Moderate -0.3 This is a straightforward modulus inequality requiring students to consider cases based on critical points x = 4 and x = -1, then solve linear inequalities in each region. While it requires systematic case analysis, the algebraic manipulation is routine and the question is a standard textbook exercise with no novel insight needed, making it slightly easier than average.
State or imply non-modular inequality \((x-4)^2 > (x+1)^2\), or corresponding equation
B1
Expand and solve a linear inequality, or equivalent
M1
Obtain critical value \(1\frac{1}{2}\)
A1
State correct answer \(x < 1\frac{1}{2}\)
A1
allow \(\leq\)
OR: State a correct linear equation for the critical value e.g. \(4-x = x+1\)
B1
Solve the linear equation for \(x\)
M1
Obtain critical value \(1\frac{1}{2}\), or equivalent
A1
State correct answer \(x < 1\frac{1}{2}\)
A1
OR: State the critical value \(1\frac{1}{2}\), or equivalent, from a graphical method or by inspection or by solving a linear inequality
B3
State correct answer \(x < 1\frac{1}{2}\)
B1
Total: [4]
# Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| State or imply non-modular inequality $(x-4)^2 > (x+1)^2$, or corresponding equation | B1 | |
| Expand and solve a linear inequality, or equivalent | M1 | |
| Obtain critical value $1\frac{1}{2}$ | A1 | |
| State correct answer $x < 1\frac{1}{2}$ | A1 | allow $\leq$ |
| **OR:** State a correct linear equation for the critical value e.g. $4-x = x+1$ | B1 | |
| Solve the linear equation for $x$ | M1 | |
| Obtain critical value $1\frac{1}{2}$, or equivalent | A1 | |
| State correct answer $x < 1\frac{1}{2}$ | A1 | |
| **OR:** State the critical value $1\frac{1}{2}$, or equivalent, from a graphical method or by inspection or by solving a linear inequality | B3 | |
| State correct answer $x < 1\frac{1}{2}$ | B1 | |
**Total: [4]**
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