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 B (MEI) 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
- 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
- Sequences and series
- Summing series
- Proof by induction
- Complex numbers and geometry
- Modulus and argument
- Loci in the complex plane
- Matrices and their inverses
- Determinants and inverses
- Matrices and simultaneous equations
- Vectors and 3D space
- The scalar product
- The equation of a plane
- Vectors
- The equation of a line
- Lines and planes
- Matrices
- The inverse of 3x3 matrice
- Series and induction
- Further series and induction
- Further Calculus
- Improper integrals
- Inverse trigonometric functions
- Further integration
- Polar coordinates
- Polar coordinates and curves
- The area of a sector
- Maclaurin series
- Finding and 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 II
- De Moivre's theorem
- Applications of de Moivre's theorem
- Further vectors
- The vector product
- Finding distances
- Second order differential equations
- Homogeneous differential equations
- Non-homogeneous differential equations
- Systems of differential equations
- Forces
- Equilibrium of rigid bodies
- Sliding and toppling
- Work, energy and power
- Work and energy
- Power
- Impulse and momentum
- Introduction
- Newton's experimental law
- Centre of mass
- Finding centres of mass
- Dimensional analysis
- Using dimensions
- Motion under a variable force
- Further projectiles
- Variable acceleration
- Circular motion
- Circular motion with a constant speed
- Circular motion with a variable speed
- Hooke's law
- Using Hooke's law
- Work and energy
- Modelling oscillations
- Simple harmonic motion
- Oscillating mechanical systems
- Centre of mass
- Solids of revolution
- Plane regions
- Oblique impact
- Collisions in two dimensions
- Discrete random variables
- Expectation and variance
- Combinations of random variables
- Discrete probability distributions
- The binomial and Poisson distributions
- The geometric and uniform distributions
- Bivariate data
- Product moment correlation
- Rank correlation
- Regression
- Chi-squared tests
- Contingency tables
- Goodness of fit
- Continuous random variables
- Probability density functions
- Expectation and variance
- Cumulative distribution functions
- Expectation algebra and the Normal distribution
- Combinations of Normal distributions
- The distribution of sample means
- Confidence intervals
- Using the Normal distribution
- Using the t-distribution
- Hypothesis testing
- Testing for a population mean
- The Wilcoxon signed rank test
- Simulation
- Simulating probability distributions
- Algorithms
- Definition and complexity
- Packing and sorting
- Modelling with graphs and networks
- Working with graphs
- Network algorithms
- Minimum spanning trees
- Shortest paths
- More network problems
- Critical path analysis
- Network flows
- Linear programming
- Formulating and solving
- Linear programming with technology
- The simplex method
- Linear programs in standard form
- Linear programs in non-standard form
- Reformulating network problems as LPs
- Modelling paths and flows
- Formulating allocation problems
- Approximations
- Errors and rounding
- Working with errors
- Solution of equations
- Interval bisection
- Method of false position
- Fixed point iteration
- Newton-Raphson and secant methods
- Numerical integration
- The trapezium and midpoint rules
- Simpson's rule
- Approximating functions
- Finding approximating functions
- Numerical differentiation
- Forward difference and central difference approximations
- Rates of convergence
- Sequences
- Numerical differentiation and integration
- Recurrence relations
- Homogeneous recurrence relations
- Non-homogeneous recurrence relations
- Groups
- Introduction to groups
- Further group theory
- Matrices
- Eigenvalues and eigenvectors
- Finding powers of square matrices
- Multivariable calculus
- Functions of more than one variable
- Partial differentiation
- Applications
- Investigation of curves
- Equations and properties of curves
- Derivatives of curves
- Limiting behaviour
- Envelopes and arc lengths
- Exploring differential equations
- Tangent fields
- Analytical solutions of differential equations
- Numerical solutions of differential equations
- Number theory
- Programming
- Prime numbers
- Congruences and modular arithmetic
- Diophantine equations
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
