Get further into power series using the fascinating Bessel's equation.
Was it possible that this dangerous driving penalty was issued in
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.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Which line graph, equations and physical processes go together?
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.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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.
Match the descriptions of physical processes to these differential
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
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 would you go about estimating populations of dolphins?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
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.
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?
Why MUST these statistical statements probably be at least a little
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Can you work out what this procedure is doing?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
How do you choose your planting levels to minimise the total loss
at harvest time?
Explore the relationship between resistance and temperature
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Go on a vector walk and determine which points on the walk are
closest to the origin.
Use your skill and judgement to match the sets of random data.
Which units would you choose best to fit these situations?
Invent scenarios which would give rise to these probability density functions.
When you change the units, do the numbers get bigger or smaller?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Formulate and investigate a simple mathematical model for the design of a table mat.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Explore the meaning of the scalar and vector cross products and see how the two are related.
A problem about genetics and the transmission of disease.
Analyse these beautiful biological images and attempt to rank them in size order.
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. . . .
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
Which dilutions can you make using only 10ml pipettes?
Estimate areas using random grids
Explore the properties of perspective drawing.