A problem about genetics and the transmission of disease.
Simple models which help us to investigate how epidemics grow and die out.
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?
Why MUST these statistical statements probably be at least a little
Use your skill and judgement to match the sets of random data.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Estimate areas using random grids
How do you choose your planting levels to minimise the total loss
at harvest time?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Formulate and investigate a simple mathematical model for the design of a table mat.
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 you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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.
Invent scenarios which would give rise to these probability density functions.
Is it really greener to go on the bus, or to buy local?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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.
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.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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?
Which line graph, equations and physical processes go together?
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.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Can you make matrices which will fix one lucky vector and crush another to zero?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Can you sketch these difficult curves, which have uses in
Explore the meaning of the scalar and vector cross products and see how the two are related.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Can you work out what this procedure is doing?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
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?
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Explore the properties of perspective drawing.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
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...
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.