Ages 16-19
UK KS5, AS and A2 level - US Grades 11-12
Core (Pure) Mathematics
Factorising simple quadratics - of the type x² + bx + c
Factorising Harder quadratics - of the type ax² + bx + c
Quadratics - completing the square - vertex coordinates, turning points
Quadratics - the discriminant - number of roots of f(x) = 0
Circles and lines - points of intersection of circles and straight lines
Harder quadratic sequences - nth term in the form an² + bn + c
Polynomial graphs - cubic, quadratic and linear graphs
Polynomial transformations - transformations of y = a(bx + c)³ + d
Differentiating polynomials - cubic, quadratic and linear graphs
Tangents and normals - to a cubic or quadratic graph
Solving equations graphically - quadratic/quadratic or quadratic/linear
Algebraic long division 1 - cubic expression divided by a linear one
Algebraic long division 2 - quartic divided by a quadratic
Solving cubic equations - the Factor Theorem and equating coefficients
Sine Rule (Rule of Sines) - lengths and angles in triangles
Cosine Rule (Rule of Cosines) - triangle lengths, angles and areas
Trigonometric transformations - transformations of eg.y = asin(bx + c) + d
Trigonometric equations - graphical representation of solutions
Integrating polynomials - integration of cubic, quadratic and linear functions
Second derivatives - of quartic functions
Quadratic inequalities - solution sets and graphical representation NEW!
Quadratics - inverses - inverses, restricted domains and ranges
Exponential functions - transformations of y = AeBx + C + D
Logarithmic functions - transformations of y = aln(bx + c) + d
Reciprocal (rational) functions - transformations of y = a/(bx + c) + d
Cobweb and staircase diagrams - for numerical solution of equations
Modulus functions - transformations of y = a|bx + c| + d
Differentiating exponentials 1 - finding the Euler constant e
Differentiating exponentials 2 - comparing graphs
Differentiating Sine and Cosine - comparing graphs
Trigonometric functions - graphs of tan, cosec, cos², inverses, etc.
Trigonometry - Asin(x) + Bcos(x) - converting to asingle function
Trapezium/Mid-Ordinate Rules - for numerical integration approximations
Equations of circles and Ellipses - in Cartesian form
Parametric equations 1 - of circles, ellipses and Lissajous figures
Parametric equations 2 - of ellipses, parabolae and rectangular hyperbolae
Probability and Statistics
Cumulative frequency - diagrams, medians, quartiles and boxplots
Histograms - unequal interval widths and frequency density
Linear interpolation - using a similar triangles method
Estimating Quantiles - using linear interpolation and cumulative frequencies
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
Correlation and Regression - bivariate data on a scattergram
Normal Distribution - vary mean and variance and find probabilities
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
Decision Mathematics
Simple network graphs 1 - unfinished applet
2-variable linear programming - graphing constraints and objective function
Further Mathematics
Complex Numbers - arithmetic and other operations on an Argand diagram
Newton-Raphson Method - numerical method demonstrated visually
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
Euler Numerical Methods - for approximating differential equations
Other
The Mandelbrot Set - play around with different settings and focus
Cubic Sequences - nth term, sequences of the form an³ + bn² + cn + d