A problem about genetics and the transmission of disease.
Estimate areas using random grids
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
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.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Simple models which help us to investigate how epidemics grow and die out.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
How do you choose your planting levels to minimise the total loss
at harvest time?
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.
Why MUST these statistical statements probably be at least a little
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Formulate and investigate a simple mathematical model for the design of a table mat.
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
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.
Go on a vector walk and determine which points on the walk are
closest to the origin.
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?
Match the descriptions of physical processes to these differential
Look at the advanced way of viewing sin and cos through their power series.
Build up the concept of the Taylor series
Use your skill and judgement to match the sets of random data.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
When you change the units, do the numbers get bigger or smaller?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which units would you choose best to fit these situations?
Explore the relationship between resistance and temperature
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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.
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.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
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?
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Invent scenarios which would give rise to these probability density functions.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?