# Integral for WJEC

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.

• WJEC GCE AS Level Mathematics - 2300QS
• WJEC GCE A Level Mathematics - 1300QS
• WJEC GCE AS Level Further Mathematics - 2305QS
• WJEC GCE A Level Mathematics - 1305QS

As well as the English language version, Welsh language versions of the exercises, on-screen tests and notes & examples are available.

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.

## 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 WJEC 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
Quadratic graphs and equations
Equations and inequalities
Simultaneous equations
Inequalities
Coordinate geometry
Points and straight lines
Circles
Trigonometry
Trigonometric functions and identities
Trigonometric 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 to integration
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
Collecting and interpreting data
Collecting data
Single variable data
Bivariate data
Probability
Working with probability
Probability distributions
Statistical distributions
The binomial distribution
The Poisson and uniform distributions
Statistical hypothesis testing
Introducing hypothesis testing
More about hypothesis testing
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
Proof
Methods of proof
Trigonometry
Circular measure and small angle approximations
Sequences and series
Sequences
Arithmetic sequences
Geometric sequences
Functions
Functions, graphs and transformations
Composite and inverse functions
The modulus function
Differentiation
The shape of curves
The chain rule
The product and quotient rules
Trigonometric functions
The reciprocal trigonometric and inverse trigonometric functions
Algebra
The general binomial expansion
Rational expressions
Partial fractions
Trigonometric identities
The compound angle formulae
Alternative forms
Further differentiation
Differentiating 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 differential equations
Numerical methods
Solution of equations
Numerical integration
Probability
Conditional probability
Statistical distributions
The normal and uniform distributions
Statistical hypothesis testing
Using the normal distribution
Testing for correlation
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
A model for friction
Working with friction

### Further Mathematics

Matrices and transformations
Introduction to matrices
Matrices and transformations
Invariance
Determinant and inverse
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
Vectors and 3-D space
The scalar product
The equation of a line
The equation of a plane
Finding distances
Matrices
Determinant and inverse of 3x3 matrices
Matrices and simultaneous equations
Trigonometry
Further trigonometric equations
Further calculus
Improper integrals
The inverse trigonometric functions
Further integration
Polar coordinates
Polar curves
The area of a sector
Maclaurin series
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
de Moivre's theorem
Applications of de Moivre's theorem
Second order differential equations
Homogeneous differential equations
Non-homogeneous differential equations
Systems of differential equations
Discrete random variables
Expectation and variance
Combinations of random variables
The Poisson distribution
More about the Poisson distribution
Continuous random variables
Probability density functions
Expectation and variance
Cumulative distribution functions
The exponential distribution
Bivariate data
Product moment correlation
Rank correlation
Regression
Chi-squared tests
Contingency tables
Goodness of fit
Statistical distributions
Combinations of Normal variables
The distribution of sample means
Samples and populations
Unbiased estimators
Confidence intervals
Using the normal distribution
Further confidence intervals
Hypothesis testing
Using the normal distribution
Using the t-distribution
Non-parametric tests
The Wilcoxon signed-rank test
Two sample and paired sample tests
Work, energy and power
Work and energy
Power
Elastic potential energy
Impulse and momentum
Introduction
Newton's experimental law
Circular motion
Motion in a horizontal circle
Motion in a vertical circle
Differentiation and integration of vectors
Using vectors
Rigid bodies
Equilibrium of rigid bodies
Centre of mass
Finding centres of mass
Solids of revolution
Kinematics
Differential equations
Impulse and momentum in two dimensions
Simple harmonic motion
Introduction to SHM
Oscillating mechanical systems

Each section contains a standard set of resources, including:

## 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 examples (Cymraeg)
• written exercises
• teaching activities
• interactive resources

Welsh language versions of WJEC notes, exercises and on-screen tests are available.

## 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.

### Revision deal!

We’re currently offering a special revision subscription to Integral - a massive 50% off the usual full-year price!

This special subscription will run until 30 June 2023.

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£145

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

### Subscription price

Are you a student or a parent/carer? Visit our student page instead

All subscriptions include:

• Unlimited staff accounts
• Access to all A level content tailored to your specification
• Advanced student tracking features
• Expert email and phone support

Subscriptions run from as early as 1 July through to 30 September the following year.

## Thinking about subscribing?

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