Inequalities Revision Notes for IGCSE Maths
These comprehensive revision notes cover everything you need to know about inequalities for the Cambridge IGCSE Mathematics 0580 examination. Written by Teacher Rig, each section includes key concepts, essential formulas, and practical exam tips to help you achieve your best grade.
Linear Inequalities
Solve linear inequalities using the same methods as equations, with one crucial difference: if you multiply or divide by a negative number, you must reverse the inequality sign. The solution is a range of values, not a single value.
Key Formulas
- Solving is like equations, but flip sign when multiplying/dividing by negative
Exam Tips
- FLIP the inequality sign when multiplying or dividing by a negative
- Keep the variable on the left for clarity
- Represent solutions on a number line: open circle for < or >, closed circle for <= or >=
Double Inequalities
A double inequality like a < x + 2 < b can be solved by performing the same operation on all three parts simultaneously. List integer values carefully, noting which endpoints are included.
Exam Tips
- Apply operations to ALL THREE parts simultaneously
- < means the endpoint is NOT included, <= means it IS included
- List integers carefully - this is a common source of lost marks
Graphical Inequalities
To represent inequalities graphically: draw the boundary line (solid for <= or >=, dashed for < or >), then shade the correct region. Test a point like (0,0) to determine which side to shade. The feasible region satisfies all inequalities simultaneously.
Exam Tips
- Use a solid line for <= or >= and a dashed line for < or >
- Test (0,0) unless the line passes through the origin
- Label the required region clearly - shade the region you want or the region you do not want, as instructed
Quadratic Inequalities
To solve a quadratic inequality: (1) solve the corresponding equation to find the critical values, (2) sketch the parabola, (3) read off the solution from the graph. For ax squared + bx + c <= 0 with a > 0, the solution is between the roots. For >= 0, the solution is outside the roots.
Key Formulas
- Solve ax squared + bx + c = 0 first to find critical values
Exam Tips
- Always sketch the parabola to see which region satisfies the inequality
- For <= 0 (below x-axis): solution is between the roots
- For >= 0 (above x-axis): solution is outside the roots (two separate intervals)
Revision Checklist
- I understand all key concepts in inequalities
- I have memorised the essential inequalities formulas
- I can apply these concepts to exam-style questions
- I have practised past paper questions on inequalities
- I know the common mistakes to avoid in inequalities questions
Frequently Asked Questions
What inequalities topics are covered in IGCSE Maths?
The IGCSE 0580 syllabus covers inequalities across both Core and Extended tiers. Key areas include linear inequalities. Key areas include double inequalities. Key areas include graphical inequalities.
How important is inequalities in the IGCSE exam?
Inequalities is a significant part of the IGCSE Mathematics exam, typically appearing in Paper 2 (non-calculator) and Paper 4 (calculator). Questions range from straightforward calculations to multi-step problems that combine inequalities with other topics.
What are the most common mistakes in inequalities?
Common mistakes include not showing full working, forgetting to state units, misreading the question, and rushing through calculations. For inequalities specifically, make sure you understand the underlying concepts rather than just memorising procedures.
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