## 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 Edexcel 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 and polynomials
- Roots and coefficients
- Complex roots of polynomials

- Sequences and series
- Summing series
- Proof by induction

- Further calculus
- Volumes of revolution

- 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 simultaneous equations

- Vectors and 3-D space
- The scalar product
- The equation of a line
- The equation of a plane
- Finding distances

- Sequences and series
- The method of differences

- Further calculus
- Improper integrals
- Inverse trigonometric functions
- Further integration

- Maclaurin series
- Using Maclaurin series

- Polar coordinates
- Polar curves
- Finding areas

- Hyperbolic functions
- Introducing hyperbolic functions
- The inverse hyperbolic functions

- Applications of integration
- Further 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

- Second order differential equations
- Homogeneous differential equations
- Non-homogeneous differential equations
- Systems of differential equations

- Inequalities (AS)
- Solving inequalities

- Coordinate systems (AS)
- The parabola and rectangular hyperbola

- Trigonometry (AS)
- The t formulae

- Vectors (AS)
- The vector product
- The scalar triple product

- Numerical methods (AS)
- Solving differential equations

- Further calculus
- Series and limits
- Leibnitz's theorem and L'Hospital's rule
- The Weierstrass substitution

- Further differential equations
- Using substitutions and series

- Further coordinate systems
- The ellipse and hyperbola

- Further vectors
- Further vector geometry

- Further numerical methods
- Simpson's rule

- Further inequalities
- Using the modulus function

- Number theory (AS)
- The Euclidean algorithm and Bezout's identity
- Modular arithmetic and divisibility tests

- Groups (AS)
- Introduction to groups
- Subgroups

- Matrices (AS)
- Eigenvalues and eigenvectors for 2x2 matrices

- Complex numbers (AS)
- Further loci and regions

- Sequences and series (AS)
- First order recurrence relations

- Further groups
- Isomorphism

- Further matrices
- Eigenvalues and eigenvectors of 3x3 matrices

- Further calculus
- Reduction formulae
- Arc lengths and surface areas

- Further complex numbers
- Transformations in the complex plane

- Further sequences and series
- Second order recurrence relations

- Further number theory
- Fermat's little theorem
- Solving linear congruences
- Combinatorics

- Work, energy and power (AS)
- Work and energy
- Power

- Impulse and momentum (AS)
- Introduction
- Newton's experimental law

- Hooke's law
- Using Hooke's law
- Work and energy

- Oblique impact
- Collisions in two dimensions

- Circular motion (AS)
- Motion in a horizontal circle

- Centre of mass (AS)
- Finding a centre of mass

- Kinematics (AS)
- Variable acceleration

- Further kinematics and circular motion
- Differential equations
- Motion in a vertical circle

- Further centres of mass
- Using integration
- Sliding and toppling

- Modelling oscillations
- Simple harmonic motion
- Oscillating mechnical systems

- Discrete random variables (AS)
- Mean and variance
- Functions of a random variable

- Discrete distributions (AS)
- The Poisson and binomial distributions
- Approximations and hypothesis tests

- Chi-squared tests (AS)
- Contingency tables
- Goodness of fit

- Further discrete distributions
- The geometric distribution
- The negative binomial distribution

- The Central Limit theorem
- The distribution of sample means

- Hypothesis testing
- Further hypothesis testing

- Probability generating functions
- Using probability generating functions

- Correlation and regression (AS)
- Product moment correlation
- Rank correlation
- Regression

- Continuous random variables (AS)
- Probability density functions
- Mean and variance
- Cumulative distribution functions

- Expectation algebra
- The sums and differences of Normal variables

- Estimation
- Unbiased estimators

- Confidence intervals
- Using the normal distribution
- Using the t-distribution

- Hypothesis testing
- Testing for a population mean
- Testing for a difference of means

- Variance
- Testing for variance

- Algorithms (AS)
- Working with algorithms
- Sorting and packing

- Networks (AS)
- Minimum spanning trees
- Shortest paths
- The route inspection problem

- Critical path analysis (AS)
- Activity networks
- Scheduling activities

- Linear programming (AS)
- Formulating and solving graphically

- Further graphs and networks
- Further algorithms on networks
- The travelling salesperson problem
- Resourcing and scheduling

- Further linear programming
- The simplex method
- The two-stage simplex and big M methods

- Allocation problems (AS)
- The Hungarian algorithm

- Flows in networks (AS)
- Maximising a flow

- Game theory (AS)
- Introduction to game theory

- Recurrence relations (AS)
- First order recurrence relations

- Transportation problems
- The transportation algorithm
- Extensions

- Further flows in networks
- Further problems in network flows

- Dynamic programming
- Introduction to dynamic programming

- Further game theory
- Using linear programming

- Further recurrence relations
- Second order recurrence relations

- Decision analysis
- Decision trees

Each section contains a standard set of resources, including: