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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the relationship between resistance and temperature
Get further into power series using the fascinating Bessel's equation.
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?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
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.
Look at the advanced way of viewing sin and cos through their power series.
Build up the concept of the Taylor series
Invent scenarios which would give rise to these probability density functions.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Was it possible that this dangerous driving penalty was issued in error?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Why MUST these statistical statements probably be at least a little bit wrong?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Go on a vector walk and determine which points on the walk are closest to the origin.
Can you make matrices which will fix one lucky vector and crush another to zero?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Is it really greener to go on the bus, or to buy local?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Explore the properties of perspective drawing.
Use vectors and matrices to explore the symmetries of crystals.
Explore the shape of a square after it is transformed by the action of a matrix.
Can you work out what this procedure is doing?
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.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Match the descriptions of physical processes to these differential equations.
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.
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?