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Laws of indices, including zero, negative and fractional powers, and why they have to take the values they do.
Simplifying surds, and rationalising denominators using the conjugate.
Roots, factorising and the quadratic formula.
Vertex form, turning points, exact solutions and proving results.
Using b² − 4ac to classify roots, and conditions on an unknown.
Linear systems and one-linear-one-quadratic by substitution.
Solving linear and quadratic inequalities with critical values and sketches.
Algebraic division and the factor theorem for factorising cubics.
Translating, stretching and reflecting curves, and why changes inside the bracket act in the opposite direction to changes outside.
Domain, range, composition order and finding inverses.
Modulus graphs, equations and inequalities via the distance idea.
Splitting rational expressions, including repeated factors.
Work through each topic to complete the section.