How much energy has gone into warming the planet?
Get some practice using big and small numbers in chemistry.
Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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?
Which dilutions can you make using only 10ml pipettes?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Was it possible that this dangerous driving penalty was issued in error?
How would you go about estimating populations of dolphins?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
Analyse these beautiful biological images and attempt to rank them in size order.
Get further into power series using the fascinating Bessel's equation.
Explore the relationship between resistance and temperature
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Match the descriptions of physical processes to these differential equations.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the properties of perspective drawing.
Is it really greener to go on the bus, or to buy local?
Can you make matrices which will fix one lucky vector and crush another to zero?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you work out which processes are represented by the graphs?
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
Have you ever wondered what it would be like to race against Usain Bolt?
Which pdfs match the curves?
Why MUST these statistical statements probably be at least a little bit wrong?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Build up the concept of the Taylor series
Who will be the first investor to pay off their debt?