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

*Integral HE* 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 of Integral 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.
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Over 800 schools and colleges subscribe to Integral for A level Mathematics and Further Mathematics

*Integral HE* covers the whole of the UK A level Mathematics specification and the compulsory pure maths content of the A level Further Mathematics specifications.

- 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

The material is presented in topics, which are further divided into sections. Each section contains a standard set of resources including:

- notes and examplesSample
- on-screen testsSample
- written exercisesSample
- videosSample
- interactive resourcesSample

Fully worked solutions are provided to all the questions that appear in the resources.

We base the costs of our annual subscriptions to *Integral HE* 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 places have been confirmed.

If youâ€™d like to subscribe or see the resources yourself, please contact Dr Richard Lissaman. Richard can arrange a free online tour and can set you up with a free trial account so that you can review the resources in detail.