IGCSE Maths Inequalities — Past Paper Question Analysis
Inequalities is a key topic in the Cambridge IGCSE Mathematics 0580 syllabus and appears consistently across all exam sessions. Understanding how inequalities questions are structured in past papers g
Inequalities is a key topic in the Cambridge IGCSE Mathematics 0580 syllabus and appears consistently across all exam sessions. Understanding how inequalities questions are structured in past papers gives you a significant advantage. This page analyses question patterns, mark allocation, and examiner expectations so you can prepare strategically. Teacher Rig uses past paper analysis as a core part of exam preparation, ensuring students are familiar with every question type they may encounter.
Question Patterns in Inequalities
| Pattern | Frequency | Papers | Marks |
|---|---|---|---|
| Solving linear inequalities | Very Common | Paper 2, Paper 4 | 2-3 marks |
| Graphical inequalities | Common | Paper 4 | 4-6 marks |
| Solving quadratic inequalities | Common | Paper 4 | 3-4 marks |
| Double inequalities | Common | Paper 2, Paper 4 | 2-3 marks |
Solving linear inequalities
Solve like an equation but remember: when multiplying or dividing by a negative number, reverse the inequality sign. List integers in the solution set if asked.
Graphical inequalities
Draw each boundary line (solid for <= or >=, dashed for < or >). Test a point to determine which side to shade. The solution region satisfies all inequalities simultaneously.
Solving quadratic inequalities
Solve the corresponding equation first to find critical values. Sketch the quadratic to determine which region satisfies the inequality.
Double inequalities
Solve both parts simultaneously by performing the same operation to all three parts. For example, in 3 < 2x + 1 < 9, subtract 1 from all parts then divide by 2.
Year-by-Year Trends
Over the past five exam sessions, inequalities questions have remained consistent in both style and difficulty. The May/June sessions tend to feature slightly more challenging inequalities problems compared to October/November. Recent papers show an increased emphasis on multi-step problems that combine inequalities with other topics, particularly in Paper 4. The total marks allocated to inequalities have remained stable, typically comprising the same proportion of the overall paper.
Mark Allocation
In Paper 2 (non-calculator), inequalities questions typically carry 4-8 marks and test conceptual understanding without complex arithmetic. In Paper 4 (calculator), inequalities questions can carry up to 10-12 marks and often involve multi-step problems with real-world contexts. Part (a) questions usually carry 1-2 marks for straightforward recall, while later parts build in difficulty and carry 3-5 marks each.
Common Question Setups
- A number line showing an inequality to write algebraically
- A set of linear inequalities to solve and list integer solutions
- A graph with shaded regions representing inequalities
- A quadratic inequality to solve using a sketch
Examiner Insights
- The most common error is forgetting to reverse the inequality when multiplying or dividing by a negative
- For graphical inequalities, always test a point to confirm the correct side
- Use a solid line for ≤ or ≥ and a dashed line for < or >
- List integer values when the question asks for them — do not just give the algebraic solution
Worked Examples
Full solutions for Inequalities
Revision Notes
Key concepts & formulas
Common Mistakes
Avoid these errors
Frequently Asked Questions
What inequality topics are on Core vs Extended?
Core covers solving simple linear inequalities and representing them on number lines. Extended adds graphical inequalities, quadratic inequalities, and more complex algebraic inequalities.
When do I reverse the inequality sign?
Reverse the inequality sign when you multiply or divide both sides by a negative number. For example, -2x > 6 becomes x < -3 when you divide by -2.
How do I shade graphical inequalities?
Draw the boundary line (solid for ≤/≥, dashed for </>) then test a point like (0,0). If it satisfies the inequality, shade that side. The final answer region satisfies ALL inequalities simultaneously.
Master Inequalities Past Paper Questions
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