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:
Interactive resources
Supporting your students to study independently
Sequences of on-screen activities allowing students to meet, explore and practise new concepts independently. They're interactive and dynamic, and come with step-by-step instruction.
Notes, examples and crucial points
Helping to clarify understanding
Thousands of pages of high-quality and extensive notes, helpfully-written to be accessible to all. They feature fully-worked examples and explain common misconceptions.
On-screen tests
To monitor progress all the way to examination
On-screen tests for assessing the level and depth of students' skills, to monitor progress all the way to examination. Immediate feedback is available through powerful analytic tools.
Exercises
To build your students confidence
Three levels of exercises:
- basic practice
- exam standard
- extension questions
Fully-worked solutions are provided to all questions.
Teaching activities
Helping you to make the most of your time
An extensive range of materials, providing lesson ideas and activities with corresponding student materials.
- Interactive
- Notes
- On-screen tests
- Exercises
- Teaching activities
