# Integral for Edexcel

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.

• Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics - 8MA0
• Pearson Edexcel Level 3 Advanced GCE in Mathematics - 9MA0
• Pearson Edexcel Level 3 Advanced Subsidiary GCE in Further Mathematics - 8FM0
• Pearson Edexcel Level 3 Advanced GCE in Further Mathematics - 9FM0

Integral resources include 6 fully-resourced lessons based on the Edexcel weather centre large data set. Topics introduced to Edexcel AS/A level Further Mathematics in 2017, such as linear congruences, Fermat’s little theorem and recurrence relations, 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 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
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
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:

## 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

• notes and examples
• 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 offer two tiers of access: Teacher and Teacher & Student

• ### Teacher

Your teachers will get access to all of the resources for AS/A level Mathematics and Further Mathematics for your chosen specification. This includes the Teaching activities section where you will find lots of ideas to use in the classroom.
• ### Teacher & Student

This will provide each of your teachers and students an individual login to Integral. Students will be able to watch teaching videos; access notes and examples, interactive books, Skillpacks and Walkthroughs; and take online, self-marked tests for each topic chapter. Teachers will have the same access as the Teacher subscription, plus they will also be able to track the online test results through powerful analytics.

The cost of a subscription to the Teacher & Student tier is based on the number of students you want to give access.

### Revision deal!

We’re currently offering a special revision subscription to Integral - a massive 50% off the usual full-year price!

This special subscription will run until 30 June 2023.

Courses and extras Teacher Teacher and Student
AS/A level Further Mathematics (individual spec)
AS/A level Further Mathematics videos
Large Data Set resources (individual spec)
AS/A level Mathematics (individual spec)
AS/A level Mathematics videos
Individual student accounts
Student tracking
Student online tests
£290£145

The cost of a subscription to the Teacher & Student tier is based on the number of students you want to give access.