Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
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
How would you go about estimating populations of dolphins?
Look at the advanced way of viewing sin and cos through their power series.
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.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which dilutions can you make using only 10ml pipettes?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Get further into power series using the fascinating Bessel's equation.
When you change the units, do the numbers get bigger or smaller?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Which units would you choose best to fit these situations?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which line graph, equations and physical processes go together?
Was it possible that this dangerous driving penalty was issued in
Work out the numerical values for these physical quantities.
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Are these estimates of physical quantities accurate?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Go on a vector walk and determine which points on the walk are
closest to the origin.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Build up the concept of the Taylor series
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Match the descriptions of physical processes to these differential
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the properties of perspective drawing.
Which of these infinitely deep vessels will eventually full up?
Formulate and investigate a simple mathematical model for the design of a table mat.
Invent scenarios which would give rise to these probability density functions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Why MUST these statistical statements probably be at least a little
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?
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.
Analyse these beautiful biological images and attempt to rank them in size order.
In this short problem, try to find the location of the roots of
some unusual functions by finding where they change sign.
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
Use your skill and judgement to match the sets of random data.
A problem about genetics and the transmission of disease.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you draw the height-time chart as this complicated vessel fills