# Integral for CCEA

A level Mathematics and Further Mathematics

Integral A level is designed to develop deep mathematical understanding and all the skills students need for their AS/A level studies and beyond.

• CCEA GCE AS Level Mathematics
• CCEA GCE A Level Mathematics
• CCEA GCE AS Level Further Mathematics
• CCEA GCE A Level Mathematics

Topics new to CCEA AS/A level Further Mathematics, such as generating functions and rook polynomials, are all covered.

Are you a student or a parent/carer?

## Give your students the confidence they need

Integral A level is designed to develop deep understanding and the skills students need to apply maths.

Integral is bursting with teaching ideas and activities to facilitate practice and understanding, and get students to discuss maths and work through problems together.

Exercises practise the hand-written maths skills they need for exams and beyond.

It’s also the ideal companion for independent learning. ## 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 CCEA 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
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
Kinematics
Displacement and distance
Speed and velocity
The constant acceleration formulae
Forces and Newton's laws
Force diagrams
Applying Newton's second law
Connected objects
Force and motion in two dimensions
Resolving forces
Newton's second law
Friction
Collecting and interpreting data
Collecting and presenting data
Bivariate data
Probability
Working with probability
The binomial distribution
Introducing the binomial distribution
Proof
Methods of proof
Trigonometry
Circular measure
Sequences and series
Sequences
Arithmetic sequences
Geometric sequences
Functions
Functions, graphs and transformations
Composite and inverse functions
The modulus function
Differentiation
The chain rule
The product and quotient rules
Trigonometric functions
The reciprocal 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
Volumes of revolution
Parametric equations
Parametric curves
Parametric differentiation
Differential equations
Forming and solving differential equations
Numerical methods
Solution of equations
Numerical integration
Kinematics
Using calculus
Motion in two dimensions
Projectiles
Introduction
General equations
Moments of forces
The moment of a force
Forces at an angle
Impulse and momentum
Introduction to impulse and momentum
Probability
Conditional probability
Statistical distributions
The normal distribution
Statistical hypothesis testing
Introducing hypothesis testing
Using the normal distribution
Testing for correlation

### 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
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 simutaneous equations
Vectors
The scalar product
The equation of a line
The equation of a plane
Further vectors
The vector product
Points, lines and planes
Work, energy and power
Work and energy
Power
Elastic strings and springs
Hooke's law
Work and energy
Circular motion
Motion in a horizontal circle
Further particle equilibrium
Equilibrium problems
Motion
Resultant and relative velocity
Further circular motion
Motion in a vertical circle
Dimensions
Using dimensions
Gravitation
The universal law of gravitation
Probability
Permutations and combinations
Discrete random variables
Introduction
Mean and variance
Linear functions of random variables
Discrete distributions
The geometric distribution
The Poisson distribution
Continuous random variables
Probability density functions
Mean and variance
Bivariate data
Regression
Graphs and networks
Definitions and notation
Trees
Shortest paths
Critical path analysis
Activity networks
Group theory
Introduction to groups
Further group theory
Boolean algebra
Truth tables
Recurrence relations
Solving recurrence relations
Series and induction
Summing series
Proof by induction
Further calculus
Improper integrals
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
Further integration
Reduction formulae
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
Modelling oscillations
Simple harmonic motion
Oscillating mechanical systems
Centre of mass
Finding centres of mass
Frameworks
Introduction to frameworks
Further circular motion
Sliding and overturning
Further kinematics
Working in three dimensions
Differential equations
Further centre of mass
Centre of mass of a solid of revolution
Centre of mass of a plane figure
Force systems in two dimensions
Resultant forces and couples
Restitution
Newton's law of restitution
Linear combinations
Combinations of Normal distributions
Estimation
Finding confidence intervals
The t-distribution
Testing for a population mean
Testing for a difference of means
Chi-squared tests
Contingency tables
Goodness of fit
Graph theory
Colouring and matching
Network flows and cuts
Algorithms on graphs
Hamiltonian cycles
PERT
The simplex algorithm
Generating functions
Using generating functions
Counting
The inclusion-exclusion principle
Rook polynomials
Group theory
Symmetry groups and Polya enumeration

Each section contains a standard set of resources, including:

## We've put a lot into it

• 120sections
• 500crucial points
• 1800written exercise questions
• 1200online test questions
• 500exam-style questions
• 300teaching ideas and resources
• 400interactive resources

## Take a look at some sample resources

• written exercises
• teaching activities
• interactive resources

## High quality and affordable

Integral has been developed by experts at MEI.

MEI is an independent charity, committed to improving maths education. Our maths education specialists have considerable classroom experience and deep expertise in the teaching and learning of maths.

As a charity, MEI is able to focus on supporting maths education, rather than generating profit. That's why we're able to offer fantastic resources at a low price. ## Easy to use

• Designed for use on both desktop and tablet devices
• Access from school, college, university and home at any time ## Subscribe

We base the costs of our annual subscriptions to Integral A level on the number of students you want to give access.