What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Explore the properties of combinations of trig functions in this open investigation.
Build up the concept of the Taylor series
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
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
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?
What's the chance of a pair of lists of numbers having sample
correlation exactly equal to zero?
Some of our more advanced investigations
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
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.
Investigate constructible images which contain rational areas.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Read all about electromagnetism in our interactive article.
How much energy has gone into warming the planet?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Explore the properties of this different sort of differential
Look at the advanced way of viewing sin and cos through their power series.
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?
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.
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 ?
Read about the mathematics behind the measuring devices used in
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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. . . .
Fancy learning a bit more about rates of reaction, but don't know
where to look? Come inside and find out more...
Ever wondered what it would be like to vaporise a diamond? Find out
Can you deduce why common salt isn't NaCl_2?
Unearth the beautiful mathematics of symmetry whilst investigating
the properties of crystal lattices
Where should runners start the 200m race so that they have all run the same distance by the finish?
Find all the periodic cycles and fixed points in this number
sequence using any whole number as a starting point.
Formulate and investigate a simple mathematical model for the design of a table mat.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
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.
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. . . .
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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?
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...
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 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?
How fast would you have to throw a ball upwards so that it would
Where we follow twizzles to places that no number has been before.
Which parts of these framework bridges are in tension and which parts are in compression?
Draw three equal line segments in a unit circle to divide the
circle into four parts of equal area.
Investigate x to the power n plus 1 over x to the power n when x
plus 1 over x equals 1.
Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?
Explore the power of aeroplanes, spaceships and horses.
Is it really greener to go on the bus, or to buy local?