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: