Which line graph, equations and physical processes go together?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Get some practice using big and small numbers in chemistry.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Get further into power series using the fascinating Bessel's equation.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Look at the advanced way of viewing sin and cos through their power series.
Was it possible that this dangerous driving penalty was issued in error?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work out the numerical values for these physical quantities.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Invent scenarios which would give rise to these probability density functions.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Why MUST these statistical statements probably be at least a little bit wrong?
How much energy has gone into warming the planet?
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Match the descriptions of physical processes to these differential equations.
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?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Match the charts of these functions to the charts of their integrals.
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?
Go on a vector walk and determine which points on the walk are closest to the origin.
Which units would you choose best to fit these situations?
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.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
When you change the units, do the numbers get bigger or smaller?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Formulate and investigate a simple mathematical model for the design of a table mat.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the relationship between resistance and temperature
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Simple models which help us to investigate how epidemics grow and die out.
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.
Can you work out what this procedure is doing?
Analyse these beautiful biological images and attempt to rank them in size order.
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
Which dilutions can you make using only 10ml pipettes?
How efficiently can you pack together disks?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Explore the properties of perspective drawing.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .