Here are several equations from real life. Can you work out which measurements are possible from each equation?
This problem explores the biology behind Rudolph's glowing red nose.
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Which line graph, equations and physical processes go together?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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.
Was it possible that this dangerous driving penalty was issued in error?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
How would you go about estimating populations of dolphins?
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore how matrices can fix vectors and vector directions.
Can you find the volumes of the mathematical vessels?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Can you make matrices which will fix one lucky vector and crush another to zero?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Which units would you choose best to fit these situations?
Which dilutions can you make using only 10ml pipettes?
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the properties of perspective drawing.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Match the descriptions of physical processes to these differential equations.
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the relationship between resistance and temperature
Get some practice using big and small numbers in chemistry.
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.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
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?
Build up the concept of the Taylor series
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the shape of a square after it is transformed by the action of a matrix.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Go on a vector walk and determine which points on the walk are closest to the origin.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Can you work out which processes are represented by the graphs?