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?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Why MUST these statistical statements probably be at least a little bit wrong?
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?
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.
Use vectors and matrices to explore the symmetries of crystals.
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.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
Can you make matrices which will fix one lucky vector and crush another to zero?
Which line graph, equations and physical processes go together?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Which pdfs match the curves?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Invent scenarios which would give rise to these probability density functions.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out which processes are represented by the graphs?
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Which of these infinitely deep vessels will eventually full up?
Explore how matrices can fix vectors and vector directions.
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 the properties of matrix transformations with these 10 stimulating questions.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Go on a vector walk and determine which points on the walk are closest to the origin.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you find the volumes of the mathematical vessels?
Can you construct a cubic equation with a certain distance between its turning points?
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Match the descriptions of physical processes to these differential equations.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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?