Standard +0.3 This is a straightforward modulus inequality requiring consideration of critical points (x = 0 and x = 1/2) and testing intervals, which is a standard technique taught in P2. While it requires systematic case analysis, it's a routine application of modulus inequality methods with no novel insight needed, making it slightly easier than average.
State or imply non-modular inequality \((2x-1)^2 < (3x)^2\) or corresponding equation
B1
Expand and make reasonable solution attempt at \(2x\) or 3-term quadratic, or equivalent
M1
Obtain critical values \(-1\) and \(\frac{1}{2}\)
A1
State correct answer \(x < -1, x > \frac{1}{2}\)
A1
Or:
Answer
Marks
State one correct equation for a critical value e.g. \(2x - 1 = 3x\)
M1
State two relevant equations separately e.g. \(2x - 1 = 3x\) and \(2x - 1 = -3x\)
A1
Obtain critical values \(-1\) and \(\frac{1}{2}\)
A1
State correct answer \(x < -1, x > \frac{1}{2}\)
A1
Or:
Answer
Marks
Guidance
State one critical value (probably \(x = -1\)), from a graphical method or by inspection or by solving a linear inequality
B1
State the other critical value correctly
B2
State correct answer \(x < -1, x > \frac{1}{2}\)
B1
4
[The answer \(\frac{1}{2} < x < -1\) scores B0.]
**Either method:**
State or imply non-modular inequality $(2x-1)^2 < (3x)^2$ or corresponding equation | B1 |
Expand and make reasonable solution attempt at $2x$ or 3-term quadratic, or equivalent | M1 |
Obtain critical values $-1$ and $\frac{1}{2}$ | A1 |
State correct answer $x < -1, x > \frac{1}{2}$ | A1 |
**Or:**
State one correct equation for a critical value e.g. $2x - 1 = 3x$ | M1 |
State two relevant equations separately e.g. $2x - 1 = 3x$ and $2x - 1 = -3x$ | A1 |
Obtain critical values $-1$ and $\frac{1}{2}$ | A1 |
State correct answer $x < -1, x > \frac{1}{2}$ | A1 |
**Or:**
State one critical value (probably $x = -1$), from a graphical method or by inspection or by solving a linear inequality | B1 |
State the other critical value correctly | B2 |
State correct answer $x < -1, x > \frac{1}{2}$ | B1 | 4 |
[The answer $\frac{1}{2} < x < -1$ scores B0.]
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