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
Investigate constructible images which contain rational areas.
Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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.
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?
Get further into power series using the fascinating Bessel's equation.
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.
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.
A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?
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?
Where should runners start the 200m race so that they have all run the same distance by the finish?
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...
Can you deduce why common salt isn't NaCl_2?
An introduction to a useful tool to check the validity of an equation.
Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...
Formulate and investigate a simple mathematical model for the design of a table mat.
Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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. . . .
Get some practice using big and small numbers in chemistry.
Read about the mathematics behind the measuring devices used in quantitative chemistry
Read all about electromagnetism in our interactive article.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
How much energy has gone into warming the planet?
Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.
A simplified account of special relativity and the twins paradox.
Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.
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.
How much peel does an apple have?
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. . . .
When is a knot invertible ?
Explore the properties of this different sort of differential equation.
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
Is the age of this very old man statistically believable?
Which parts of these framework bridges are in tension and which parts are in compression?
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?
How fast would you have to throw a ball upwards so that it would never land?
Explore the power of aeroplanes, spaceships and horses.
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?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?