Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Can you work out what this procedure is doing?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How would you go about estimating populations of dolphins?
Get further into power series using the fascinating Bessel's equation.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which dilutions can you make using only 10ml pipettes?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Was it possible that this dangerous driving penalty was issued in
Which line graph, equations and physical processes go together?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Go on a vector walk and determine which points on the walk are
closest to the origin.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Work out the numerical values for these physical quantities.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Get some practice using big and small numbers in chemistry.
How much energy has gone into warming the planet?
Build up the concept of the Taylor series
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.
Explore the relationship between resistance and temperature
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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.
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 meaning of the scalar and vector cross products and see how the two are related.
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.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Why MUST these statistical statements probably be at least a little
Explore the properties of perspective drawing.
Have you ever wondered what it would be like to race against Usain Bolt?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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?
Analyse these beautiful biological images and attempt to rank them in size order.
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Which of these infinitely deep vessels will eventually full up?
Invent scenarios which would give rise to these probability density functions.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Does weight confer an advantage to shot putters?
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Match the descriptions of physical processes to these differential
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?
When you change the units, do the numbers get bigger or smaller?