## 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 OCR A 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

- Simultaneous equations and inequalities
- Simultaneous equations
- Inequalities

- Coordinate geometry
- Points and straight lines
- Circles

- Trigonometry
- Functions and identities
- 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
- Finding the area under a curve
- Further integration

- Vectors
- Working with vectors

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

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

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

- Variable acceleration
- Using calculus

- Collecting and interpreting data
- Collecting data
- Single variable data
- Bivariate data

- Probability
- Working with probability
- Probability distributions

- The binomial distribution
- Introduction to the binomial distribution

- Statistical hypothesis testing
- Introduction to hypothesis testing
- More about Hypothesis testing

- Large data set
- Large data set resources

- Proof
- Methods of proof

- Trigonometry
- Working with radians
- Circular measure and small angle approximations

- Sequences and series
- Sequences
- Arithmetic sequences
- Geometry sequences

- Functions
- Functions, graphs and transformations
- Composite and inverse functions
- Modulus function

- Differentiation
- The shape of curves
- Chain rule
- Product and quotient rule

- Trigonometric functions
- The reciprocal and inverse trigonometry functions

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

- Trigonometric identities
- The compound angle formulae
- Alternative forms

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

- Integration
- Finding areas
- Integration by substitution
- Further techniques for integration
- Integration by parts

- Parametric equations
- Parametric curves
- Parametric differentiation

- Vectors
- Vectors in three dimensions

- Differential equations
- Forming and solving

- Numerical methods
- Solving equations
- Numerical integration

- Kinematics
- Motion in two dimensions

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

- Moments of forces
- Rigid bodies

- Projectiles
- Introduction
- General equations

- Friction
- Working with friction

- Probability
- Conditional probability

- Statistical distributions
- The normal distribution

- Statistical hypothesis testing
- Using the normal distribution
- Correlation and association

### 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

- Proof
- Proof by induction

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

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

- Vectors and 3-D space
- The scalar product
- The equation of a line
- The vector product

- Vectors
- The equation of a plane
- Lines and planes

- Matrices
- Matrices and simultaneous equations

- Series and induction
- Summing series
- Further series and induction

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

- Polar coordinates
- Polar curves
- Finding areas

- Maclaurin series
- Using Maclaurin series

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

- Applications of integration
- Volumes of revolution
- Mean values and general integration

- First order differential equations
- Introduction
- Integrating factors

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

- Further vectors
- Finding distances

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

- Probability (AS)
- Permutations and combinations

- Discrete random variables (AS)
- Mean and variance
- Linear functions of random variables

- Discrete distributions (AS)
- The binomial and Poisson distributions
- The geometric and uniform distributions

- Chi-squared tests (AS)
- Contingency tables
- Goodness of fit

- Bivariate data
- Product moment correlation
- Rank correlation
- Regression

- Continuous random variables
- Probability density functions
- Mean and variance
- Functions of a random variable
- Cumulative distribution functions

- The normal distribution
- Combinations of normal distributions
- The distribution of sample means

- Confidence intervals and hypothesis testing
- Confidence intervals
- Hypothesis testing

- Non-parametric tests
- Single sample tests
- Two sample and paired sample tests

- Work, energy and power (AS)
- Work and energy
- Power

- Impulse and momentum (AS)
- Introduction
- Newton's experimental law

- Circular motion (AS)
- Motion in a circle

- Dimensional analysis (AS)
- Using dimensions

- Centre of mass
- Finding centres of mass
- Solids of revolution
- Plane regions
- Sliding and toppling

- Motion under a variable force
- Differential equations
- Work, energy and impulse

- Further circular motion
- Circular motion with variable speed

- Hooke's law
- Using Hooke's law
- Work and energy

- Oblique impact
- Collisions in two dimensions

- Mathematical preliminaries (AS)
- Terminology and counting
- Working with sets

- Algorithms (AS)
- Working with algorithms
- Sorting and packing

- Graphs and networks (AS)
- Definitions and notation
- Minimum spanning trees
- Shortest paths

- Critical path analysis (AS)
- Activity networks

- Linear programming (AS)
- Formulating and solving graphically

- Game theory (AS)
- Introduction to game theory

- Further mathematical preliminaries
- Sets, arrangements and derangements

- Further graph theory
- Hamiltonian and planar graphs

- Further algorithms
- Further packing and sorting

- Further networks
- The route inspection problem
- The travelling salesperson problem

- Further critical path analysis
- Resourcing and scheduling

- Further linear programming
- The simplex method

- Further game theory
- Using linear programming

- Sequences and series (AS)
- Sequences
- Recurrence relations

- Number theory (AS)
- Division, Euclid's lemma and modular arithmetic
- Primes, number bases and divisibility

- Groups (AS)
- Introduction to groups
- Subgroups

- Vectors (AS)
- The vector product

- Surfaces and partial differentiation (AS)
- Functions of more than one variable
- Partial differentiation

- Further recurrence relations
- Second order recurrence relations

- Further number theory
- Fermat's little theorem
- More results in modular arithmetic
- Simultaneous linear congruences
- Quadratic residues

- Further groups
- Properties of groups

- Further vectors
- The scalar triple product

- Further surfaces
- Further partial differentiation and applications

- Calculus
- Reduction formulae
- Arc lengths and surface areas

Each section contains a standard set of resources, including: