Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Work out the numerical values for these physical quantities.
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
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
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?
Get further into power series using the fascinating Bessel's equation.
Match the charts of these functions to the charts of their integrals.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
Formulate and investigate a simple mathematical model for the design of a table mat.
Get some practice using big and small numbers in chemistry.
Which units would you choose best to fit these situations?
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?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
How much energy has gone into warming the planet?
Explore the relationship between resistance and temperature
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Match the descriptions of physical processes to these differential
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
When you change the units, do the numbers get bigger or smaller?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Estimate areas using random grids
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 biological contexts.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore how matrices can fix vectors and vector directions.
Explore the shape of a square after it is transformed by the action
of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
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.
Invent scenarios which would give rise to these probability density functions.
A problem about genetics and the transmission of disease.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
This problem explores the biology behind Rudolph's glowing red nose.