Standard +0.3 This is a standard modulus inequality requiring consideration of critical points (x = -1 and x = -5/3) and testing regions, but follows a routine method taught in P2. It's slightly above average difficulty due to the algebraic manipulation needed across multiple cases, but remains a textbook-style question with no novel insight required.
State or imply non-modular inequality \((x+1)^2 < (3x+5)^2\), 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 \(-2\) and \(-\frac{3}{2}\)
A1
State correct answer \(x < -2\) or \(x > -\frac{3}{2}\)
A1
Or
Answer
Marks
Guidance
Obtain one critical value, e.g. \(x = -2\), 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 \(x < -2\) or \(x > -\frac{3}{2}\)
B1
[4]
State or imply non-modular inequality $(x+1)^2 < (3x+5)^2$, 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 $-2$ and $-\frac{3}{2}$ | A1 |
State correct answer $x < -2$ or $x > -\frac{3}{2}$ | A1 |
**Or**
Obtain one critical value, e.g. $x = -2$, 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 $x < -2$ or $x > -\frac{3}{2}$ | B1 | [4]
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