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.
What You'll Learn
- Solving quadratics by factorising
- Using the quadratic formula
- Completing the square to solve or find turning points
- Recognising the discriminant and what it tells you about solutions
- Setting up quadratic equations from context problems
Watch Out For These Mistakes
Students make these errors again and again. Knowing them in advance gives you a head start.
Forgetting that x squared = 9 gives x = 3 and x = -3 (two solutions)
Sign errors when substituting into the quadratic formula
Failing to rearrange the equation to equal zero before factorising
What Examiners Say About Quadratic Equations
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
Factorising
Factorising is the reverse of expanding brackets and is essential for solving quadratics, simplifying expressions, and working with algebraic fractions. Students progress from single-bracket factorisation to double brackets and the difference of two squares.
Quadratic Graphs
Quadratic graphs produce a characteristic U-shape (parabola). Students must plot quadratics from tables, identify key features like turning points and roots, and use graphs to solve equations.
Simultaneous Equations
Simultaneous equations require students to find values that satisfy two equations at the same time. Students solve pairs of linear equations, then go on to one linear and one quadratic equation together.
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