Integral for OCR B (MEI)

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 B (MEI) A level specifications covered

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.

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Make the most of your time

Integral has everything you need, all in one place.
Our rich bank of easy-to-navigate resources covers the whole curriculum, providing you with thousands of teaching and learning materials.
Track and assess your students progress using powerful analytics.
The resources include teaching ideas and classroom activities, allowing you to focus on planning, teaching and reviewing.

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.

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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

Year 1 (AS): Pure

Problem solving: Problem solving and modelling; Notation and proof

Surds and Indices: Surds; Indices

Quadratic functions: Quadratic graphs and equations; The quadratic formula

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

Year 1 (AS): Mechanics

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

Year 1 (AS): Statistics

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; More about Hypothesis testing

Large data set: Large data set resources

Year 2: Pure

Proof: Methods of proof

Trigonometry: Working with radians; 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

Year 2: Mechanics

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

Year 2: Statistics

Probability: Conditional probability

Statistical distributions: The normal distribution

Statistical hypothesis testing: Using the normal distribution; Correlation and association

Further Mathematics

Year 1 (AS): Pure

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

Year 2: Pure

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

Mechanics part a

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

Mechanics part b

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

Statistics part a

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

Statistics part b

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

Modelling with Algorithms

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

Numerical Methods

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

Extra Pure

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

Further Pure with Technology

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:

Interactive resources

Supporting your students to study independently

Sequences of on-screen activities allowing students to meet, explore and practise new concepts independently. They're interactive and dynamic, and come with step-by-step instruction.

Notes, examples and crucial points

Helping to clarify understanding

Thousands of pages of high-quality and extensive notes, helpfully-written to be accessible to all. They feature fully-worked examples and explain common misconceptions.

On-screen tests

To monitor progress all the way to examination

On-screen tests for assessing the level and depth of students' skills, to monitor progress all the way to examination. Immediate feedback is available through powerful analytic tools.

Exercises

To build your students confidence

Three levels of exercises:

basic practice
exam standard
extension questions

Fully-worked solutions are provided to all questions.

Teaching activities

Helping you to make the most of your time

An extensive range of materials, providing lesson ideas and activities with corresponding student materials.

Previous resource Next resource

Interactive
Notes
On-screen tests
Exercises
Teaching activities

We've put a lot into it

120sections
700pages of helpful notes
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 examplesSample
written exercisesSample
teaching activitiesSample
interactive resourcesSample

I have found the videos invaluable, particularly when teaching Further Mathematics, in order to support my own understanding before teaching the students.

The additional teaching resources, including the group work activities and interesting starter activities that have supported our students in their understanding of the topics taught, are fantastic.

Staff and students alike have benefitted from using the Walkthroughs, with students able to access these from home in order to build their confidence. With the Large Data Sets, Integral has been the only place where we’ve found quality resources that we can pick up and use without having to tweak or produce our own.

Communication with the staff at Integral is also a massive plus for us. Whenever we have had issues or questions, they have responded quickly with explanations and have worked with us when there were details we weren’t sure about.

Sheena

Maths teacher

Jack Hunt School

The teaching activities section for each topic is a gold mine. I love the links to GeoGebra tasks which allow us to explore concepts more deeply with students. I use the problem solving shorts as starters or intermittently through a lesson once a concept has been taught. The matching activities save time re-inventing the wheel, and we’ve found our students really engage with them, and like to compete with each other to be the best! In short – the resources allow us to plan more engaging and effective lessons in less time.

All students have their own accounts and we direct them to the notes and examples, walkthrough activities and skill packs during independent learning time. I like that we are able to track whether a student has accessed a resource or not. We use the level 1 exercises through teaching and build into the level 2 exercises either as part of the lesson or independent study. Having the solutions online is really valuable, as the students can see where they went wrong without having to seek out a member of staff. These practice questions supplement our textbook questions and later in the year can be used as revision. The level 3 exercises are great for stretch and challenge independent tasks and our top students really enjoy tackling these.

I love that Integral is a resource which develops the much needed skill of independence in our students. We set the topic assessments as end of topic homework tasks, and grade these to exam standard. I like the mix of questions, some are accessible to all and others are problem solving and pose more of a challenge. We track their results of these to help us monitor student progress throughout the year.

Finally, I find the tutor forum to be a brilliant place to ask and answer questions; collaborative working on a National level! We also use Integral for our Core Maths teaching and learning and our Level 2 Further Maths class – we await the updated version of this qualification with great anticipation for the new spec!

Suzy

Maths teacher

Helston Community College

Integral resources enabled me to make statistics hands-on and practical for the students. Integral meant I could concentrate on delivery rather than creating lots of resources.

My students also use the section tests. The way Integral reports on them allows me to quickly identify any misconceptions my students might have.

Emma

Maths teacher

Brompton Academy

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.

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

Integral for OCR B (MEI)

Make the most of your time

Give your students the confidence they need

Integrated with Hodder Education's eTextbooks