A problem about genetics and the transmission of disease.
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.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Simple models which help us to investigate how epidemics grow and die out.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Use your skill and judgement to match the sets of random data.
Estimate areas using random grids
How do you choose your planting levels to minimise the total loss
at harvest time?
Formulate and investigate a simple mathematical model for the design of a table mat.
Why MUST these statistical statements probably be at least a little
Invent scenarios which would give rise to these probability density functions.
Which line graph, equations and physical processes go together?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How efficiently can you pack together disks?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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?
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.
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?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
Use vectors and matrices to explore the symmetries of crystals.
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 properties of perspective drawing.
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 dilutions can you make using only 10ml pipettes?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you sketch these difficult curves, which have uses in
Explore how matrices can fix vectors and vector directions.
Can you work out which processes are represented by the graphs?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Get some practice using big and small numbers in chemistry.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
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?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Go on a vector walk and determine which points on the walk are
closest to the origin.
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action
of a matrix.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
How much energy has gone into warming the planet?
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation