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.
Get further into power series using the fascinating Bessel's equation.
Look at the advanced way of viewing sin and cos through their power series.
Work out the numerical values for these physical quantities.
Which dilutions can you make using only 10ml pipettes?
Get some practice using big and small numbers in chemistry.
Match the descriptions of physical processes to these differential
How much energy has gone into warming the planet?
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Go on a vector walk and determine which points on the walk are
closest to the origin.
Which units would you choose best to fit these situations?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Are these estimates of physical quantities accurate?
Build up the concept of the Taylor series
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
Which line graph, equations and physical processes go together?
When you change the units, do the numbers get bigger or smaller?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Explore the properties of perspective drawing.
Why MUST these statistical statements probably be at least a little
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Invent scenarios which would give rise to these probability density functions.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you find the volumes of the mathematical vessels?
Formulate and investigate a simple mathematical model for the design of a table mat.
Analyse these beautiful biological images and attempt to rank them in size order.
Was it possible that this dangerous driving penalty was issued in
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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.
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?
A problem about genetics and the transmission of disease.
Estimate areas using random grids
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Explore the shape of a square after it is transformed by the action
of a matrix.
Can you draw the height-time chart as this complicated vessel fills
Explore how matrices can fix vectors and vector directions.