Further Mathematics

Further Mathematics

Advanced pure, mechanics, and statistics

Resources›A Level›Further Mathematics

Core Pure

12 topics

Complex Numbers

AS

Argand diagrams, modulus-argument form, de Moivre's theorem, roots

complex numbersArgandde Moivre+1

Matrices

AS

Matrix algebra, determinants, inverse matrices, transformations

matricesdeterminantsinverse+1

Further Algebra and Functions

AS

Roots of polynomials, summation of series, proof by induction

polynomialsrootssummation+1

Further Calculus

AS

Series expansions, improper integrals, volumes of revolution

seriesMaclaurinimproper integrals+1

Further Vectors

AS

Vector product, triple scalar product, vector equations of planes

vector productcross productplanes+1

Polar Coordinates

A2

Polar curves, area in polar form, tangents to polar curves

polar coordinatespolar curvesarea+1

Hyperbolic Functions

A2

Definitions, identities, inverse hyperbolic functions

hyperbolicsinhcosh+1

Differential Equations

A2

First and second order, integrating factor, auxiliary equation

differential equationsintegrating factorauxiliary equation

Further Trigonometry

AS

Inverse trigonometric functions, addition formulae applications

inverse trigarcsinarccos+1

Further Calculus Techniques

A2

Integration using partial fractions, reduction formulae

partial fractionsreduction formulaeintegration

Further Differential Equations

A2

Coupled differential equations, phase planes

coupled equationsphase planesstability

Coordinate Systems

A2

Parabolic and elliptic coordinates, transformations

coordinate systemsparabolicelliptic+1

Further Mechanics

6 topics

Momentum and Collisions

AS

Impulse, conservation of momentum, oblique collisions

momentumimpulsecollisions+1

Work, Energy and Power

AS

Work-energy principle, power, variable forces

workenergypower+1

Elastic Strings and Springs

AS

Hooke's law, elastic potential energy, oscillations

Hooke's lawelastic energysprings+1

Circular Motion

A2

Angular velocity, centripetal force, conical pendulum

circular motionangular velocitycentripetal+1

Centres of Mass

A2

Composite bodies, frameworks, toppling and sliding

centre of masscomposite bodiestoppling+1

Simple Harmonic Motion

A2

SHM equations, damped and forced oscillations

SHMoscillationsdamping+1

Further Statistics

5 topics

Discrete Distributions

AS

Poisson, geometric, negative binomial distributions

Poissongeometricdiscrete+1

Continuous Distributions

AS

Continuous uniform, exponential, normal approximations

continuousuniformexponential+1

Hypothesis Testing

A2

Tests for correlation, goodness of fit, contingency tables

hypothesis testingcorrelationgoodness of fit

Chi-squared Tests

A2

Chi-squared distribution, goodness of fit, independence

chi-squaredgoodness of fitindependence+1

Non-parametric Tests

A2

Sign test, Wilcoxon tests, Mann-Whitney U test

non-parametricsign testWilcoxon+1