Here are some real world applications of A level Mathematics and Further Mathematics. Solutions to the worksheets are available by contacting the FMSP or your local FMSP Area Coordinator.
The maths of Google (PowerPoint)
The maths of Google (Worksheet)
Graphs and Euler Cycles (PowerPoint)
Graphs and Euler Cycles (Worksheet)
Vectors and Computer Graphics (Worksheet)
Examples of the maths behind science (exhibited at the Royal Society)
Stereo mission
Menger sponge
Clever
How do crabs and sharks sense depth
Graphical Passwords
How to hold a molecule
These exemplars were created as part of the Mathematics in Work Competition for students on the Year in Industry (YinI) programme. This competition is run by MEI and supported by the IMA.
All winning exemplars from the Industry Competition.
Alice Hardy  Praxair Surface Technologies Ltd 

Alice receiving her prize from MEI's Programme Leader (Industry) Janice Richards. 

Will Springthorpe  Delphi Stonehouse 

Peter Rayner (Will’s manager), Janice Richards (MEI), Dave Friday (Director & General Manager, Delphi (Heavy Duty Business)), Will and Chris Ward (EDT). 
The force of wind on a simple frame structure  Hannah Davies
Switch mode power supply (SMPS) design  Ylber Doniku
Application of trigonometry in design and manufacturing of tooling in the industry  Sina Fattahi
Using Mathematics to allow plasma spray guns to coat parts with complex geometrics  Alice Hardy
The application of integration to measure volumes  William Springthorpe
Using stresses to determine the wall thickness of a natural gas saturator  Maryam Sufi
Calculating the cost of steam leaks  Guy Wilson
Nilman Ekanayake  PEI Genesis UK LTD 

Nilman receiving his prize from MEI's Programme Leader (Industry) Richard Browne. 
Mathematical calculations used within Dixon ring characteristics  Robert Alford
Rotational Leg to Hull Stiffness for Tubular Legs in a Jack Up Rig  Alex Dotsch
How a Cyclone Works  Jessie Fullenkemper
Using mathematics to model the flight of a rocket  Robin Herd
Probability in control systems  Amber Hilton
Prototype lorry trailer development  Lewis Jecketts
Viscosity Temperature Graphs of Lubricants  Eunjin Lee
Use of trigonometry in calculating the Maximum orientation error in the manufacturing process  Nilman Ekanayake
Use of Pythagoras’s Theorem and Trigonometry in Analysis of a Bolted Connection  Amy Roberts
The Use of Statistics in Biodiversity Indicators  Sophie Rogers
Fixture and fittings  Kester Sleeman
The distribution of work to meet customer demand  Kelly Streeter
Photographs of the presentations of a certificate and £100 to each of the two winners of the 2010 competition can be seen below. The winning and highly commended exemplars then follow.
Cameron Blackwell  Balfour Beatty Mott MacDonald 

Cameron receiving his prize from MEI's Stephen Lee. 

Joe Andrews  Invensys Controls UK Ltd 

Joe being presented with his prize by Charlie Stripp, MEI Chief Executive. 
The Use of Mathematics in Train Wheelset Management  William Balcombe
Checking computer generated data  Cameron Blackwell
Use of Boolean Logic and Probabilistic Analysis in work  Benjamin Brocklehurst
The use of drag coefficients in hydrodynamics  Helen Lacey
Constructing platforms using trigonometry and geometry  Hasnain Mir Mohammed
Flow rates in fuel pipes  Peter Moran
Inflight refulling  Cameron Smith
The use of mathematics (mechanics) in the testing of an automotive engine component
Jet engines with Pythagoras