How much energy has gone into warming the planet?
Get further into power series using the fascinating Bessel's equation.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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.
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.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Explore the power of aeroplanes, spaceships and horses.
How fast would you have to throw a ball upwards so that it would never land?
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?
Is the age of this very old man statistically believable?
Build up the concept of the Taylor series
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Ever wondered what it would be like to vaporise a diamond? Find out inside...
Work out the numerical values for these physical quantities.
Read all about electromagnetism in our interactive article.
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
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.
Explore the properties of this different sort of differential equation.
Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...
Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices
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. . . .
Read about the mathematics behind the measuring devices used in quantitative chemistry
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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.
An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.
Can you deduce why common salt isn't NaCl_2?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Is it really greener to go on the bus, or to buy local?
When is a knot invertible ?
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.
Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.
Where we follow twizzles to places that no number has been before.
Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.
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. . . .
How much peel does an apple have?
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?
Some of our more advanced investigations
Explore the properties of combinations of trig functions in this open investigation.
A simplified account of special relativity and the twins paradox.
Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?
Use trigonometry to determine whether solar eclipses on earth can be perfect.