Standard +0.3 This is a straightforward modulus inequality requiring consideration of critical points (x=0 and x=3) and testing intervals, which is a standard technique taught in P2. While it requires systematic case analysis, it's a routine application of the method with no conceptual surprises, making it slightly easier than average.
State or imply non-modular inequality \((x-3)^2 > (2x)^2\) or corresponding quadratic equation or pair of linear equations \((x-3) = \pm 2x\)
M1
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations
M1
Obtain critical values \(x = 1\) and \(x = -3\)
A1
State answer \(-3 < x < 1\)
A1
[4]
OR:
Answer
Marks
Guidance
Obtain critical value \(x = -3\) from a graphical method, or by inspection, or by solving a linear inequality or linear equation
B1
Obtain the critical value \(x = 1\) similarly
B2
State answer \(-3 < x < 1\)
B1
[4]
State or imply non-modular inequality $(x-3)^2 > (2x)^2$ or corresponding quadratic equation or pair of linear equations $(x-3) = \pm 2x$ | M1 |
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations | M1 |
Obtain critical values $x = 1$ and $x = -3$ | A1 |
State answer $-3 < x < 1$ | A1 | [4]
**OR:**
Obtain critical value $x = -3$ from a graphical method, or by inspection, or by solving a linear inequality or linear equation | B1 |
Obtain the critical value $x = 1$ similarly | B2 |
State answer $-3 < x < 1$ | B1 | [4]