Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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. . . .
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?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
Formulate and investigate a simple mathematical model for the design of a table mat.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Look at the advanced way of viewing sin and cos through their power series.
How fast would you have to throw a ball upwards so that it would never land?
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. . . .
Explore the power of aeroplanes, spaceships and horses.
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.
Can you deduce why common salt isn't NaCl_2?
An introduction to a useful tool to check the validity of an equation.
Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices
Explore the properties of this different sort of differential equation.
Read about the mathematics behind the measuring devices used in quantitative chemistry
Read all about electromagnetism in our interactive article.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Is it really greener to go on the bus, or to buy local?
Ever wondered what it would be like to vaporise a diamond? Find out inside...
Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
An introduction to bond angle geometry.
Get some practice using big and small numbers in chemistry.
An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.
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...
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Work out the numerical values for these physical quantities.
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.
How much peel does an apple have?
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. . . .
Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
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.
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.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Use trigonometry to determine whether solar eclipses on earth can be perfect.