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
- Quadratic equations and graphs
- The quadratic formula
- 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
- Measures of spread
- 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
- More about 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
- More about 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: