Standard +0.8 This requires solving an inequality involving two modulus expressions, necessitating systematic case analysis across multiple critical points (x = 1/2 and x = -2), then solving quadratic inequalities in each region and combining solutions. More demanding than routine single-modulus problems but follows a standard technique for P3 level.
State or imply non-modular inequality \((2x-1)^2 > 3^2(x+2)^2\), or corresponding quadratic equation, or pair of linear equations
B1
Make reasonable attempt at solving a 3-term quadratic, or solve two linear equations for \(x\)
M1
Obtain critical values \(x = -7\) and \(x = -1\)
A1
State final answer \(-7 < x < -1\)
A1
Alternative method for Question 1:
Answer
Marks
Guidance
Answer
Mark
Guidance
Obtain critical value \(x = -1\) from a graphical method, or by solving a linear equation or linear inequality
B1
Obtain critical value \(x = -7\) similarly
B2
State final answer \(-7 < x < -1\)
B1
Do not condone \(\leqslant\) for \(<\) in the final answer
Total: 4 marks
## Question 1:
| Answer | Mark | Guidance |
|--------|------|----------|
| State or imply non-modular inequality $(2x-1)^2 > 3^2(x+2)^2$, or corresponding quadratic equation, or pair of linear equations | B1 | |
| Make reasonable attempt at solving a 3-term quadratic, or solve two linear equations for $x$ | M1 | |
| Obtain critical values $x = -7$ and $x = -1$ | A1 | |
| State final answer $-7 < x < -1$ | A1 | |
**Alternative method for Question 1:**
| Answer | Mark | Guidance |
|--------|------|----------|
| Obtain critical value $x = -1$ from a graphical method, or by solving a linear equation or linear inequality | B1 | |
| Obtain critical value $x = -7$ similarly | B2 | |
| State final answer $-7 < x < -1$ | B1 | Do not condone $\leqslant$ for $<$ in the final answer |
**Total: 4 marks**