Mathematics
Mathematics
A Level Maths
Students follow the Edexcel A Level Maths Course
Specification Link A level maths
Year 1: AS 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
MEI Further Mathematics Specification Link
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. |