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Master algebraic skills from linear equations to quadratic graphs. Algebra underpins almost every GCSE and IGCSE maths paper.
Linear equations are one of the most frequently tested algebra topics at GCSE level. Students must isolate the unknown variable by applying inverse operations, handling brackets and fractions along the way.
Quadratic equations appear throughout the higher tier GCSE paper and are a significant step up from linear equations. Students need to factorise, complete the square, and use the quadratic formula to find solutions.
Simultaneous equations require students to find values that satisfy two equations at the same time. Foundation students solve linear pairs, while higher-tier students tackle 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 at higher tier 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 tested at higher tier. 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. Higher-tier questions involve subjects that appear twice or under roots and powers.
Function notation is a higher-tier topic that formalises the input-output relationship. Students evaluate, combine, and find inverses of functions, building skills that are directly extended at A-Level.
Straight-line graphs are tested at every tier and 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) and are tested at both foundation and higher tier. 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.
“Candidates who recognised that the numerator and denominator should be first factorised to create products were frequently successful. However, a common wrong approach was to merely cancel the x² in the first step with (x² − 25)/(x² − x − 20) = −25/(−x − 20) = 5/(x + 4), or similar, commonly seen.”
Source: CIE 0580 · November 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.
“This 'show that' question was often not attempted. Candidates who did attempt it often did not gain credit as they generally used the answer of k = 8 as part of their working. Candidates should be reminded that in any 'show that' question candidates must not use what they are asked to show as part of their answer.”
Source: CIE 0580 · November 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.
“A small number incorrectly simplified the power by adding to give 6 rather than multiplying to give 9. Others correctly multiplied the powers but also multiplied the coefficient giving the incorrect answer of 12x⁹.”
Source: CIE 0580 · June 2024 · Paper 2 · Q21b
Based on 3of 510+ insights extracted from CIE 0580 examiner reports (2018–2024).
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