Standard +0.3 This is a straightforward modulus inequality requiring consideration of cases based on sign changes at x=0 and x=2/3. While it involves multiple cases and some algebraic manipulation, it's a standard textbook exercise testing routine application of modulus properties without requiring novel insight or extended reasoning.
State or imply non-modular inequality \(x^2 > (3x - 2)^2\), or corresponding equation
M1
Expand and make reasonable solution attempt at 2- or 3-term quadratic, or equivalent
M1
Obtain critical values \(\frac{1}{2}\) and \(1\)
A1
State correct answer \(\frac{1}{2} < x < 1\)
A1
OR
Answer
Marks
State one correct linear equation for a critical value
M1
State two equations separately
A1
Obtain critical values \(\frac{1}{2}\) and \(1\)
A1
State correct answer \(\frac{1}{2} < x < 1\)
A1
OR
Answer
Marks
State one critical value from a graphical method or inspection or by solving a linear inequality
B1
State the other critical value correctly
B2
State correct answer \(\frac{1}{2} < x < 1\)
B1
Total: 4 marks
| State or imply non-modular inequality $x^2 > (3x - 2)^2$, or corresponding equation | M1 |
| Expand and make reasonable solution attempt at 2- or 3-term quadratic, or equivalent | M1 |
| Obtain critical values $\frac{1}{2}$ and $1$ | A1 |
| State correct answer $\frac{1}{2} < x < 1$ | A1 |
**OR**
| State one correct linear equation for a critical value | M1 |
| State two equations separately | A1 |
| Obtain critical values $\frac{1}{2}$ and $1$ | A1 |
| State correct answer $\frac{1}{2} < x < 1$ | A1 |
**OR**
| State one critical value from a graphical method or inspection or by solving a linear inequality | B1 |
| State the other critical value correctly | B2 |
| State correct answer $\frac{1}{2} < x < 1$ | B1 |
**Total: 4 marks**
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