# Integral for Cambridge International

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.

• Cambridge International AS & A Level Mathematics - 9709
• Cambridge International AS & A Level Further Mathematics - 9231

Integral resource place emphasis on the development of problem-solving, communication and mathematical modelling which are key concepts in the most recent Cambridge International syllabus.

## 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.

## Stay informed about how we are supporting international schools

Join our mailing list to receive information about how we are continuing to develop Integral to support schools outside the UK teaching AS/A level Mathematics and Further Mathematics.

## Integral supports the whole curriculum

Integral A level covers the whole of the Cambridge International AS/A level Mathematics and Further Mathematics syllabuses. The material is presented in topics, which are further divided into sections.

### Mathematics

Problem solving
Problem solving and modelling
Writing mathematics and proof
Algebra
Using and manipulating surds
Simultaneous equations
Inequalities
Coordinate geometry
Coordinates and straight lines
Drawing curves
The circle
Sequences and series
Definitions and notation
Arithmetic progressions
Geometric progressions
Binomial expansions
Functions and transformations
The language of functions
Using transformations
Differentiation
Introduction to differentiation
Using differentiation
Further applications of differentiation
The chain rule
Trigonometry
Functions and identities
Equations
The sine and cosine rules
Integration
Introduction to integration
Finding the area under a curve
Further integration
Finding volumes by integration
Trigonometry
Trigonometrical functions
Solving equations
Circular measure
Algebra
Solution of polynomial equations
The modulus function
Logarithms and exponentials
Exponential functions and logarithms
Modelling curves
The natural logarithm and exponential functions
Trigonometry
Reciprocal trigonometrical functions
Compound-angle and double-angle formulae
The forms $$r \cos(\theta \pm \alpha), r \sin(\theta \pm \alpha)$$
Further algebra
The general binomial expansion
Partial fractions
Differentiation
The product and quotient rules
Differentiating natural logarithms and exponentials
Differentiating trigonometrical functions
Differentiating functions defined implicitly
Parametric differentiation
Numerical solution of equations
Interval estimation and fixed-point iteration
Further calculus
Integration by substitution
The use of partial fractions in integration
Integration by parts
Differential equations
Forming and solving differential equations
Vectors
Vectors in two and three dimensions
The angle between two vectors
The vector equation of a line
Complex numbers
Working with complex numbers
Sets of points in an Argand diagram
The modulus-argument form of complex numbers
Complex numbers and equations
Integration
Integrating other functions
Numerical integration
Motion in a straight line
The language of motion
Acceleration
The constant acceleration formulae
Using the formulae
Forces and Newton's laws of motion
Force diagrams and motion
Applying Newton's second law along a line
Newton's second law
Connected objects
Forces in equilibrium and resultant forces
Resultant forces
Newton's second law in two dimensions
Momentum
Conservation of momentum
General motion in a straight line
Using calculus
A model for friction
Modelling with friction
Energy, work and power
Energy and work
Power
Exploring data
Data and measures of central tendency
Representing and interpreting data
Further work with data
Probability
Working with probability
Conditional probability
Discrete random variables
Introduction
Expectation and variance
The normal distribution
Using the normal distribution
Permutations and combinations
Using permutations and combinations
Discrete probability distributions
The binomial distribution
The geometric distribution
Continuous random variables
Probability density functions
Mean, variance, median and percentiles
Hypothesis testing using the binomial distribution
Introducing hypothesis testing
Hypothesis testing and confidence intervals using the normal distribution
Hypothesis testing using the Normal distribution
Confidence intervals
The Poisson distribution
Introduction to the Poisson distribution
Linear combinations of random variables
Combining two or more random variables
Sampling
Sampling

### Further Mathematics

Matrices and transformations
Introduction to matrices
Transformations
Invariance
Series and induction
Summing series
Proof by induction
Roots of polynomials
Roots and coefficients
Rational functions and graphs
Graphs of rational functions
Sketching curves related to $$y = f(x)$$
Polar coordinates
Polar coordinates and curves
Finding the area enclosed by a polar curve
Matrices and their inverses
The determinant and inverse of a 2x2 matrix
The inverse of a 3x3 matrix
Vectors
The vector equation of a plane
Points, lines and planes
The vector product
Hyperbolic functions
The hyperbolic and inverse hyperbolic functions
Matrices
Simultaneous equations and intersecting planes
Eigenvalues and eigenvectors
Powers of square matrices
Differentiation
Differentiating further functions
Maclaurin series
Integration
Integrating further functions
Integration using reduction formulae
Approximation of areas using rectangles
Arc lengths and surface areas
Complex numbers
de Moivre's theorem
Applications of de Moivre's theorem
Differential equations
Integrating factors
Second order homogeneous differential equations
Non-homogeneous differential equations
Motion of a projectile
Projectile problems
The path of a projectile
Moments of forces
Rigid bodies
The moment of a force that acts at an angle
Centre of mass
Finding a centre of mass
Sliding and toppling
Circular motion
Motion in a horizontal circle
Motion in a vertical circle
Hooke's law
Elastic strings and springs
Work and energy
Linear motion under a variable force
Differential equations
Momentum
Newton's experimental law
Oblique impacts
Continuous random variables
Further probability density functions
The cumulative distribution function
Inference using normal and t-distributions
Using the t-distribution
Working with two samples
Chi-squared tests
The chi-squared test for a contingency table
Goodness of fit tests
Non-parametric tests
Single sample tests
Paired-sample and two-sample tests
Probability generating functions
Using probability generating functions

Each section contains a standard set of resources, including:

## We've put a lot into it

• 120sections
• 500crucial points
• 1800written exercise questions
• 1200online test questions
• 500exam-style questions
• 300teaching ideas and resources
• 400interactive resources

## Take a look at some sample resources

• written exercises
• teaching activities
• interactive resources

Have you seen our Integral for Cambridge International AS/A level Mathematics and Further Mathematics brochure? ## 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 base the costs of our annual subscriptions to Integral A level on the number of students you want to give access.