Look at the advanced way of viewing sin and cos through their power series.
Build up the concept of the Taylor series
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Explore the properties of combinations of trig functions in this open investigation.
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.
Explore the power of aeroplanes, spaceships and horses.
Some of our more advanced investigations
What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?
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.
Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.
An introduction to a useful tool to check the validity of an equation.
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. . . .
Read all about electromagnetism in our interactive article.
Work out the numerical values for these physical quantities.
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.
Ever wondered what it would be like to vaporise a diamond? Find out inside...
How fast would you have to throw a ball upwards so that it would never land?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
How much energy has gone into warming the planet?
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?
Get some practice using big and small numbers in chemistry.
Explore the properties of this different sort of differential equation.
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?
Is the age of this very old man statistically believable?
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
Read about the mathematics behind the measuring devices used in quantitative chemistry
Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...
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. . . .
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...
A simplified account of special relativity and the twins paradox.
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. . . .
Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices
Can you deduce why common salt isn't NaCl_2?
Formulate and investigate a simple mathematical model for the design of a table mat.
Investigate constructible images which contain rational areas.
An introduction to bond angle geometry.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
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.
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?
Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
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.