This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
How much energy has gone into warming the planet?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Get some practice using big and small numbers in chemistry.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which line graph, equations and physical processes go together?
Look at the advanced way of viewing sin and cos through their power series.
Get further into power series using the fascinating Bessel's equation.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
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?
Which units would you choose best to fit these situations?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
When you change the units, do the numbers get bigger or smaller?
Why MUST these statistical statements probably be at least a little
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Invent scenarios which would give rise to these probability density functions.
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?
Work out the numerical values for these physical quantities.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Build up the concept of the Taylor series
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Go on a vector walk and determine which points on the walk are
closest to the origin.
Was it possible that this dangerous driving penalty was issued in
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the relationship between resistance and temperature
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
How would you go about estimating populations of dolphins?
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Match the descriptions of physical processes to these differential
Which dilutions can you make using only 10ml pipettes?
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 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.
Are these estimates of physical quantities accurate?
How efficiently can you pack together disks?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
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.
Is it really greener to go on the bus, or to buy local?
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.
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the properties of perspective drawing.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Match the charts of these functions to the charts of their integrals.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
Use trigonometry to determine whether solar eclipses on earth can be perfect.