Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Why MUST these statistical statements probably be at least a little
Which line graph, equations and physical processes go together?
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?
Get further into power series using the fascinating Bessel's equation.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Invent scenarios which would give rise to these probability density functions.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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.
Get some practice using big and small numbers in chemistry.
Formulate and investigate a simple mathematical model for the design of a table mat.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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.
Build up the concept of the Taylor series
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which countries have the most naturally athletic populations?
Work out the numerical values for these physical quantities.
Was it possible that this dangerous driving penalty was issued in
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.
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
A problem about genetics and the transmission of disease.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the relationship between resistance and temperature
Which units would you choose best to fit these situations?
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?
Estimate areas using random grids
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
How would you go about estimating populations of dolphins?
Analyse these beautiful biological images and attempt to rank them in size order.
When you change the units, do the numbers get bigger or smaller?
Match the descriptions of physical processes to these differential
Are these estimates of physical quantities accurate?
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?
Can you work out what this procedure is doing?
Who will be the first investor to pay off their debt?