Algebra is the largest section of Edexcel IGCSE Maths — from basic manipulation through quadratics, simultaneous equations, and function notation to graph transformations.
Linear: solve by inverse operations. Quadratic ax² + bx + c = 0: factorisation, completing the square, formula x = (-b ± √(b²-4ac))/2a. Discriminant: b²-4ac determines nature of roots. Simultaneous: elimination or substitution (one linear + one quadratic for Higher). Inequalities: solve like equations (flip sign when ×/÷ by negative). Represent on number line.
Arithmetic: nth term = a + (n-1)d. Quadratic sequences: second differences constant. Geometric sequences (Higher). Function notation: f(x), composite fg(x) = f(g(x)), inverse f⁻¹(x). Graph transformations: f(x) + a (up), f(x + a) (left), af(x) (stretch vertical), f(ax) (stretch horizontal 1/a), −f(x) (reflect x-axis), f(−x) (reflect y-axis).
Use the quadratic formula when you just need the roots/solutions — it always works and is quick. Use completing the square when: (1) the question specifically asks for it, (2) you need to find the vertex/turning point of a parabola (vertex = (-b/2a, c-b²/4a)), (3) you need to express a quadratic in vertex form a(x+p)²+q, or (4) you\'re solving a disguised quadratic. For sketch and maximum/minimum problems, completing the square is essential because it directly gives the vertex. The formula just gives x-intercepts.
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