Here are several equations from real life. Can you work out which measurements are possible from each equation?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
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.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Can you match these equations to these graphs?
Get further into power series using the fascinating Bessel's equation.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Which dilutions can you make using only 10ml pipettes?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Was it possible that this dangerous driving penalty was issued in
Why MUST these statistical statements probably be at least a little
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.
Get some practice using big and small numbers in chemistry.
Work out the numerical values for these physical quantities.
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.
How much energy has gone into warming the planet?
Build up the concept of the Taylor series
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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 relationship between resistance and temperature
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
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?
Look at the advanced way of viewing sin and cos through their power series.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
How efficiently can you pack together disks?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
Can you work out which processes are represented by the graphs?
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Explore the properties of perspective drawing.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
Are these estimates of physical quantities accurate?
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Explore the meaning of the scalar and vector cross products and see how the two are related.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Can you find the volumes of the mathematical vessels?
Match the descriptions of physical processes to these differential
Can you draw the height-time chart as this complicated vessel fills
Which units would you choose best to fit these situations?