By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
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.
Use your skill and judgement to match the sets of random data.
How do you choose your planting levels to minimise the total loss
at harvest time?
A problem about genetics and the transmission of disease.
Why MUST these statistical statements probably be at least a little
Which countries have the most naturally athletic populations?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which line graph, equations and physical processes go together?
Was it possible that this dangerous driving penalty was issued in
Get further into power series using the fascinating Bessel's equation.
Go on a vector walk and determine which points on the walk are
closest to the origin.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Simple models which help us to investigate how epidemics grow and die out.
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?
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.
Invent scenarios which would give rise to these probability density functions.
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.
Get some practice using big and small numbers in chemistry.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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 much energy has gone into warming the planet?
Which units would you choose best to fit these situations?
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Estimate areas using random grids
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
Look at the advanced way of viewing sin and cos through their power series.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
When you change the units, do the numbers get bigger or smaller?
Match the descriptions of physical processes to these differential
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...
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.
Explore how matrices can fix vectors and vector directions.
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?