Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
Find the distance of the shortest air route at an altitude of 6000
metres between London and Cape Town given the latitudes and
longitudes. A simple application of scalar products of vectors.
Shows that Pythagoras for Spherical Triangles reduces to
Pythagoras's Theorem in the plane when the triangles are small
relative to the radius of the sphere.
Which of these infinitely deep vessels will eventually full up?
Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.
Explore the properties of perspective drawing.
Explore the meaning of the scalar and vector cross products and see how the two are related.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
Is it really greener to go on the bus, or to buy local?
Can you sketch these difficult curves, which have uses in
Go on a vector walk and determine which points on the walk are
closest to the origin.
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Which pdfs match the curves?
Have you ever wondered what it would be like to race against Usain Bolt?
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Why MUST these statistical statements probably be at least a little
Explore the properties of matrix transformations with these 10 stimulating questions.
How do you choose your planting levels to minimise the total loss
at harvest time?
Which line graph, equations and physical processes go together?
Use vectors and matrices to explore the symmetries of crystals.
Explore how matrices can fix vectors and vector directions.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out which processes are represented by the graphs?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Can you work out what this procedure is doing?
Get some practice using big and small numbers in chemistry.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Can you construct a cubic equation with a certain distance between
its turning points?
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Invent scenarios which would give rise to these probability density functions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
A problem about genetics and the transmission of disease.
Explore the shape of a square after it is transformed by the action
of a matrix.
How much energy has gone into warming the planet?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Use your skill and judgement to match the sets of random data.
In this short problem, try to find the location of the roots of
some unusual functions by finding where they change sign.
Look at the advanced way of viewing sin and cos through their power series.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Work with numbers big and small to estimate and calulate various quantities in biological contexts.