Get further into power series using the fascinating Bessel's equation.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Look at the advanced way of viewing sin and cos through their power series.
Was it possible that this dangerous driving penalty was issued in
Which line graph, equations and physical processes go together?
Get some practice using big and small numbers in chemistry.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
How much energy has gone into warming the planet?
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Why MUST these statistical statements probably be at least a little
Work out the numerical values for these physical quantities.
How do you choose your planting levels to minimise the total loss
at harvest time?
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?
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?
Go on a vector walk and determine which points on the walk are
closest to the origin.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Can you work out what this procedure is doing?
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.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Invent scenarios which would give rise to these probability density functions.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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.
When you change the units, do the numbers get bigger or smaller?
Match the descriptions of physical processes to these differential
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Which units would you choose best to fit these situations?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Estimate areas using random grids
Analyse these beautiful biological images and attempt to rank them in size order.
A problem about genetics and the transmission of disease.
Formulate and investigate a simple mathematical model for the design of a table mat.
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Simple models which help us to investigate how epidemics grow and die out.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the relationship between resistance and temperature
Explore the meaning of the scalar and vector cross products and see how the two are related.