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.
Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
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?
Work out the numerical values for these physical quantities.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
Get some practice using big and small numbers in chemistry.
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Look at the advanced way of viewing sin and cos through their power series.
How much energy has gone into warming the planet?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Build up the concept of the Taylor series
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.
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.
Have you ever wondered what it would be like to race against Usain Bolt?
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?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Why MUST these statistical statements probably be at least a little
Explore the properties of perspective drawing.
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?
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.
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.
Which countries have the most naturally athletic populations?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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.
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?
When you change the units, do the numbers get bigger or smaller?
Was it possible that this dangerous driving penalty was issued in
Which units would you choose best to fit these situations?
How would you go about estimating populations of dolphins?
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
Match the descriptions of physical processes to these differential
Are these estimates of physical quantities accurate?