A problem about genetics and the transmission of disease.
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 would you design the tiering of seats in a stadium so that all spectators have a good view?
Simple models which help us to investigate how epidemics grow and die out.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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.
Can you work out what this procedure is doing?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Does weight confer an advantage to shot putters?
How would you go about estimating populations of dolphins?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Why MUST these statistical statements probably be at least a little bit wrong?
Is it really greener to go on the bus, or to buy local?
This problem explores the biology behind Rudolph's glowing red nose.
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Use vectors and matrices to explore the symmetries of crystals.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
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.
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.
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 mathematical modelling?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Which line graph, equations and physical processes go together?
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.
The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.
Explore how matrices can fix vectors and vector directions.
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?
Invent scenarios which would give rise to these probability density functions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Get some practice using big and small numbers in chemistry.
Analyse these beautiful biological images and attempt to rank them in size order.
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.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Which pdfs match the curves?
Can you match these equations to these graphs?
Look at the advanced way of viewing sin and cos through their power series.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Who will be the first investor to pay off their debt?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.