Laws of indices and surds

Quadratic functions and their graphs

The discriminant

Solving quadratics and completing the square

Simultaneous equations

Representing inequalities graphically

Linear and quadratic inequalities

Manipulating and factorising polynomials

Sketching graphs of functions

Transformations of graphs

Equation of a straight line

Parallel and perpendicular lines

Sine and cosine rules and area of a triangle

Radian measure, arc length and sector area

Trigonometric functions and their graphs

The derivative as a gradient and rate of change

Differentiating powers of x

Tangents and normals

Indefinite integration

Finding a curve from its gradient

Structure of proof and proof by exhaustion

Disproof by counter example

Algebraic division

Factor Theorem and Remainder Theorem

Equation of a circle

Circle properties

Sequences and recurrence relations

Arithmetic sequences and series

Geometric sequences and series

Binomial expansion for positive integer powers

Exponential functions and their graphs

Laws of logarithms

Solving equations of the form a^x = b

Trigonometric identities

Solving trigonometric equations

Stationary points and increasing and decreasing functions

Optimisation problems

Definite integrals and area under a curve

Area between a curve and a line or two curves

The trapezium rule

Simplifying rational expressions

Functions: domain, range and composition

Inverse functions and their graphs

The modulus function

Combining graph transformations

Secant, cosecant and cotangent

Inverse trigonometric functions

Further trigonometric identities

Addition and double angle formulae

The forms R cos(theta ± a) and R sin(theta ± a)

The exponential function e^x

The natural logarithm ln x

Logarithmic graphs and modelling

Differentiating exponential, logarithmic and trigonometric functions

Product, quotient and chain rules

Differentiating inverse functions and implicit relationships

Exponential growth and decay models

Integrating standard functions

Integration by recognition and trigonometric identities

Location of roots

Iterative methods

Proof by contradiction

Partial fractions

Parametric equations

Binomial series for any rational power

Implicit and parametric differentiation

Forming differential equations and connected rates of change

Volumes of revolution

Integration by substitution

Integration by parts

Integration using partial fractions

Separable first order differential equations

Area under a curve given parametrically

Vectors in two and three dimensions

Vector equations of lines

The scalar product

Mathematical modelling in mechanics

Vectors and resultants

Displacement, velocity, acceleration and force as vectors

Motion graphs

Constant acceleration formulae

Newton's laws of motion

Connected particles, pulleys and inclined planes

Momentum and impulse

Friction

Forces as vectors and resolving forces

Equilibrium of a particle

Moments of a force

Statistical modelling

Histograms, stem and leaf diagrams and box plots

Measures of location

Measures of dispersion

Skewness and outliers

Elementary probability and sample spaces

Conditional probability and independence

Sum and product laws

Scatter diagrams and linear regression

Product moment correlation coefficient

Probability functions and cumulative distribution functions

Expectation and variance of discrete random variables

The discrete uniform distribution

The Normal distribution

Algorithms, flow charts and bin packing

Sorting and searching algorithms

Graph theory terminology

Minimum spanning trees

Dijkstra's algorithm

The route inspection problem

The travelling salesman problem

Bounds for the travelling salesman problem

Activity networks and precedence tables

Critical paths and float

Gantt charts and scheduling

Formulating linear programs

Graphical solution of linear programs