Inequalities
Inequalities extend equation-solving skills by introducing ranges of solutions rather than single values. Students must solve, represent on number lines, and shade regions on graphs defined by multiple inequalities.
What You'll Learn
- Solving linear inequalities in one variable
- Representing solutions on a number line
- Solving quadratic inequalities
- Shading regions defined by inequalities on a graph
Watch Out For These Mistakes
Students make these errors again and again. Knowing them in advance gives you a head start.
Forgetting to reverse the inequality sign when multiplying or dividing by a negative number
Confusing open and closed circles on number lines (open for strict, closed for inclusive)
Writing the solution set the wrong way round for quadratic inequalities
What Examiners Say About Inequalities
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
- Misconception●●●●●
You can ONLY cancel FACTORS (things multiplied), not terms added/subtracted. Factorise numerator and denominator first, then cancel matching brackets. Never cancel x² from x² − 25.
Source: CIE 0580 · May/June 2021 · Paper 4 · Q7a
- Presentation●●●●●
In 'show that k = 8' questions, you must DERIVE 8, not assume it. Starting from 'k = 8' and working both ways is circular and scores zero. Work from the given info towards the target.
Source: CIE 0580 · May/June 2021 · Paper 3 · Q5
- Common Mistake●●●●●
When raising a power to a power, MULTIPLY the exponents: (x³)³ = x⁹, not x⁶. But for coefficients like (4x³)³, the coefficient is raised: 4³ = 64, not 4 × 3 = 12.
Source: CIE 0580 · Feb/March 2024 · Paper 2 · Q21b
Based on 3of 500+ insights extracted from CIE 0580 examiner reports (2018–2024).
Exam Coverage
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
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Related Topics
Solving Linear Equations
Linear equations are one of the most frequently tested algebra topics at Cambridge IGCSE level. Students must isolate the unknown variable by applying inverse operations, handling brackets and fractions along the way.
Quadratic Equations
Quadratic equations are a significant step up from linear equations. Students need to factorise, complete the square, and use the quadratic formula to find solutions.
Graphing Linear Equations
Straight-line graphs form the basis for understanding gradients, intercepts and real-world modelling. Students need to plot lines from equations, find gradients and interpret y = mx + c.
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