# Integral for Higher Education

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, or those who have deferred entry until 2021, 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.

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

## Content

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
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
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 examples
• on-screen tests
• written exercises
• videos
• interactive resources

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

I have reviewed all these materials – from my nearly 40 years’ teaching and supporting first year mathematical sciences students, and the past 7 years being heavily involved with the design, development, accreditation, implementation, and monitoring of the 2017 reformed A levels with DfE, ALCAB, Ofqual, RS ACME and the learned societies, I can highly recommend these resources to all relevant colleagues in your institutions.

Paul Glaister

Professor of Mathematics and Mathematics Education

Department of Mathematics and Statistics, University of Reading

## Subscriptions and pricing

We base the costs of our annual subscriptions to Integral HE on the number of students you want to give access.

### Subscription price

All subscriptions include:

• Unlimited staff accounts