# Further Mathematics

###### Author and programmer: Ron Barrow

### UK KS5, AS and A2 level Further Mathematics - US Grades 11-12

#### Core (Pure) Further Mathematics

Inverses of 3×3 matrices using cofactors and determinants

Complex conjugate roots of quadratics

The Graph of `y² = f(x)` - for cubic `f(x)`

Complex Numbers - arithmetic and other operations on an Argand diagram

Polar Coordinates - functions graphed with different conventions

Hyperbolic Functions - basic graphs of cosh, sech, arctanh, cosech², etc.

Complex Roots - `n`th roots of complex numbers - Argand diagram

Complex Transformations of the Circle - examples on an Argand diagram

2D Matrix Transformations - determinants, eigenvectors, eigenvalues

Cobweb and staircase diagrams - for numerical solution of equations

#### Probability and Statistics

Venn Diagrams 1 - with two overlapping regions + de Morgan's Laws

Venn Diagrams 2 - with three overlapping regions + de Morgan's Laws

Conditional Probabilities - examples with the roll of two fair dice

Binomial + Normal - Binomial probabilities and Normal approximations

Poisson + Normal - Poisson probabilities and Normal approximations

Binomial + Poisson - Binomial probabilities and Poisson approximations

Central Limit Theorem - the mean of samples from a non-normal distribution

Symmetric Confidence Intervals - non-normal distribution, known variance

#### Numerical Methods

Newton-Raphson Method - numerical method demonstrated visually

Euler Numerical Methods - for approximating differential equations

#### Other

The Mandelbrot Set - play around with different settings and focus

Cubic Sequences - `n`th term, sequences of the form a`n`³ + b`n`² + c`n` + d