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:
Interactive resources
Supporting your students to study independently
Sequences of on-screen activities allowing students to meet, explore and practise new concepts independently. They're interactive and dynamic, and come with step-by-step instruction.
Notes, examples and crucial points
Helping to clarify understanding
Thousands of pages of high-quality and extensive notes, helpfully-written to be accessible to all. They feature fully-worked examples and explain common misconceptions.
On-screen tests
To monitor progress all the way to examination
On-screen tests for assessing the level and depth of students' skills, to monitor progress all the way to examination. Immediate feedback is available through powerful analytic tools.
Exercises
To build your students confidence
Three levels of exercises:
- basic practice
- exam standard
- extension questions
Fully-worked solutions are provided to all questions.
Teaching activities
Helping you to make the most of your time
An extensive range of materials, providing lesson ideas and activities with corresponding student materials.
- Interactive
- Notes
- On-screen tests
- Exercises
- Teaching activities
