*Integral for Higher Education* is designed for undergraduates who want to review and recap topics studied at A level and are learning new topics that build on them. It helps ensure students build a solid mathematical foundation for their degree course.

*Integral for Higher Education* will be particularly valuable for students starting courses in 2020 who were unable to complete Year 13 due to Covid-19, and for those transitioning from foundation courses.

In developing this version for Higher Education, we’ve drawn on our extensive experience of creating resources for A level Mathematics and Further Mathematics. The result is a comprehensive set of high-quality resources, designed to engage undergraduates in self-learning, build confidence, and develop deep mathematical understanding.

Over 800 schools and colleges subscribe to Integral for A level Mathematics and Further Mathematics

*Integral for Higher Education* covers the whole of the UK A level Mathematics specification and the compulsory pure maths content of the A level Further Mathematics specifications. The material is presented in topics, which are further divided into sections.

- 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 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
- Positive integer powers
- The general binomial expansion

- Differentiation I
- Positive integer powers
- Maximum and minimum points
- Negative and rational powers
- The second derivative

- Integration I
- Introduction
- Finding the area under a curve
- Further integration

- Vectors
- Vectors in 2D
- Vectors in 3D

- Exponentials and logarithms
- Exponential functions and logarithms
- Natural logarithms and exponentials
- Modelling curves

- Trigonometry II
- Working with radians
- Circular measure and small angle approximations

- Sequences
- Sequences
- Arithmetic sequences
- Geometry sequences

- Functions
- Functions, graphs and transformations
- Composite and inverse functions
- Modulus function

- Differentiation II
- The shape of curves
- Product rule and quotient rule
- Chain rule

- Trigonometry III
- The reciprocal and inverse trigonometry functions
- Compound angle formulae and alternate forms

- Rational functions and partial fractions
- Rational functions
- Partial fractions

- Differentiation III
- Differentiation exponentials and logarithms
- Differentiating trigonometric functions
- Implicit differentiation

- Integration II
- Finding areas
- Integration by substitution
- Integration with logs
- Integration by parts

- Parametric equations
- Parametric curves
- Parametric differentiation

- Differential equations
- Forming and solving

- Numerical methods
- Solving equations
- Approximating integrals

- Kinematics
- Displacement and distance
- Speed and velocity
- The constant acceleration formulae
- Motion in two dimensions

- Moments of forces
- Rigid bodies

- Forces and Newton’s laws
- Force diagrams and equilibrium
- Apply Newton’s second law in one dimension
- Connected objects
- Resolving forces
- Newton’s second law in two dimensions

- Variable acceleration
- Using calculus

- Projectiles
- Introduction
- General equations of projectiles

- Friction
- Working with friction

- Collecting and interpreting data
- Collecting data
- Single variable data
- Bivariate data

- The binomial distribution
- Introduction to the binomial distribution

- Probability
- Working with probability
- Probability distributions
- Conditional probability

- Statistical distributions
- Introduction to the normal distribution

- Hypothesis testing
- Introduction to hypothesis testing
- Hypothesis testing with the binomial distribution
- Using the normal distribution
- Correlation and association

- Matrices
- Introduction to matrices
- Matrices and transformations
- Invariance
- Determinants and inverses of 2x2 matrices
- Matrices and simultaneous equations
- Determinants and inverses of 3x3 matrices

- Complex Numbers I
- Introduction to complex numbers
- The Argand diagram
- Modulus and argument
- Loci in the complex plane

- Roots of polynomials
- Roots and coefficients
- Complex roots of polynomials

- Sequences and series
- Summing series
- Introduction to proof by induction
- Further series and induction

- Vectors I
- The scalar product
- The equation of a plane
- The equation of a line
- Lines and planes

- 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
- Inverse hyperbolic functions

- Applications of integration
- Volumes of revolution
- Mean values and general integration

- First order differential equations
- Introduction to first order differential equations
- Integrating factors

- Complex Numbers II
- De Moivre's theorem
- Exponential notation and applications of De Moivre's theorem

- Vectors II
- The vector product
- Finding distances

- Second order differential equations
- Homogeneous differential equations
- Non-homogeneous differential equations
- Systems of differential equations

Each section contains a standard set of resources, including:

- 120sections
- 700pages of helpful notes
- 500crucial points
- 1800written exercise questions
- 1200online test questions
- 500exam-style questions
- 300teaching ideas and resources
- 400interactive resources

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.

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

We base the costs of our annual subscriptions to *Integral for Higher Education* on the number of students you want to give access.

Please contact us to discuss your requirements£400

All subscriptions include:

- Unlimited staff accounts
- Access to all Higher Education content
- Advanced student tracking features
- Expert email and phone support

Subscriptions run from as early as 1 July through to 30 September the following year. This means you can provide new students with access as soon as their place has been confirmed.

Let us show you around the resources. We'll arrange a free online tour, at your convenience, for staff at your university.

Book a tour