Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Match the charts of these functions to the charts of their integrals.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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?
Work out the numerical values for these physical quantities.
Get further into power series using the fascinating Bessel's equation.
How would you go about estimating populations of dolphins?
Which line graph, equations and physical processes go together?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Can you construct a cubic equation with a certain distance between its turning points?
Why MUST these statistical statements probably be at least a little bit wrong?
Was it possible that this dangerous driving penalty was issued in error?
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
Get some practice using big and small numbers in chemistry.
Invent scenarios which would give rise to these probability density functions.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Can you sketch these difficult curves, which have uses 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?
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?
Look at the advanced way of viewing sin and cos through their power series.
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.
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?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
When you change the units, do the numbers get bigger or smaller?
Estimate areas using random grids
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in physical 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.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore how matrices can fix vectors and vector directions.
A problem about genetics and the transmission of disease.