Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which dilutions can you make using only 10ml pipettes?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which line graph, equations and physical processes go together?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
When you change the units, do the numbers get bigger or smaller?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Get further into power series using the fascinating Bessel's equation.
Are these estimates of physical quantities accurate?
Was it possible that this dangerous driving penalty was issued in error?
How would you go about estimating populations of dolphins?
Match the descriptions of physical processes to these differential equations.
Work out the numerical values for these physical quantities.
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 find the volumes of the mathematical vessels?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Analyse these beautiful biological images and attempt to rank them in size order.
This problem explores the biology behind Rudolph's glowing red nose.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Use vectors and matrices to explore the symmetries of crystals.
Have you ever wondered what it would be like to race against Usain Bolt?
Can you make matrices which will fix one lucky vector and crush another to zero?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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.
Can you work out which processes are represented by the graphs?
Which pdfs match the curves?
Why MUST these statistical statements probably be at least a little bit wrong?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Which of these infinitely deep vessels will eventually full up?
Explore the relationship between resistance and temperature
Who will be the first investor to pay off their debt?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Can you match the charts of these functions to the charts of their integrals?
Build up the concept of the Taylor series