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: