Use your skill and judgement to match the sets of random data.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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.
Simple models which help us to investigate how epidemics grow and die out.
How do you choose your planting levels to minimise the total loss
at harvest time?
Which countries have the most naturally athletic populations?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
How would you go about estimating populations of dolphins?
A problem about genetics and the transmission of disease.
Which line graph, equations and physical processes go together?
Is it really greener to go on the bus, or to buy local?
Why MUST these statistical statements probably be at least a little
Have you ever wondered what it would be like to race against Usain Bolt?
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.
Does weight confer an advantage to shot putters?
How efficiently can you pack together disks?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Estimate areas using random grids
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?
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.
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.
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
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. . . .
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.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the properties of perspective drawing.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
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
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Explore the shape of a square after it is transformed by the action
of a matrix.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you work out what this procedure is doing?
Can you work out which processes are represented by the graphs?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?