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 B (MEI) 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
- 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
- Sequences and series
- Summing series
- Proof by induction
- Complex numbers and geometry
- Modulus and argument
- Loci in the complex plane
- Matrices and their inverses
- Determinants and inverses
- Matrices and simultaneous equations
- Vectors and 3D space
- The scalar product
- The equation of a plane
- Vectors
- The equation of a line
- Lines and planes
- Matrices
- The inverse of 3x3 matrice
- Series and induction
- Further series and induction
- Further Calculus
- Improper integrals
- Inverse trigonometric functions
- Further integration
- Polar coordinates
- Polar coordinates and curves
- The area of a sector
- Maclaurin series
- Finding and 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 II
- De Moivre's theorem
- Applications of de Moivre's theorem
- Further vectors
- The vector product
- Finding distances
- Second order differential equations
- Homogeneous differential equations
- Non-homogeneous differential equations
- Systems of differential equations
- Forces
- Equilibrium of rigid bodies
- Sliding and toppling
- Work, energy and power
- Work and energy
- Power
- Impulse and momentum
- Introduction
- Newton's experimental law
- Centre of mass
- Finding centres of mass
- Dimensional analysis
- Using dimensions
- Motion under a variable force
- Further projectiles
- Variable acceleration
- Circular motion
- Circular motion with a constant speed
- Circular motion with a variable speed
- Hooke's law
- Using Hooke's law
- Work and energy
- Modelling oscillations
- Simple harmonic motion
- Oscillating mechanical systems
- Centre of mass
- Solids of revolution
- Plane regions
- Oblique impact
- Collisions in two dimensions
- Discrete random variables
- Expectation and variance
- Combinations of random variables
- Discrete probability distributions
- The binomial and Poisson distributions
- The geometric and uniform distributions
- Bivariate data
- Product moment correlation
- Rank correlation
- Regression
- Chi-squared tests
- Contingency tables
- Goodness of fit
- Continuous random variables
- Probability density functions
- Expectation and variance
- Cumulative distribution functions
- Expectation algebra and the Normal distribution
- Combinations of Normal distributions
- The distribution of sample means
- Confidence intervals
- Using the Normal distribution
- Using the t-distribution
- Hypothesis testing
- Testing for a population mean
- The Wilcoxon signed rank test
- Simulation
- Simulating probability distributions
- Algorithms
- Definition and complexity
- Packing and sorting
- Modelling with graphs and networks
- Working with graphs
- Network algorithms
- Minimum spanning trees
- Shortest paths
- More network problems
- Critical path analysis
- Network flows
- Linear programming
- Formulating and solving
- Linear programming with technology
- The simplex method
- Linear programs in standard form
- Linear programs in non-standard form
- Reformulating network problems as LPs
- Modelling paths and flows
- Formulating allocation problems
- Approximations
- Errors and rounding
- Working with errors
- Solution of equations
- Interval bisection
- Method of false position
- Fixed point iteration
- Newton-Raphson and secant methods
- Numerical integration
- The trapezium and midpoint rules
- Simpson's rule
- Approximating functions
- Finding approximating functions
- Numerical differentiation
- Forward difference and central difference approximations
- Rates of convergence
- Sequences
- Numerical differentiation and integration
- Recurrence relations
- Homogeneous recurrence relations
- Non-homogeneous recurrence relations
- Groups
- Introduction to groups
- Further group theory
- Matrices
- Eigenvalues and eigenvectors
- Finding powers of square matrices
- Multivariable calculus
- Functions of more than one variable
- Partial differentiation
- Applications
- Investigation of curves
- Equations and properties of curves
- Derivatives of curves
- Limiting behaviour
- Envelopes and arc lengths
- Exploring differential equations
- Tangent fields
- Analytical solutions of differential equations
- Numerical solutions of differential equations
- Number theory
- Programming
- Prime numbers
- Congruences and modular arithmetic
- Diophantine equations
Each section contains a standard set of resources, including: