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: