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Mobile tutorials

For A Level Waldomaths recommends Autograph Autograph software

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 - nth 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


The Mandelbrot Set - play around with different settings and focus
Cubic Sequences - nth term, sequences of the form an³ + bn² + cn + d