Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
Which dilutions can you make using only 10ml pipettes?
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 much energy has gone into warming the planet?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Get some practice using big and small numbers in chemistry.
Get further into power series using the fascinating Bessel's equation.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
How would you go about estimating populations of dolphins?
Have you ever wondered what it would be like to race against Usain Bolt?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Was it possible that this dangerous driving penalty was issued in error?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which line graph, equations and physical processes go together?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Explore the relationship between resistance and temperature
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Match the descriptions of physical processes to these differential equations.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
Is it really greener to go on the bus, or to buy local?
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?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Why MUST these statistical statements probably be at least a little bit wrong?
Build up the concept of the Taylor series
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Explore how matrices can fix vectors and vector directions.
Invent scenarios which would give rise to these probability density functions.
Can you find the volumes of the mathematical vessels?
Formulate and investigate a simple mathematical model for the design of a table mat.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Can you work out what this procedure is doing?
Are these estimates of physical quantities accurate?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.