AQA C3 2016 June — Question 3 5 marks

Exam BoardAQA
ModuleC3 (Core Mathematics 3)
Year2016
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicModulus function
TypeSolve |quadratic| compared to linear: algebraic inequality
DifficultyStandard +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.
Spec1.02g Inequalities: linear and quadratic in single variable1.02l Modulus function: notation, relations, equations and inequalities

3 Solve $$x ^ { 2 } \geqslant | 5 x - 6 |$$ [5 marks]

Question 3:
AnswerMarks Guidance
Answer/WorkingMark 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
# 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
3 Solve

$$x ^ { 2 } \geqslant | 5 x - 6 |$$

[5 marks]

\hfill \mbox{\textit{AQA C3 2016 Q3 [5]}}