Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work out the numerical values for these physical quantities.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Get some practice using big and small numbers in chemistry.
How much energy has gone into warming the planet?
Explore the relationship between resistance and temperature
Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Was it possible that this dangerous driving penalty was issued in
Look at the advanced way of viewing sin and cos through their power series.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Which dilutions can you make using only 10ml pipettes?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Build up the concept of the Taylor series
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How would you go about estimating populations of dolphins?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Invent scenarios which would give rise to these probability density functions.
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Match the descriptions of physical processes to these differential
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Why MUST these statistical statements probably be at least a little
Can you work out what this procedure is doing?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Is it really greener to go on the bus, or to buy local?
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.
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the properties of perspective drawing.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the meaning of the scalar and vector cross products and see how the two are related.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Which of these infinitely deep vessels will eventually full up?
Match the charts of these functions to the charts of their integrals.