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.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work out the numerical values for these physical quantities.
Get some practice using big and small numbers in chemistry.
How much energy has gone into warming the planet?
Get further into power series using the fascinating Bessel's equation.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which units would you choose best to fit these situations?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Which dilutions can you make using only 10ml pipettes?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
When you change the units, do the numbers get bigger or smaller?
Which line graph, equations and physical processes go together?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Why MUST these statistical statements probably be at least a little bit wrong?
Was it possible that this dangerous driving penalty was issued in error?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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...
How would you go about estimating populations of dolphins?
The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?
Explore the relationship between resistance and temperature
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action of a matrix.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
Are these estimates of physical quantities accurate?
Can you work out what this procedure is doing?
Estimate areas using random grids
Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.
Explore the properties of perspective drawing.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Who will be the first investor to pay off their debt?
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
Use vectors and matrices to explore the symmetries of crystals.