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?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Get further into power series using the fascinating Bessel's equation.
Explore the properties of this different sort of differential equation.
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Build up the concept of the Taylor series
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which parts of these framework bridges are in tension and which parts are in compression?
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. . . .
Ever wondered what it would be like to vaporise a diamond? Find out inside...
Formulate and investigate a simple mathematical model for the design of a table mat.
When is a knot invertible ?
Explore the power of aeroplanes, spaceships and horses.
How fast would you have to throw a ball upwards so that it would never land?
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. . . .
Explore the properties of combinations of trig functions in this open investigation.
Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.
Some of our more advanced investigations
What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?
How much peel does an apple have?
An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.
Get some practice using big and small numbers in chemistry.
Read about the mathematics behind the measuring devices used in quantitative chemistry
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
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...
An introduction to a useful tool to check the validity of an equation.
Can you deduce why common salt isn't NaCl_2?
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. . . .
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.
Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.
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...
Is the age of this very old man statistically believable?
Work out the numerical values for these physical quantities.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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?
A simplified account of special relativity and the twins paradox.
Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Investigate constructible images which contain rational areas.
An introduction to bond angle geometry.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Is it really greener to go on the bus, or to buy local?