# Ages 16-19

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

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

#### Core (Pure) Mathematics

Coordinate Geometry 1 - lengths, mid-points of line segments

Straight line graphs 3 - two forms of the equation

Factorising simple quadratics - of the type `x`² + b`x` + c

Factorising Harder quadratics - of the type a`x`² + b`x` + 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 - `n`th term in the form a`n`² + b`n` + c

Polynomial graphs - cubic, quadratic and linear graphs

Polynomial transformations - transformations of y = a(b`x` + c)³ + d

Differentiating (powers of x) - first and second derivatives

Tangents and normals - to a cubic or quadratic graph

Solving equations graphically - quadratic/quadratic or quadratic/linear

Binomial Expansions - calculated term-by-term

Binomial Series - calculated term-by-term NEW!

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 sin, cos, tan

Trigonometric equations - graphs and solutions in degrees

Trigonometric equations - graphs and solutions in radians

Integrating polynomials - integration of cubic, quadratic and linear functions

Quadratic inequalities - solution sets and graphical representation

Quadratics - inverses - restricted domains and ranges

Exponential functions - transformations of `y` = a`e`^{bx + c} + d

Logarithmic functions - transformations of y = a`ln`(b`x` + c) + d

Reciprocal (rational) functions - transformations of y = a/(b`x` + c) + d

Cobweb and staircase diagrams - for numerical solution of equations

Modulus functions - transformations of y = a|b`x` + 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 a single function

Sectors, Arcs, Segments of Circles - using Radians

Trapezium/Mid-Ordinate/Simpson Rules - for numerical integration

Equations of Circles and Ellipses - in Cartesian form

Equations of Circles - in Cartesian and Expanded Forms

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...

.. has now moved to a new page

#### 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