## 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 WJEC 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
- Modelling curves

- Collecting and interpreting data
- Collecting data
- Single variable data
- Bivariate data

- Probability
- Working with probability
- Probability distributions

- Statistical distributions
- The binomial distribution
- The Poisson and uniform distributions

- Statistical hypothesis testing
- Introducing hypothesis testing
- More about hypothesis testing

- 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

- Proof
- Methods of proof

- Trigonometry
- Working with radians
- Circular measure and small angle approximations

- Sequences and series
- Sequences
- Arithmetic sequences
- Geometric sequences

- Functions
- Functions, graphs and transformations
- Composite and inverse functions
- The modulus function

- Differentiation
- The shape of curves
- The chain rule
- The product and quotient rules

- Trigonometric functions
- The reciprocal trigonometric 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

- Parametric equations
- Parametric curves
- Parametric differentiation

- Vectors
- Vectors in three dimensions

- Differential equations
- Forming and solving differential equations

- Numerical methods
- Solution of equations
- Numerical integration

- Probability
- Conditional probability

- Statistical distributions
- The normal and uniform distributions

- Statistical hypothesis testing
- Using the normal distribution
- Testing for correlation

- 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

- A model for friction
- Working with friction

### Further Mathematics

- Matrices and transformations
- Introduction to matrices
- Matrices and transformations
- Invariance
- Determinant and inverse

- 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

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

- Matrices
- Determinant and inverse of 3x3 matrices
- Matrices and simultaneous equations

- Trigonometry
- Further trigonometric equations

- Further calculus
- Improper integrals
- The 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

- 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

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

- Discrete random variables
- Expectation and variance
- Combinations of random variables

- The Poisson distribution
- More about the Poisson distribution

- Continuous random variables
- Probability density functions
- Expectation and variance
- Cumulative distribution functions
- The exponential distribution

- Bivariate data
- Product moment correlation
- Rank correlation
- Regression

- Chi-squared tests
- Contingency tables
- Goodness of fit

- Statistical distributions
- Combinations of Normal variables
- The distribution of sample means

- Samples and populations
- Unbiased estimators

- Confidence intervals
- Using the normal distribution
- Further confidence intervals

- Hypothesis testing
- Using the normal distribution
- Using the t-distribution

- Non-parametric tests
- The Wilcoxon signed-rank test
- Two sample and paired sample tests

- Work, energy and power
- Work and energy
- Power
- Elastic potential energy

- Impulse and momentum
- Introduction
- Newton's experimental law

- Circular motion
- Motion in a horizontal circle
- Motion in a vertical circle

- Differentiation and integration of vectors
- Using vectors

- Rigid bodies
- Equilibrium of rigid bodies

- Centre of mass
- Finding centres of mass
- Solids of revolution

- Kinematics
- Differential equations
- Impulse and momentum in two dimensions

- Simple harmonic motion
- Introduction to SHM
- Oscillating mechanical systems

Each section contains a standard set of resources, including: