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Completing the square rewrites a quadratic as a squared bracket plus a number. It shows the turning point of a quadratic curve at a glance and solves quadratics that do not factorise, giving exact answers with surds.
Students make these errors again and again. Knowing them in advance gives you a head start.
Using b instead of half of b inside the bracket
Forgetting to subtract the square of the number in the bracket from the constant
Taking out the factor from the x squared and x terms but not multiplying the correction by it
Losing the minus root when taking the square root of both sides
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
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
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
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).
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
Useful for this topic:
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.
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.
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.
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