# Integral for OCR B (MEI)

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 B (MEI) - H630
• OCR A Level Mathematics B (MEI) - H640
• OCR AS Level Further Mathematics B (MEI) - H635
• OCR A Level Further Mathematics B (MEI) - H645

Integral resources include fully-resourced statistics lessons based on the MEI large data sets. Topics new to MEI AS/A level Further Mathematics such as recurrence relations, network flows and reformulating network problems using linear programming are all covered. Further Pure with Technology has a full set of resources, including videos based on the Python programming language.

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 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
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
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:

## 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.

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

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