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.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work out the numerical values for these physical quantities.
Get some practice using big and small numbers in chemistry.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Get further into power series using the fascinating Bessel's equation.
Was it possible that this dangerous driving penalty was issued in
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?
Which units would you choose best to fit these situations?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
When you change the units, do the numbers get bigger or smaller?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Which line graph, equations and physical processes go together?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Match the descriptions of physical processes to these differential
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Why MUST these statistical statements probably be at least a little
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
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?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
How would you go about estimating populations of dolphins?
Invent scenarios which would give rise to these probability density functions.
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
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
Match the charts of these functions to the charts of their integrals.
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.
Can you work out what this procedure is doing?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the properties of perspective drawing.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.