## Integral supports the whole curriculum

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

- Algebraic expressions
- Expressions and indices
- Surds

- Quadratics
- Quadratic graphs and equations
- Solving quadratics

- Straight line graphs
- Equations of straight lines

- Equations and inequalities
- Simultaneous equations
- Inequalities

- Graphs and transformations
- Sketching graphs
- Transformations of graphs

- Trigonometry and radian measure
- Sine, cosine and area rules
- Radians

- Calculus
- Introduction to differentiation
- Extending differentiation
- Integration

- Algebra and proof
- Algebraic division
- Proof

- Coordinate geometry
- Circle equations

- Exponentials and logarithms
- Exponential functions and logarithms

- The binomial expansion
- Using the binomial expansion

- Sequences and series
- Sequences
- Arithmetic sequences
- Geometric sequences

- Trigonometry
- Trigonometric identities and equations

- Calculus
- Maxima and minima
- Integration as an area
- Trapezium rule

- Algebra and functions
- Rational expressions
- Functions, graphs and transformations
- Composite and inverse functions
- The modulus function

- Integration
- Integrating other functions

- Trigonometry
- Trigonometric reciprocals and inverses
- The compound angle formulae
- Alternative forms

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

- Differentiation
- The chain rule
- The product and quotient rules
- Differentiating exponentials and logarithms
- Differentiating trigonometric functions

- Numerical methods
- Solution of equations

- Algebra and proof
- Proof by contradiction
- Partial fractions

- Differential equations
- Introduction to differential equations

- Binomial expansion
- The general binomial expansion

- Calculus
- Implicit differentiation
- Integration by substitution
- The use of partial fractions in integration
- Integration by parts
- Volumes of revolution

- Parametric equations
- Parametric curves
- Parametric differentiation

- Vectors
- Vectors in two and three dimensions
- The angle between two vectors
- The vector equation of a line

- Complex numbers
- Introduction to complex numbers
- The Argand diagram
- Modulus argument
- Solving polynomial equations

- Roots of quadratic equations
- Roots and coefficients

- Numerical solutions of equations
- Solving equations

- Coordinate systems
- The parabola and rectangular hyperbola

- Matrices and transformations
- Introduction to matrices
- Matrices and transformations
- Determinants and inverses

- Series and induction
- Summing series
- Proof by induction

- Inequalities
- Solving inequalities
- Inequalities involving the modulus function

- Series
- The method of differences
- Maclaurin series
- Taylor series

- Polar coordinates
- Polar curves
- Finding areas

- Complex numbers
- de Moivre's theorem
- Applications of de Moivre's theorem
- Loci in the complex plane
- Transformations in the complex plane

- First order differential equations
- Separation of variables
- Integrating factors

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

- Hyperbolic functions
- Hyperbolic and inverse hyperbolic functions

- Further calculus
- Differentiating further functions
- Using standard integrals
- More integration techniques

- Further integration
- Reduction formulae
- Arc lengths and surface areas

- Further matrix algebra
- Matrices and transformations in three dimensions
- Eigenvalues and eigenvectors

- Further coordinate systems
- The ellipse and hyperbola

- Vectors
- The vector product
- The scalar triple product
- The equation of a plane
- Points, lines and planes

- Constant acceleration
- Displacement and distance
- Speed and velocity
- The constant acceleration formulae
- Working with vectors

- Moments
- The moment of a force

- Dynamics of a particle
- Force diagrams and equilibrium
- Applying Newton's second law
- Connected objects

- Momentum and impulse
- Introduction

- Forces and motion in two dimensions
- Resolving forces
- Newton's second law in two dimensions
- Friction

- Kinematics
- Projectiles
- Variable acceleration

- Centre of mass
- Finding centres of mass

- Work, energy and power
- Work and energy
- Power

- Momentum and impulse
- Newton's law of restitution

- Statics of rigid bodies
- Equilibrium of rigid bodies

- Further kinematics and dynamics
- Variable acceleration
- Variable force

- Elastic strings and springs
- Using Hooke's law
- Work and energy

- Simple harmonic motion
- Modelling oscillations
- Oscillating mechanical systems

- Circular motion
- Motion in a horizontal circle
- Motion in a vertical circle

- Statics of rigid bodies
- Solids of revolution
- Plane regions

- Working with data
- Measures of location
- Measures of spread
- Representing data

- Correlation and regression
- Correlation
- Regression

- Discrete random variables
- Introduction
- Expectation and variance

- The normal distribution
- Using the normal distribution

- Probability
- Working with probability
- Conditional probability

- Statistical distributions
- The binomial distribution
- The Poisson distribution
- Using approximations

- Continuous random variables
- Probability density functions
- Mean and variance
- Cumulative distribution functions

- Hypothesis testing
- Introducing hypothesis testing
- More about hypothesis testing

- Combinations of random variables
- Combinations of normal distributions

- Estimation, confidence intervals and tests
- Sampling and estimation
- Confidence intervals
- Hypothesis testing

- Chi-squared tests
- Contingency tables
- Goodness of fit

- Correlation
- Rank correlation

- Algorithms
- Working with algorithms
- Sorting and packing

- Algorithms on graphs
- Minimum spanning trees
- Shortest paths

- Further algorithms on graphs
- The route inspection problem
- The travelling salesperson problem

- Critical path analysis
- Activity networks
- Scheduling activities

- Linear programming
- Formulating and solving graphically

Each section contains a standard set of resources, including: