Can you work out what this procedure is doing?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Does weight confer an advantage to shot putters?
Was it possible that this dangerous driving penalty was issued in
Which line graph, equations and physical processes go together?
Have you ever wondered what it would be like to race against Usain Bolt?
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Work out the numerical values for these physical quantities.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Get some practice using big and small numbers in chemistry.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Invent scenarios which would give rise to these probability density functions.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Go on a vector walk and determine which points on the walk are
closest to the origin.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How much energy has gone into warming the planet?
Explore the relationship between resistance and temperature
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Look at the advanced way of viewing sin and cos through their power series.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
This problem explores the biology behind Rudolph's glowing red nose.
Build up the concept of the Taylor series
Why MUST these statistical statements probably be at least a little
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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...
Match the descriptions of physical processes to these differential
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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.
Are these estimates of physical quantities accurate?
Analyse these beautiful biological images and attempt to rank them in size order.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
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. . . .
How efficiently can you pack together disks?
Explore the properties of perspective drawing.
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.
Which units would you choose best to fit these situations?
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?
When you change the units, do the numbers get bigger or smaller?