# Mathematics

## A Level Maths

Students follow the Edexcel A Level Maths Course

## Year 1:  A- Level Maths

Core Topics

Applied Topics

Algebraic Expressions: Indices, Factorising, Expanding brackets, Surds Data Collection: Population, sampling, Types of data.
Quadratics: Solving, Completing the square, Functions, Graphs, Discriminant, Modelling Measures of Location and Spread: Central tendency and other measures of location, variance and Standard Deviation
Equations and Inequalities: Linear and Quadratic simultaneous Equations, Linear and Quadratic Inequalities, Regions Representations of Data: Outliers, Boxplots, Cumulative Frequency, Histograms, Comparing Data.
Graphs and Transformations: Cubic, quartic and reciprocal Graphs, Points of intersection, Graph and function  transformations Correlation: Linear regression
Coordinate Geometry: Straight line graphs Probability: Calculations, Venn Diagrams, Mutually exclusive and Independent events, Tree Diagrams
Circles: Equations, tangent and chord properties Statistical Distributions: Probability, Binomial, Cumulative probabilities.
Algebraic Methods: Algebraic fractions, Factor theorem, Proof Hypothesis Testing: Critical values, one and two tailed Tests.
Binomial Expansion Modelling in mechanics: assumptions, vectors
Trigonometry: Non right-angled Trigonometry, Area of triangles, Graphs and transformations, Angles I 4 quadrants, Exact values, Equations Constant acceleration Equations
Vectors: Representation, Magnitude and direction, Geometrical Problems and Modelling Forces and Motion: Forces and acceleration, Connected particles
Calculus: Differentiation, Gradients, tangents, normal, Increasing and decreasing functions, Integration, Definite and indefinite integrals, Areas. Variable acceleration: Functions of time, Differentiation, Integration, Constant acceleration.
Exponentials and logarithms: Log Laws, natural log, solving Log equations, Logs and non-linear data.

## Year 2:  A level Maths

Core Topics

Applied Topics

Algebraic Methods: Proof, Algebraic and Partial Fractions, Repeated factors, Algebraic division Regression, correlation and hypothesis testing
Functions and Graphs: Modulus, Mappings, Composite, Inverse, Transformations Conditional Probability: Set notation, Venn Diagrams, Formulae, Tree Diagrams
Sequence and Series: Arithmetic and Geometric. Normal Distribution: Probabilities, standard normal distributions, mean and standard deviation, Approximating Binomial Distributions. Hypothesis testing.
Binomial Expansion: when power is fractional and/or negative. Moments: Moments, Equilibrium, Centres of Mass, Tilting
Radians: Arc length and sector area, Solving Trigonometric Equations, Small angle approximations Forces and Friction; Resolving, Inclined planes
Trigonometry: Reciprocal and Inverse Trigonometric Functions, Addition Formulae, Double angle formulae, Simplifying acosx±bsinx, Proof, Modelling Projectiles: Horizontal and Vertical components, Projectile Motion formulae.
Parametric Equations: Trigonometry Identities, Curves sketching, Points of intersection, Modelling. Applications of Forces: Static Particles and modelling, Static rigid bodies, Dynamics and inclined planes, connected particles
Differentiation: Trigonometry, Exponentials and Logarithms, Chain Rule, Product Rule, Quotient Rule, Parametric, Implicit, Rates of Change. Further Kinematics: Vectors and projectiles, Variable acceleration in one direction, Differentiating vectors, Integrating Vectors
Numerical Methods: Iteration, Newton-Raphson.
Integration: Standard Functions, Reverse Chain Rule, Integration by substitution, Integration by parts, Partial fractions, Area, Trapezium Rule, Solving Differential Equations, Modelling.
Vectors: 3D, Solving geometric problems, Applications to mechanics.

## A Level Further Maths MEI OCR

### Year 1 / AS Further Maths

Pure

Statistics

Matrices and transformations : matrices, multiplication of matrices, transformations, successive transformations, invariance. Discrete Random Variables: Notation and conditions, expectation and variance
Introduction to complex numbers: Extending the number system, division of complex numbers, representing geometrically Discrete Probability Distributions: Binomial Distribution, Poisson distribution, link between Binomial and Poisson, other discrete distributions.
Roots of Polynomials: Polynomials, cubic equations, quartic equations, solving equations with complex roots Bivariate Data: Describing variables, interpreting scatter diagrams, product moment correlation and rank correlation, least squares regression line y on x and x on y
Sequences and Series: Using standard results, method of differences, proof by induction. Chi Squared Tests: Contingency tables and goodness of fit tests for discrete distributions.
Complex Numbers and Geometry: Modulus and argument, multiplying and dividing in modulus argument form, loci in the argand diagram Modelling with Algorithms Year 1
Matrices and their inverses: Determinant, inverse, solving simultaneous equations using matrices. Algorithms
Vectors and 3D space: Finding the angle between two vectors, the equation of a plane, intersection of planes. Modelling with Graphs and networks
Network Algorithms – shortest path, critical path analysis, network flows
Linear Programming
Simplex Method
Reformulating network problem as linear programming problems

## Year 2 / A Further Maths

Pure

Mechanics (Year 2)

Vectors: Vector equation of a line, lines and planes, vector product, finding distances. Kinematics – Variable acceleration, constant acceleration
Matrices: Inverse of a 3 x 3, intersection of 3 planes. Forces and Motion – Newton’s Laws, vectors, forces in equilibrium, resultant forces
Series and induction: Summing series, further proof by induction Friction
Further Calculus: Improper integrals, calculus with inverse trig functions, partial fractions, further integration. Moments and forces Moments of forces at angles, sliding and toppling
Polar coordinates: Sketching curves with polar cords, finding area enclosed by a polar curve. Work, energy and power – Energy and momentum, Gravitational potential energy, Work and Kinetic Energy, Power
Maclaurin series: Polynomial Approximations and Maclaurin series for standard functions. Impulse and Momentum – Conservation of momentum
Hyperbolic Functions: Hyperbolic functions, inverse hyperbolic functions, integration using inverse hyperbolic functions. Centre of Mass – Two and three dimensional bodies
Application of Integration: Volumes of revolution, mean value of a function, general integration. Dimensional Analysis – Dimensions of quantities, Dimensional consistency, method of dimensions
1st Order Differential Equations: Modelling rates of change, separation of variables, integrating factors.
2nd Order Differential Equations: Higher order differential equations, auxiliary equations with complex roots, non-homogeneous differential equations, systems of differential equations.