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 AQA 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
- Determinants and inverses
- Complex numbers
- Introduction to complex numbers
- The Argand diagram
- Roots of polynomials
- Roots and coefficients
- Complex roots of polynomials
- Conics
- The conic sections
- Hyperbolic functions
- Introducing hyperbolic functions
- Sequences and series
- Summing series
- Proof by induction
- Maclaurin series
- Further calculus
- Volumes of revolution
- Complex numbers and geometry
- Modulus and argument
- Loci in the complex plane
- Polar coordinates
- Polar curves
- Rational functions and further algebra
- Graphs of rational functions
- Inequalities
- Vectors and 3-D space
- The scalar product
- The equation of a line
- Vectors
- The equation of a plane
- Matrices
- Inverse of a 3x3 matrix
- Matrices and simultaneous equations
- Factorising determinants
- Conics
- Composite transformations
- Further algebra and graphs
- Further graphs involving rational functions
- Further calculus
- Improper integrals
- Inverse trigonometric functions
- Further integration
- Polar coordinates
- Finding areas
- Series and limits
- The method of differences using partial fractions
- Maclaurin series
- Limits
- Further matrices
- Eigenvalues and eigenvectors
- Hyperbolic functions
- Further hyperbolic functions
- Using inverse hyperbolic functions
- Further integration
- General integration and limits
- Reduction formulae
- Arc lengths and surface area
- First order differential equations
- Introduction
- Integrating factors
- Numerical methods
- Numerical integration
- Differential equations
- Complex numbers
- de Moivre's theorem
- Applications of de Moivre's theorem
- Further vectors
- Lines and planes
- The vector product
- Second order differential equations
- Homogeneous differential equations
- Modelling oscillations
- Non-homogeneous differential equations
- Systems of differential equations
- Discrete random variables (AS)
- Mean and variance
- Combinations of random variables
- Distributions and hypothesis testing (AS)
- The Poisson and uniform distributions
- Hypothesis testing and errors
- Continuous random variables (AS)
- Probability density functions
- Mean and variance
- Functions of random variables
- Chi-squared tests (AS)
- Contingency tables
- Confidence intervals (AS)
- Using the Normal distribution
- Further random variables
- Further discrete random variables
- Cumulative distribution functions
- The rectangular and exponential distributions
- Further hypothesis testing and confidence intervals
- Using the t-distribution
- Further hypothesis testing
- 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 with constant speed
- Elastic strings and springs (AS)
- Hooke's law
- Work and energy
- Dimensional analysis (AS)
- Using dimensions
- Working in two dimensions
- Work, energy and power
- Impulse and momentum
- Moments of forces
- Equilibrium of rigid bodies
- Sliding and toppling
- Centre of mass
- Finding centres of mass
- Solids of revolution
- Plane figures
- Further circular motion
- Motion in a horizontal circle
- Motion in a vertical circle
- Graphs and networks (AS)
- Definitions
- Minimum spanning trees
- The travelling salesperson problem
- Further networks (AS)
- The route inspection problem
- Network flows
- Critical path analysis (AS)
- Activity networks
- Linear programming (AS)
- Formulating and solving graphically
- Game theory (AS)
- Introduction to game theory
- Binary operations (AS)
- Properties of binary operations
- Further graphs and networks
- Further graph theory
- Further network flows
- Further critical path analysis
- Scheduling and resourcing
- Further linear programming
- The simplex method
- Games as linear programming problems
- Group theory
- Introduction
- Subgroups and isomorphisms
Each section contains a standard set of resources, including: