Standard +0.3 This requires understanding modulus inequalities and systematic case analysis by considering critical points at x=a and x=3a. While it involves multiple cases, the algebraic manipulation within each case is straightforward, making it slightly above average difficulty but still a standard textbook exercise for P3 level.
State non-modular inequality \((x-3a)^2 > (x-a)^2\), or corresponding equation
B1
OR:
Answer
Marks
State a correct linear equation for the critical value, e.g. \(-3a = -(x-a)\), or corresponding inequality
B1
Solve the linear equation for \(x\), or equivalent
M1
Obtain critical value \(2a\)
A1
State correct answer \(x < 2a\) only
A1
OR:
Answer
Marks
Guidance
Make recognizable sketches of both \(y =
x - 3a
\) and \(y =
Obtain a critical value from the intersection of the graphs
M1
Obtain critical value \(2a\)
A1
Obtain correct answer \(x < 2a\) only
A1
Total: [4]
**EITHER:**
Expand and solve the inequality, or equivalent | M1 |
Obtain critical value $2a$ | A1 |
State correct answer $x < 2a$ only | A1 |
State non-modular inequality $(x-3a)^2 > (x-a)^2$, or corresponding equation | B1 |
**OR:**
State a correct linear equation for the critical value, e.g. $-3a = -(x-a)$, or corresponding inequality | B1 |
Solve the linear equation for $x$, or equivalent | M1 |
Obtain critical value $2a$ | A1 |
State correct answer $x < 2a$ only | A1 |
**OR:**
Make recognizable sketches of both $y = |x - 3a|$ and $y = |x - a|$ on a single diagram | B1 |
Obtain a critical value from the intersection of the graphs | M1 |
Obtain critical value $2a$ | A1 |
Obtain correct answer $x < 2a$ only | A1 |
**Total: [4]**
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