Standard +0.3 This is a standard modulus inequality requiring case-by-case analysis based on critical points x = 1 and x = -1/2. Students must consider three intervals, square both sides or use sign analysis, then combine solutions. Slightly above average difficulty due to the algebraic manipulation required, but follows a well-practiced technique for A-level Pure Mathematics 3.
State or imply non-modular inequality \(3(x-1)^2 < (2x+1)^2\) or corresponding quadratic equation, or pair of linear equations \(3(x-1) = \pm(2x+1)\)
B1
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations
M1
Obtain critical values \(x = \frac{2}{5}\) and \(x = 4\)
A1
State answer \(\frac{2}{5} < x < 4\)
A1
[Do not condone \(\leq\) for \(<\).]
OR
Obtain critical value \(x = \frac{2}{5}\) or \(x = 4\) from a graphical method, or by inspection, or by solving a linear equation or inequality
B1
Obtain critical values \(x = \frac{2}{5}\) and \(x = 4\)
B2
State answer \(\frac{2}{5} < x < 4\)
B1
[4]
**EITHER** | |
State or imply non-modular inequality $3(x-1)^2 < (2x+1)^2$ or corresponding quadratic equation, or pair of linear equations $3(x-1) = \pm(2x+1)$ | B1 |
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations | M1 |
Obtain critical values $x = \frac{2}{5}$ and $x = 4$ | A1 |
State answer $\frac{2}{5} < x < 4$ | A1 | [Do not condone $\leq$ for $<$.]
**OR** | |
Obtain critical value $x = \frac{2}{5}$ or $x = 4$ from a graphical method, or by inspection, or by solving a linear equation or inequality | B1 |
Obtain critical values $x = \frac{2}{5}$ and $x = 4$ | B2 |
State answer $\frac{2}{5} < x < 4$ | B1 | [4]