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: