Standard +0.3 This requires squaring both sides to eliminate moduli, then solving a quadratic inequality—a standard technique for |expression| > |expression| problems. It's slightly above average difficulty due to the algebraic manipulation required, but follows a well-established method taught in P2 with no novel insight needed.
State or imply non-modular inequality \((x + 2)^2 > \left(\frac{1}{2}x - 2\right)^2\), or corresponding equation or pair of linear equations
M1
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations
M1
Obtain critical values \(-8\) and \(0\)
A1
State correct answer \(x < -8\) or \(x > 0\)
A1
[4]
OR
Answer
Marks
Guidance
Obtain one critical value, e.g. \(x = -8\), by solving a linear equation (or inequality) or from a graphical method or by inspection
B1
Obtain the other critical value similarly
B2
State correct answer \(x < -8\) or \(x > 0\)
B1
[4]
State or imply non-modular inequality $(x + 2)^2 > \left(\frac{1}{2}x - 2\right)^2$, or corresponding equation or pair of linear equations | M1 |
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations | M1 |
Obtain critical values $-8$ and $0$ | A1 |
State correct answer $x < -8$ or $x > 0$ | A1 | [4] |
**OR**
Obtain one critical value, e.g. $x = -8$, by solving a linear equation (or inequality) or from a graphical method or by inspection | B1 |
Obtain the other critical value similarly | B2 |
State correct answer $x < -8$ or $x > 0$ | B1 | [4] |