Explore the relationship between resistance and temperature
Can you match these equations to these graphs?
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?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you draw the height-time chart as this complicated vessel fills with water?
Can you work out which processes are represented by the graphs?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
Get further into power series using the fascinating Bessel's equation.
How would you go about estimating populations of dolphins?
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?
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?
Which pdfs match the curves?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Get some practice using big and small numbers in chemistry.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Which dilutions can you make using only 10ml pipettes?
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Explore the properties of matrix transformations with these 10 stimulating questions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Use vectors and matrices to explore the symmetries of crystals.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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.
Who will be the first investor to pay off their debt?
When you change the units, do the numbers get bigger or smaller?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Build up the concept of the Taylor series
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.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore how matrices can fix vectors and vector directions.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Invent scenarios which would give rise to these probability density functions.
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?
A problem about genetics and the transmission of disease.
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?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.