Mathematical language, notation and argument

Proof by deduction and exhaustion

Disproof by counter-example

Mathematical problem solving

Mathematical modelling

Laws of indices

Surds

Quadratic functions and graphs

Solving quadratic equations

Simultaneous equations

Linear and quadratic inequalities

Inequalities represented graphically

Polynomial manipulation and algebraic division

The factor theorem

Rational expressions and algebraic division

Sketching polynomial and reciprocal graphs

Using graphs to solve equations

Transformations of graphs

Combinations of transformations

Modelling with functions

Straight lines

Equation of a circle

Circle properties and tangents

Binomial expansion for positive integer n

Sine and cosine rules and area of a triangle

Trigonometric graphs and exact values

Trigonometric identities

Solving trigonometric equations

Exponential functions

Logarithms and their laws

Solving exponential equations

Logarithmic graphs

Exponential growth and decay

Gradient of a curve and differentiation from first principles

Convex and concave curves and points of inflection

Differentiating powers of x

Tangents and normals

Stationary points and increasing and decreasing functions

Integration as the reverse of differentiation

Definite integrals and area under a curve

Area between curves

Vectors in two dimensions

Magnitude, direction and position vectors

Vectors in three dimensions

Vectors in problem solving

Sampling

Data presentation and diagrams

Measures of central tendency and spread

Outliers and data cleaning

Scatter diagrams, correlation and regression

The large data set

Mutually exclusive and independent events

Conditional probability

Modelling with probability

The binomial distribution

Language of hypothesis testing

Hypothesis test for a binomial proportion

Quantities and units in mechanics

The language of kinematics and motion graphs

Constant acceleration (suvat) equations

Calculus in kinematics

Forces and Newton's first law

Newton's second law, weight and gravity

Newton's third law, pulleys and connected particles

Proof by contradiction

The modulus function

Composite and inverse functions

Partial fractions

Parametric and Cartesian forms

Parametric equations in modelling

Binomial expansion for rational n

Sequences and recurrence relations

Sigma notation and arithmetic series

Geometric series

Modelling with sequences and series

Radian measure, arc length and sector area

Small angle approximations

Reciprocal and inverse trigonometric functions

Compound and double angle formulae

The R-formula (a cos + b sin)

Trigonometric proofs and applications

Differentiating exponentials, logarithms and trigonometric functions

Product, quotient and chain rules

Implicit and parametric differentiation

Constructing differential equations

Integrating exponentials and trigonometric functions

Integration as the limit of a sum

Integration by substitution

Integration by parts

Integration using partial fractions

Separable differential equations

Locating roots by change of sign

Iteration and Newton-Raphson

The trapezium rule

Numerical methods in context

The Normal distribution

Choosing and critiquing statistical models

Hypothesis tests for correlation

Hypothesis test for the mean of a Normal distribution

Motion in two dimensions with vectors

Projectiles

Resolving forces and resultants

Friction

Moments