Edexcel IGCSE Maths topic guide

Algebra and Functions

Algebra questions reward a method that can be followed line by line. Keeping equality balanced, showing substitutions and checking solutions makes it easier to secure method marks even when arithmetic later goes wrong.

Foundation and Higher relevance

Core content for Foundation and Higher, with non-linear simultaneous equations, functions, algebraic proof and differentiation concentrated in Higher material.

Topic coverage

Algebraic notation and simplification
Expanding and factorising
Linear equations and inequalities
Simultaneous equations
Quadratic equations
Algebraic fractions and proof
Sequences and arithmetic series
Direct and inverse proportion
Rearranging formulae
Functions and mappings
Differentiation and rates of change

Worked example

Question: Solve 2x² − 7x − 15 = 0 by factorising.

Find two terms whose product is −30x² and whose sum is −7x: −10x and 3x.
Split the middle term: 2x² − 10x + 3x − 15.
Factor by grouping: 2x(x − 5) + 3(x − 5) = (2x + 3)(x − 5).
Set each factor to zero.

Answer: x = −3/2 or x = 5.

Common errors

Changing a sign when moving a term without applying the same operation to both sides.
Stopping after factorising instead of solving each factor.
Discarding valid solutions from a quadratic or simultaneous equation.

Revision checklist

I can expand and factorise linear and quadratic expressions.
I can show substitutions clearly in simultaneous equations.
I can check a solution by substituting it into the original equation.