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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.
Take our free diagnostic quiz to find out which algebra topics need the most work, then practise with our AI tutor.