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:
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
