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: