How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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?
Use vectors and matrices to explore the symmetries of crystals.
Invent scenarios which would give rise to these probability density functions.
Simple models which help us to investigate how epidemics grow and die out.
Who will be the first investor to pay off their debt?
Which pdfs match the curves?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Why MUST these statistical statements probably be at least a little bit wrong?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How do you choose your planting levels to minimise the total loss at harvest time?
Get some practice using big and small numbers in chemistry.
Are these estimates of physical quantities accurate?
Was it possible that this dangerous driving penalty was issued in error?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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.
A problem about genetics and the transmission of disease.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Explore the properties of matrix transformations with these 10 stimulating questions.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Analyse these beautiful biological images and attempt to rank them in size order.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Which line graph, equations and physical processes go together?
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.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
Work out the numerical values for these physical quantities.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Explore the relationship between resistance and temperature
Can you make matrices which will fix one lucky vector and crush another to zero?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore the shape of a square after it is transformed by the action of a matrix.
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Explore how matrices can fix vectors and vector directions.
Which of these infinitely deep vessels will eventually full up?
Look at the advanced way of viewing sin and cos through their power series.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
When you change the units, do the numbers get bigger or smaller?
Match the descriptions of physical processes to these differential equations.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which units would you choose best to fit these situations?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
How would you go about estimating populations of dolphins?
This problem explores the biology behind Rudolph's glowing red nose.