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:
Interactive resources
Supporting your students to study independently
Sequences of on-screen activities allowing students to meet, explore and practise new concepts independently. They're interactive and dynamic, and come with step-by-step instruction.
Notes, examples and crucial points
Helping to clarify understanding
Thousands of pages of high-quality and extensive notes, helpfully-written to be accessible to all. They feature fully-worked examples and explain common misconceptions.
On-screen tests
To monitor progress all the way to examination
On-screen tests for assessing the level and depth of students' skills, to monitor progress all the way to examination. Immediate feedback is available through powerful analytic tools.
Exercises
To build your students confidence
Three levels of exercises:
- basic practice
- exam standard
- extension questions
Fully-worked solutions are provided to all questions.
Teaching activities
Helping you to make the most of your time
An extensive range of materials, providing lesson ideas and activities with corresponding student materials.
- Interactive
- Notes
- On-screen tests
- Exercises
- Teaching activities
