Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
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?
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?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Build up the concept of the Taylor series
Go on a vector walk and determine which points on the walk are
closest to the origin.
Invent scenarios which would give rise to these probability density functions.
Work out the numerical values for these physical quantities.
Why MUST these statistical statements probably be at least a little
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?
How do you choose your planting levels to minimise the total loss
at harvest time?
A problem about genetics and the transmission of disease.
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?
Get some practice using big and small numbers in chemistry.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Use your skill and judgement to match the sets of random data.
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?
When you change the units, do the numbers get bigger or smaller?
Match the descriptions of physical processes to these differential
Estimate areas using random grids
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Which units would you choose best to fit these situations?
Are these estimates of physical quantities accurate?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Analyse these beautiful biological images and attempt to rank them in size order.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Explore the relationship between resistance and temperature
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Formulate and investigate a simple mathematical model for the design of a table mat.
Simple models which help us to investigate how epidemics grow and die out.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Which dilutions can you make using only 10ml pipettes?