Here are several equations from real life. Can you work out which measurements are possible from each equation?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Match the descriptions of physical processes to these differential equations.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which line graph, equations and physical processes go together?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Was it possible that this dangerous driving penalty was issued in error?
Get further into power series using the fascinating Bessel's equation.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
This problem explores the biology behind Rudolph's glowing red nose.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Work out the numerical values for these physical quantities.
Use vectors and matrices to explore the symmetries of crystals.
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?
Have you ever wondered what it would be like to race against Usain Bolt?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How would you go about estimating populations of dolphins?
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore how matrices can fix vectors and vector directions.
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.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Get some practice using big and small numbers in chemistry.
Can you work out what this procedure is doing?
Which dilutions can you make using only 10ml pipettes?
Can you make matrices which will fix one lucky vector and crush another to zero?
Why MUST these statistical statements probably be at least a little bit wrong?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Analyse these beautiful biological images and attempt to rank them in size order.
Look at the advanced way of viewing sin and cos through their power series.
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?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these estimates of physical quantities accurate?
Build up the concept of the Taylor series
Which units would you choose best to fit these situations?
Explore the shape of a square after it is transformed by the action of a matrix.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Who will be the first investor to pay off their debt?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore the meaning of the scalar and vector cross products and see how the two are related.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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.