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.
Estimate areas using random grids
Why MUST these statistical statements probably be at least a little
Use your skill and judgement to match the sets of random data.
How do you choose your planting levels to minimise the total loss
at harvest time?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
How efficiently can you pack together disks?
Formulate and investigate a simple mathematical model for the design of a table mat.
Which countries have the most naturally athletic populations?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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.
Which line graph, equations and physical processes go together?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
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?
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.
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. . . .
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Can you make matrices which will fix one lucky vector and crush another to zero?
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
Is it really greener to go on the bus, or to buy local?
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?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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?
Can you work out which processes are represented by the graphs?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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.
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.