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 OCR A 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 of polynomials
- Roots and coefficients
- Complex roots of polynomials
- Proof
- Proof by induction
- Complex numbers and geometry
- Modulus and argument
- Loci in the complex plane
- Matrices and their inverses
- Determinants and inverses
- Inverse of a 3x3 matrix
- Vectors and 3-D space
- The scalar product
- The equation of a line
- The vector product
- Vectors
- The equation of a plane
- Lines and planes
- Matrices
- Matrices and simultaneous equations
- Series and induction
- Summing series
- Further series and induction
- Further calculus
- Improper integrals
- Inverse trigonometric functions
- Further integration
- Polar coordinates
- Polar curves
- Finding areas
- 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
- Further vectors
- Finding distances
- Second order differential equations
- Homogeneous differential equations
- Non-homogeneous differential equations
- Systems of differential equations
- Probability (AS)
- Permutations and combinations
- Discrete random variables (AS)
- Mean and variance
- Linear functions of random variables
- Discrete distributions (AS)
- The binomial and Poisson distributions
- The geometric and uniform distributions
- Chi-squared tests (AS)
- Contingency tables
- Goodness of fit
- Bivariate data
- Product moment correlation
- Rank correlation
- Regression
- Continuous random variables
- Probability density functions
- Mean and variance
- Functions of a random variable
- Cumulative distribution functions
- The normal distribution
- Combinations of normal distributions
- The distribution of sample means
- Confidence intervals and hypothesis testing
- Confidence intervals
- Hypothesis testing
- Non-parametric tests
- Single sample tests
- Two sample and paired sample tests
- Work, energy and power (AS)
- Work and energy
- Power
- Impulse and momentum (AS)
- Introduction
- Newton's experimental law
- Circular motion (AS)
- Motion in a circle
- Dimensional analysis (AS)
- Using dimensions
- Centre of mass
- Finding centres of mass
- Solids of revolution
- Plane regions
- Sliding and toppling
- Motion under a variable force
- Differential equations
- Work, energy and impulse
- Further circular motion
- Circular motion with variable speed
- Hooke's law
- Using Hooke's law
- Work and energy
- Oblique impact
- Collisions in two dimensions
- Mathematical preliminaries (AS)
- Terminology and counting
- Working with sets
- Algorithms (AS)
- Working with algorithms
- Sorting and packing
- Graphs and networks (AS)
- Definitions and notation
- Minimum spanning trees
- Shortest paths
- Critical path analysis (AS)
- Activity networks
- Linear programming (AS)
- Formulating and solving graphically
- Game theory (AS)
- Introduction to game theory
- Further mathematical preliminaries
- Sets, arrangements and derangements
- Further graph theory
- Hamiltonian and planar graphs
- Further algorithms
- Further packing and sorting
- Further networks
- The route inspection problem
- The travelling salesperson problem
- Further critical path analysis
- Resourcing and scheduling
- Further linear programming
- The simplex method
- Further game theory
- Using linear programming
- Sequences and series (AS)
- Sequences
- Recurrence relations
- Number theory (AS)
- Division, Euclid's lemma and modular arithmetic
- Primes, number bases and divisibility
- Groups (AS)
- Introduction to groups
- Subgroups
- Vectors (AS)
- The vector product
- Surfaces and partial differentiation (AS)
- Functions of more than one variable
- Partial differentiation
- Further recurrence relations
- Second order recurrence relations
- Further number theory
- Fermat's little theorem
- More results in modular arithmetic
- Simultaneous linear congruences
- Quadratic residues
- Further groups
- Properties of groups
- Further vectors
- The scalar triple product
- Further surfaces
- Further partial differentiation and applications
- Calculus
- Reduction formulae
- Arc lengths and surface areas
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
