Algebra, Sequences and Series
Polynomials, quadratics, inequalities, indices and logarithms, and the two standard sequences.
01Algebraic Operations and PolynomialsDividing polynomials, the remainder and factor theorems, factorising and solving cubics, finding unknown coefficients, and simplifying algebraic fractions.100 questions02Quadratic Functions and EquationsCompleting the square, maximum and minimum values, the discriminant and the nature of the roots, the sum and product of the roots, and whether a line meets a curve.100 questions03InequalitiesQuadratic and rational inequalities — finding critical values, reading the answer off a sketch, and why you must never multiply through by an expression whose sign you do not know.100 questions04Surds, Indices and LogarithmsThe laws of indices, simplifying surds and rationalising denominators, the definition and laws of logarithms, and solving exponential and logarithmic equations.100 questions05Sequences and SeriesArithmetic and geometric progressions — the nth term, the sum of n terms, the sum to infinity and when it exists, and sigma notation.100 questions