## 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: