficulty due to the algebraic manipulation required, but follows a well-practiced technique with no novel insight needed.
State or imply non-modular inequality \((x+2)^2 > (3x-1)^2\), or corresponding quadratic equation, or pair of linear equations \(2(x+2) = \pm(3x-1)\)
B1
Make reasonable attempt at solving a 3-term quadratic, or solve two linear equations for \(x\)
M1
Obtain critical values \(x = -\frac{3}{5}\) and \(x = 5\)
A1
State final answer \(-\frac{3}{5} < x < 5\)
A1
Alternative method:
Obtain critical value \(x = 5\) from graphical method, or by inspection, or by solving a linear equation or inequality
B1
Obtain critical value \(x = -\frac{3}{5}\) similarly
B2
State final answer \(-\frac{3}{5} < x < 5\)
B1
Total
4
**Question 1:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| State or imply non-modular inequality $(x+2)^2 > (3x-1)^2$, or corresponding quadratic equation, or pair of linear equations $2(x+2) = \pm(3x-1)$ | B1 | |
| Make reasonable attempt at solving a 3-term quadratic, or solve two linear equations for $x$ | M1 | |
| Obtain critical values $x = -\frac{3}{5}$ and $x = 5$ | A1 | |
| State final answer $-\frac{3}{5} < x < 5$ | A1 | |
| **Alternative method:** | | |
| Obtain critical value $x = 5$ from graphical method, or by inspection, or by solving a linear equation or inequality | B1 | |
| Obtain critical value $x = -\frac{3}{5}$ similarly | B2 | |
| State final answer $-\frac{3}{5} < x < 5$ | B1 | |
| **Total** | **4** | |
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