Standard +0.8 This requires systematic case analysis of the modulus (splitting at x=6/5), solving two quadratic inequalities, then carefully combining solution sets. More conceptually demanding than routine modulus equations, requiring strong algebraic manipulation and set reasoning, but still within standard C3 scope.
- Correct inequalities implies correct critical values if not seen explicitly
- Solutions of 1, 2 scores B1
- If strict inequalities used throughout penalise 1 mark; if some correct and some strict then mark as scheme
# Question 3:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x^2 - 5x + 6 = 0 \Rightarrow x = 2, 3$ | B1 | B1 can be earned for any correct 2 solutions |
| $x^2 + 5x - 6 = 0 \Rightarrow x = -6, 1$ | B1 | |
| $x \leq -6$ | B1 | or $-6 \geq x$ |
| $x \geq 3$ | B1 | or $3 \leq x$ |
| $1 \leq x \leq 2$ | B1 | And no extras seen |
**Notes:**
- Correct inequalities implies correct critical values if not seen explicitly
- Solutions of 1, 2 scores B1
- If strict inequalities used **throughout** penalise 1 mark; if some correct and some strict then mark as scheme