A problem about genetics and the transmission of disease.
Estimate areas using random grids
Why MUST these statistical statements probably be at least a little bit wrong?
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 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.
Where should runners start the 200m race so that they have all run the same distance by the finish?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Have you ever wondered what it would be like to race against Usain Bolt?
How do you choose your planting levels to minimise the total loss at harvest time?
Does weight confer an advantage to shot putters?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Use your skill and judgement to match the sets of random data.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Explore the meaning of the scalar and vector cross products and see how the two are related.
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?
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.
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. . . .
Go on a vector walk and determine which points on the walk are closest to the origin.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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?
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?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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.
Explore the shape of a square after it is transformed by the action of a matrix.
Get some practice using big and small numbers in chemistry.
Explore the properties of perspective drawing.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Can you work out what this procedure is doing?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Can you work out which processes are represented by the graphs?
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Invent scenarios which would give rise to these probability density functions.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.