## Integral supports the whole curriculum

**Integral A level** covers the whole of the UK A level Mathematics and Further Mathematics curriculum, including content tailored for CCEA specifications. The material is presented in topics, which are further divided into sections.

### Mathematics

- Problem solving
- Problem solving and modelling
- Notation and proof

- Surds and indices
- Surds
- Indices

- Quadratic functions
- Quadratic graphs and equations
- The quadratic formula

- Equations and inequalities
- Simultaneous equations
- Inequalities

- Coordinate geometry
- Points and straight lines
- Circles

- Trigonometry
- Trigonometric functions and identities
- Trigonometric equations
- The sine and cosine rules

- Polynomials
- Polynomial functions and graphs
- Dividing and factorising polynomials

- Graphs and transformations
- Sketching graphs
- Transformations of graphs

- The binomial expansion
- Using the binomial expansion

- Differentiation
- Introduction to differentiation
- Maximum and minimum points
- Extending the rule
- More differentiation

- Integration
- Introduction to integration
- Finding the area under a curve
- Further integration

- Vectors
- Working with vectors

- Exponentials and logarithms
- Exponential functions and logarithms
- Natural logarithms and exponentials

- Kinematics
- Displacement and distance
- Speed and velocity
- The constant acceleration formulae

- Forces and Newton's laws
- Force diagrams
- Applying Newton's second law
- Connected objects

- Force and motion in two dimensions
- Resolving forces
- Newton's second law
- Friction

- Collecting and interpreting data
- Collecting and presenting data
- Measures of spread
- Bivariate data

- Probability
- Working with probability

- The binomial distribution
- Introducing the binomial distribution

- Proof
- Methods of proof

- Trigonometry
- Working with radians
- Circular measure

- Sequences and series
- Sequences
- Arithmetic sequences
- Geometric sequences

- Functions
- Functions, graphs and transformations
- Composite and inverse functions
- The modulus function

- Differentiation
- The chain rule
- The product and quotient rules

- Trigonometric functions
- The reciprocal and inverse trigonometric functions

- Algebra
- The general binomial expansion
- Rational expressions
- Partial fractions

- Trigonometric identities
- The compound angle formulae
- Alternative forms

- Further differentiation
- Differentiating exponentials and logarithms
- Differentiating trigonometric functions
- Implicit differentiation

- Integration
- Finding areas
- Integration by substitution
- Further techniques for integration
- Integration by parts
- Volumes of revolution

- Parametric equations
- Parametric curves
- Parametric differentiation

- Differential equations
- Forming and solving differential equations

- Numerical methods
- Solution of equations
- Numerical integration

- Kinematics
- Using calculus
- Motion in two dimensions

- Projectiles
- Introduction
- General equations

- Moments of forces
- The moment of a force
- Forces at an angle

- Impulse and momentum
- Introduction to impulse and momentum

- Probability
- Conditional probability

- Statistical distributions
- The normal distribution

- Statistical hypothesis testing
- Introducing hypothesis testing
- More about hypothesis testing
- Using the normal distribution
- Testing for correlation

### Further Mathematics

- Matrices and transformations
- Introduction to matrices
- Matrices and transformations
- Invariance

- Complex numbers
- Introduction to complex numbers
- The Argand diagram

- Roots of polynomials
- Roots and coefficients
- Complex roots of polynomials

- Complex numbers and geometry
- Modulus and argument
- Loci in the complex plane

- Matrices and their inverses
- Determinants and inverses
- Inverse of a 3x3 matrix
- Matrices and simutaneous equations

- Vectors
- The scalar product
- The equation of a line
- The equation of a plane

- Further vectors
- The vector product
- Points, lines and planes

- Work, energy and power
- Work and energy
- Power

- Elastic strings and springs
- Hooke's law
- Work and energy

- Circular motion
- Motion in a horizontal circle

- Further particle equilibrium
- Equilibrium problems

- Motion
- Resultant and relative velocity

- Further circular motion
- Motion in a vertical circle

- Dimensions
- Using dimensions

- Gravitation
- The universal law of gravitation

- Probability
- Permutations and combinations

- Discrete random variables
- Introduction
- Mean and variance
- Linear functions of random variables

- Discrete distributions
- The geometric distribution
- The Poisson distribution

- Continuous random variables
- Probability density functions
- Mean and variance

- Bivariate data
- Regression

- Graphs and networks
- Definitions and notation
- Trees
- Shortest paths

- Critical path analysis
- Activity networks

- Group theory
- Introduction to groups
- Further group theory

- Boolean algebra
- Truth tables

- Recurrence relations
- Solving recurrence relations

- Series and induction
- Summing series
- Proof by induction

- Further calculus
- Improper integrals
- Inverse trigonometric functions
- Further integration

- Polar coordinates
- Polar curves
- The area of a sector

- Maclaurin series
- Using Maclaurin series

- Hyperbolic functions
- Introducing hyperbolic functions
- The inverse hyperbolic functions

- Further integration
- Reduction formulae
- General integration

- First order differential equations
- Introduction
- Integrating factors

- Complex numbers
- de Moivre's theorem
- Applications of de Moivre's theorem

- Second order differential equations
- Homogeneous differential equations
- Non-homogeneous differential equations

- Modelling oscillations
- Simple harmonic motion
- Oscillating mechanical systems

- Centre of mass
- Finding centres of mass

- Frameworks
- Introduction to frameworks

- Further circular motion
- Sliding and overturning

- Further kinematics
- Working in three dimensions
- Differential equations

- Further centre of mass
- Centre of mass of a solid of revolution
- Centre of mass of a plane figure

- Force systems in two dimensions
- Resultant forces and couples

- Restitution
- Newton's law of restitution

- Linear combinations
- Combinations of Normal distributions

- Estimation
- Finding confidence intervals

- The t-distribution
- Testing for a population mean
- Testing for a difference of means

- Chi-squared tests
- Contingency tables
- Goodness of fit

- Graph theory
- Colouring and matching
- Network flows and cuts

- Algorithms on graphs
- Hamiltonian cycles
- PERT
- The simplex algorithm

- Generating functions
- Using generating functions

- Counting
- The inclusion-exclusion principle
- Rook polynomials

- Group theory
- Symmetry groups and Polya enumeration

Each section contains a standard set of resources, including: