Why MUST these statistical statements probably be at least a little
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.
A problem about genetics and the transmission of disease.
How do you choose your planting levels to minimise the total loss
at harvest time?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Use your skill and judgement to match the sets of random data.
Estimate areas using random grids
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
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Which line graph, equations and physical processes go together?
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.
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.
Simple models which help us to investigate how epidemics grow and die out.
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?
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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.
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.
How much energy has gone into warming the planet?
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
Match the descriptions of physical processes to these differential
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the relationship between resistance and temperature
When you change the units, do the numbers get bigger or smaller?
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which units would you choose best to fit these situations?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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?
Can you work out which processes are represented by the graphs?
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
How efficiently can you pack together disks?
Explore how matrices can fix vectors and vector directions.
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.