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Master algebraic skills from linear equations to quadratic graphs. Algebra underpins almost every Cambridge IGCSE maths paper.
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 are a significant step up from linear equations. Students need to factorise, complete the square, and use the quadratic formula to find solutions.
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.
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.
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.
Sequence questions test pattern recognition and formula derivation. Students work with arithmetic, geometric, quadratic and special sequences, finding nth-term rules and using them to solve problems.
Algebraic fractions combine fraction skills with algebraic manipulation and are a step up from basic fractions. Students must simplify, add, subtract, multiply and divide fractions that contain variables, often needing to factorise first.
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.
Expanding brackets (distribution) is a fundamental algebraic skill used across many topics. Students multiply each term inside the bracket by the term outside, progressing to double-bracket expansion and expressions raised to powers.
Rearranging formulae requires students to change the subject of an equation, using the same inverse-operation skills as solving equations but with multiple variables. Harder questions involve subjects that appear twice or under roots and powers.
Function notation formalises the input-output relationship. Students evaluate, combine, and find inverses of functions, building skills that are directly extended in further study.
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.
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.
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).
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