Get further into power series using the fascinating Bessel's equation.
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Read all about electromagnetism in our interactive article.
Dip your toe into the fascinating topic of genetics. From Mendel's theories to some cutting edge experimental techniques, this article gives an insight into some of the processes underlying. . . .
An introduction to a useful tool to check the validity of an equation.
Ever wondered what it would be like to vaporise a diamond? Find out inside...
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
How much energy has gone into warming the planet?
How fast would you have to throw a ball upwards so that it would never land?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?
Which parts of these framework bridges are in tension and which parts are in compression?
Explore the power of aeroplanes, spaceships and horses.
Explore the properties of this different sort of differential equation.
Some of our more advanced investigations
Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Get some practice using big and small numbers in chemistry.
Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.
Read about the mathematics behind the measuring devices used in quantitative chemistry
Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices
Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...
Can you deduce why common salt isn't NaCl_2?
How much peel does an apple have?
We all know that smoking poses a long term health risk and has the potential to cause cancer. But what actually happens when you light up a cigarette, place it to your mouth, take a tidal breath. . . .
An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.
Explore the properties of combinations of trig functions in this open investigation.
There has been a murder on the Stevenson estate. Use your analytical chemistry skills to assess the crime scene and identify the cause of death...
Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.
Work out the numerical values for these physical quantities.
We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?
Formulate and investigate a simple mathematical model for the design of a table mat.
All types of mathematical problems serve a useful purpose in mathematics teaching, but different types of problem will achieve different learning objectives. In generalmore open-ended problems have. . . .
Look at the advanced way of viewing sin and cos through their power series.
When is a knot invertible ?
Is the age of this very old man statistically believable?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?
Two polygons fit together so that the exterior angle at each end of their shared side is 81 degrees. If both shapes now have to be regular could the angle still be 81 degrees?
A simplified account of special relativity and the twins paradox.
An introduction to bond angle geometry.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.
Is it really greener to go on the bus, or to buy local?
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?