Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
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.
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.
Explore the properties of perspective drawing.
Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Have you ever wondered what it would be like to race against Usain Bolt?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Can you make matrices which will fix one lucky vector and crush another to zero?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Can you sketch these difficult curves, which have uses in
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?
Why MUST these statistical statements probably be at least a little
Which pdfs match the curves?
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
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 the properties of matrix transformations with these 10 stimulating questions.
Is it really greener to go on the bus, or to buy local?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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.
Can you work out what this procedure is doing?
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Get some practice using big and small numbers in chemistry.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Which of these infinitely deep vessels will eventually full up?
Explore how matrices can fix vectors and vector directions.
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.
Who will be the first investor to pay off their debt?