Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Look at the advanced way of viewing sin and cos through their power series.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Ever wondered what it would be like to vaporise a diamond? Find out inside...
Work with numbers big and small to estimate and calculate various quantities in physical 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. . . .
Build up the concept of the Taylor series
Explore the power of aeroplanes, spaceships and horses.
Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices
How fast would you have to throw a ball upwards so that it would never land?
Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 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?
An introduction to a useful tool to check the validity of an equation.
Can you deduce why common salt isn't NaCl_2?
An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.
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. . . .
Work out the numerical values for these physical quantities.
Is the age of this very old man statistically believable?
Read about the mathematics behind the measuring devices used in quantitative chemistry
Get some practice using big and small numbers in chemistry.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the properties of this different sort of differential equation.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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.
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?
Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.
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.
Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...
This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.
A simplified account of special relativity and the twins paradox.
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...
Explore the properties of combinations of trig functions in this open investigation.
Some of our more advanced investigations
What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?
Which parts of these framework bridges are in tension and which parts are in compression?
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. . . .
Is it really greener to go on the bus, or to buy local?
When is a knot invertible ?
Where we follow twizzles to places that no number has been before.
How much peel does an apple have?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Investigate constructible images which contain rational areas.
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?