A problem about genetics and the transmission of disease.
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Simple models which help us to investigate how epidemics grow and die out.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
Why MUST these statistical statements probably be at least a little bit wrong?
Which line graph, equations and physical processes go together?
Which pdfs match the curves?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Get further into power series using the fascinating Bessel's equation.
Use vectors and matrices to explore the symmetries of crystals.
Can you make matrices which will fix one lucky vector and crush another to zero?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Which dilutions can you make using only 10ml pipettes?
Where should runners start the 200m race so that they have all run the same distance by the finish?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Get some practice using big and small numbers in chemistry.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Explore the properties of matrix transformations with these 10 stimulating questions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How much energy has gone into warming the planet?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Estimate areas using random grids
Look at the advanced way of viewing sin and cos through their power series.
Build up the concept of the Taylor series
Explore the relationship between resistance and temperature
When you change the units, do the numbers get bigger or smaller?
Who will be the first investor to pay off their debt?
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?
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.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore how matrices can fix vectors and vector directions.
Explore the shape of a square after it is transformed by the action of a matrix.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
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.
Invent scenarios which would give rise to these probability density functions.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.