# Integral for AQA

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.

• AQA AS Mathematics - 7356
• AQA A-level Mathematics - 7357
• AQA AS Further Mathematics - 7366
• AQA A-level Further Mathematics - 7367

Our resources include 5 fully-resourced lessons based on the AQA cars large data set, as well as some lessons on the previous food large data set. Topics new to AQA AS/A level Further Mathematics such as binary operations and group theory 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. ## Integrated with Hodder Education's eTextbooks

These Integral resources are fully integrated with Hodder Education's Dynamic Learning eTextbooks.

## 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 AQA 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
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
Large data set
Large data set resources
Proof
Methods of proof
Trigonometry
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
Determinants and inverses
Complex numbers
Introduction to complex numbers
The Argand diagram
Roots of polynomials
Roots and coefficients
Complex roots of polynomials
Conics
The conic sections
Hyperbolic functions
Introducing hyperbolic functions
Sequences and series
Summing series
Proof by induction
Maclaurin series
Further calculus
Volumes of revolution
Complex numbers and geometry
Modulus and argument
Loci in the complex plane
Polar coordinates
Polar curves
Rational functions and further algebra
Graphs of rational functions
Inequalities
Vectors and 3-D space
The scalar product
The equation of a line
Vectors
The equation of a plane
Matrices
Inverse of a 3x3 matrix
Matrices and simultaneous equations
Factorising determinants
Conics
Composite transformations
Further algebra and graphs
Further graphs involving rational functions
Further calculus
Improper integrals
Inverse trigonometric functions
Further integration
Polar coordinates
Finding areas
Series and limits
The method of differences using partial fractions
Maclaurin series
Limits
Further matrices
Eigenvalues and eigenvectors
Hyperbolic functions
Further hyperbolic functions
Using inverse hyperbolic functions
Further integration
General integration and limits
Reduction formulae
Arc lengths and surface area
First order differential equations
Introduction
Integrating factors
Numerical methods
Numerical integration
Differential equations
Complex numbers
de Moivre's theorem
Applications of de Moivre's theorem
Further vectors
Lines and planes
The vector product
Second order differential equations
Homogeneous differential equations
Modelling oscillations
Non-homogeneous differential equations
Systems of differential equations
Discrete random variables (AS)
Mean and variance
Combinations of random variables
Distributions and hypothesis testing (AS)
The Poisson and uniform distributions
Hypothesis testing and errors
Continuous random variables (AS)
Probability density functions
Mean and variance
Functions of random variables
Chi-squared tests (AS)
Contingency tables
Confidence intervals (AS)
Using the Normal distribution
Further random variables
Further discrete random variables
Cumulative distribution functions
The rectangular and exponential distributions
Further hypothesis testing and confidence intervals
Using the t-distribution
Further hypothesis testing
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 with constant speed
Elastic strings and springs (AS)
Hooke's law
Work and energy
Dimensional analysis (AS)
Using dimensions
Working in two dimensions
Work, energy and power
Impulse and momentum
Moments of forces
Equilibrium of rigid bodies
Sliding and toppling
Centre of mass
Finding centres of mass
Solids of revolution
Plane figures
Further circular motion
Motion in a horizontal circle
Motion in a vertical circle
Graphs and networks (AS)
Definitions
Minimum spanning trees
The travelling salesperson problem
Further networks (AS)
The route inspection problem
Network flows
Critical path analysis (AS)
Activity networks
Linear programming (AS)
Formulating and solving graphically
Game theory (AS)
Introduction to game theory
Binary operations (AS)
Properties of binary operations
Further graphs and networks
Further graph theory
Further network flows
Further critical path analysis
Scheduling and resourcing
Further linear programming
The simplex method
Games as linear programming problems
Group theory
Introduction
Subgroups and isomorphisms

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.