# Integral for OCR A

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.

• OCR AS Level Mathematics A - H230
• OCR A Level Mathematics A - H240
• OCR AS Level Further Mathematics A - H235
• OCR A Level Further Mathematics A - H245

Integral resources include fully-resourced statistics lessons based on the OCR census data sets. Topics new to OCR AS/A level Further Mathematics such as recurrence relations, Fermat’s little theorem and linear congruences 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 eBooks

These Integral resources are fully integrated with Hodder Education's Boost eBooks.

## 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
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 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
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:

## 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 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.